diff --git a/src/scgenerator/evaluator.py b/src/scgenerator/evaluator.py
index c4a471c..3ed4a03 100644
--- a/src/scgenerator/evaluator.py
+++ b/src/scgenerator/evaluator.py
@@ -5,7 +5,7 @@ from typing import Any, Callable, Optional, Union
 
 import numpy as np
 
-from . import math, operators, utils, solver
+from . import math, operators, utils
 from .const import MANDATORY_PARAMETERS
 from .errors import EvaluatorError, NoDefaultError
 from .physics import fiber, materials, pulse, units
@@ -324,6 +324,7 @@ default_rules: list[Rule] = [
     Rule("L_D", pulse.L_D),
     Rule("L_NL", pulse.L_NL),
     Rule("L_sol", pulse.L_sol),
+    Rule("c_to_a_factor", lambda: 1.0, priorities=-1),
     # Fiber Dispersion
     Rule("w_for_disp", units.m, ["wl_for_disp"]),
     Rule("hr_w", fiber.delayed_raman_w),
@@ -377,7 +378,6 @@ default_rules: list[Rule] = [
     Rule("loss_op", operators.NoLoss, priorities=-1),
     Rule("plasma_op", operators.NoPlasma, priorities=-1),
     Rule("conserved_quantity", operators.NoConservedQuantity, priorities=-1),
-    Rule("integrator", solver.ERK54),
 ]
 
 envelope_rules = default_rules + [
@@ -387,6 +387,7 @@ envelope_rules = default_rules + [
     Rule("pre_field_0", pulse.initial_field_envelope, priorities=1),
     Rule("spec_0", np.fft.fft, ["field_0"]),
     Rule("field_0", np.fft.ifft, ["spec_0"]),
+    Rule("c_to_a_factor", pulse.c_to_a_factor),
     # Dispersion
     Rule(["wl_for_disp", "dispersion_ind"], fiber.lambda_for_envelope_dispersion),
     Rule("beta2_coefficients", fiber.dispersion_coefficients),
@@ -418,7 +419,6 @@ envelope_rules = default_rules + [
     Rule("dispersion_op", operators.DirectDispersion),
     Rule("linear_operator", operators.EnvelopeLinearOperator),
     Rule("conserved_quantity", operators.conserved_quantity),
-    Rule("integrator", solver.ConservedQuantityIntegrator),
 ]
 
 full_field_rules = default_rules + [
@@ -442,6 +442,4 @@ full_field_rules = default_rules + [
         operators.FullFieldLinearOperator,
     ),
     Rule("nonlinear_operator", operators.FullFieldNonLinearOperator),
-    # Integration
-    Rule("integrator", solver.LocalErrorIntegrator),
 ]
diff --git a/src/scgenerator/operators.py b/src/scgenerator/operators.py
index 79cf2b7..9f40022 100644
--- a/src/scgenerator/operators.py
+++ b/src/scgenerator/operators.py
@@ -52,6 +52,24 @@ class SpectrumDescriptor:
             self.__field2 = math.abs2(self.field)
         return self.__field2
 
+    def force_values(self, spec2: np.ndarray, field: np.ndarray, field2: np.ndarray):
+        """force these values instead of recomputing them
+
+        Parameters
+        ----------
+        spectrum : np.ndarray
+            spectrum
+        spec2 : np.ndarray
+            |spectrum|^2
+        field : np.ndarray
+            field = converter(spectrum)
+        field2 : np.ndarray
+            |field|^2
+        """
+        self.__spec2 = spec2
+        self.__field = field
+        self.__field2 = field2
+
     def __delete__(self, instance):
         raise AttributeError("Cannot delete Spectrum field")
 
@@ -64,7 +82,6 @@ class CurrentState:
     length: float
     z: float
     current_step_size: float
-    previous_step_size: float
     step: int
     C_to_A_factor: np.ndarray
     converter: Callable[[np.ndarray], np.ndarray] = np.fft.ifft
@@ -74,19 +91,33 @@ class CurrentState:
     def z_ratio(self) -> float:
         return self.z / self.length
 
-    def replace(self, new_spectrum: np.ndarray, **new_params) -> CurrentState:
+    def replace(self, new_spectrum: np.ndarray) -> CurrentState:
         """returns a new state with new attributes"""
-        params = dict(
-            solution=new_spectrum,
+        return CurrentState(
+            self.length,
+            self.z,
+            self.current_step_size,
+            self.step,
+            self.C_to_A_factor,
+            self.converter,
+            new_spectrum,
+        )
+
+    def with_params(self, **params) -> CurrentState:
+        """returns a new CurrentState with modified params, except for the solution"""
+        my_params = dict(
             length=self.length,
             z=self.z,
             current_step_size=self.current_step_size,
-            previous_step_size=self.previous_step_size,
             step=self.step,
             C_to_A_factor=self.C_to_A_factor,
             converter=self.converter,
         )
-        return CurrentState(**(params | new_params))
+        new_state = CurrentState(solution=self.solution.spectrum, **(my_params | params))
+        new_state.solution.force_values(
+            self.solution.spec2, self.solution.field, self.solution.field2
+        )
+        return new_state
 
     def copy(self) -> CurrentState:
         return replace(self, solution=self.solution.spectrum)
diff --git a/src/scgenerator/parameter.py b/src/scgenerator/parameter.py
index cb13b14..9b3b8f1 100644
--- a/src/scgenerator/parameter.py
+++ b/src/scgenerator/parameter.py
@@ -6,7 +6,7 @@ import os
 import time
 from copy import copy
 from dataclasses import dataclass, field, fields
-from functools import lru_cache
+from functools import lru_cache, wraps
 from math import isnan
 from pathlib import Path
 from typing import Any, Callable, ClassVar, Iterable, Iterator, Set, Type, TypeVar, Union
@@ -19,7 +19,7 @@ from .errors import EvaluatorError
 from .evaluator import Evaluator
 from .logger import get_logger
 from .operators import AbstractConservedQuantity, LinearOperator, NonLinearOperator
-from .solver import Integrator, StepTaker
+from .solver import Integrator
 from .utils import fiber_folder, update_path_name
 from .variationer import VariationDescriptor, Variationer
 
@@ -37,6 +37,7 @@ def type_checker(*types):
             def validator(*args):
                 pass
 
+        @wraps(validator)
         def _type_checker_wrapped(name, n):
             if not isinstance(n, types):
                 raise TypeError(
@@ -377,7 +378,6 @@ class Parameters:
     # computed
     linear_operator: LinearOperator = Parameter(type_checker(LinearOperator))
     nonlinear_operator: NonLinearOperator = Parameter(type_checker(NonLinearOperator))
-    step_taker: StepTaker = Parameter(type_checker(StepTaker))
     integrator: Integrator = Parameter(type_checker(Integrator))
     conserved_quantity: AbstractConservedQuantity = Parameter(
         type_checker(AbstractConservedQuantity)
@@ -391,6 +391,7 @@ class Parameters:
     alpha: float = Parameter(non_negative(float, int))
     gamma_arr: np.ndarray = Parameter(type_checker(np.ndarray))
     A_eff_arr: np.ndarray = Parameter(type_checker(np.ndarray))
+    c_to_a_factor: np.ndarray = Parameter(type_checker(float, np.ndarray))
     w: np.ndarray = Parameter(type_checker(np.ndarray))
     l: np.ndarray = Parameter(type_checker(np.ndarray))
     w_c: np.ndarray = Parameter(type_checker(np.ndarray))
diff --git a/src/scgenerator/physics/__init__.py b/src/scgenerator/physics/__init__.py
index f59df64..f7008bf 100644
--- a/src/scgenerator/physics/__init__.py
+++ b/src/scgenerator/physics/__init__.py
@@ -104,8 +104,11 @@ def find_optimal_depth(
     ind = w > (w0 / 10)
     disp[ind] = material_dispersion(units.m.inv(w[ind]), material)
 
-    propagate = lambda z: spectrum * np.exp(-0.5j * disp * w_c ** 2 * z)
-    integrate = lambda z: math.abs2(np.fft.ifft(propagate(z)))
+    def propagate(z):
+        return spectrum * np.exp(-0.5j * disp * w_c ** 2 * z)
+
+    def integrate(z):
+        return math.abs2(np.fft.ifft(propagate(z)))
 
     def score(z):
         return -np.nansum(integrate(z) ** 6)
diff --git a/src/scgenerator/physics/fiber.py b/src/scgenerator/physics/fiber.py
index f097887..7bea7e3 100644
--- a/src/scgenerator/physics/fiber.py
+++ b/src/scgenerator/physics/fiber.py
@@ -1127,3 +1127,7 @@ def capillary_loss(wl: np.ndarray, he_mode: tuple[int, int], core_radius: float)
 
 def extinction_distance(loss: T, ratio=1 / e) -> T:
     return np.log(ratio) / -loss
+
+
+def L_eff(loss: T, length: float) -> T:
+    return -np.expm1(-loss * length) / loss
diff --git a/src/scgenerator/physics/materials.py b/src/scgenerator/physics/materials.py
index cda8c74..8d8e073 100644
--- a/src/scgenerator/physics/materials.py
+++ b/src/scgenerator/physics/materials.py
@@ -1,3 +1,4 @@
+import functools
 from typing import Any
 
 import numpy as np
@@ -110,15 +111,7 @@ def number_density_van_der_waals(
     return np.min(roots)
 
 
-def sellmeier_scalar(
-    wavelength: float,
-    material_dico: dict[str, Any],
-    pressure: float = None,
-    temperature: float = None,
-) -> float:
-    return float(sellmeier(np.array([wavelength]), material_dico, pressure, temperature)[0])
-
-
+@functools.singledispatch
 def sellmeier(
     wl_for_disp: np.ndarray,
     material_dico: dict[str, Any],
@@ -187,6 +180,17 @@ def sellmeier(
     return chi
 
 
+@sellmeier.register
+def sellmeier_scalar(
+    wavelength: float,
+    material_dico: dict[str, Any],
+    pressure: float = None,
+    temperature: float = None,
+) -> float:
+    """n^2 - 1"""
+    return float(sellmeier(np.array([wavelength]), material_dico, pressure, temperature)[0])
+
+
 def delta_gas(w, material_dico):
     """returns the value delta_t (eq. 24 in Markos(2017))
     Parameters
diff --git a/src/scgenerator/physics/plasma.py b/src/scgenerator/physics/plasma.py
index cad4f09..155b0d8 100644
--- a/src/scgenerator/physics/plasma.py
+++ b/src/scgenerator/physics/plasma.py
@@ -64,8 +64,7 @@ class Plasma:
         field_abs = np.abs(field)
         delta = 1e-14 * field_abs.max()
         rate = self.rate(field_abs)
-        exp_int = expm1_int(rate, self.dt)
-        electron_density = N0 * exp_int
+        electron_density = free_electron_density(rate, self.dt, N0)
         dn_dt = (N0 - electron_density) * rate
         out = self.dt * cumulative_simpson(
             dn_dt * self.Ip / (field + delta)
@@ -79,7 +78,5 @@ def adiabadicity(w: np.ndarray, I: float, field: np.ndarray) -> np.ndarray:
     return w * np.sqrt(2 * me * I) / (e * np.abs(field))
 
 
-def free_electron_density(
-    field: np.ndarray, dt: float, N0: float, rate: IonizationRate
-) -> np.ndarray:
-    return N0 * (1 - np.exp(-dt * cumulative_simpson(rate(field))))
+def free_electron_density(rate: np.ndarray, dt: float, N0: float) -> np.ndarray:
+    return N0 * expm1_int(rate, dt)
diff --git a/src/scgenerator/physics/pulse.py b/src/scgenerator/physics/pulse.py
index c3f0099..d3eff47 100644
--- a/src/scgenerator/physics/pulse.py
+++ b/src/scgenerator/physics/pulse.py
@@ -215,6 +215,10 @@ def convert_field_units(envelope: np.ndarray, n: np.ndarray, A_eff: float) -> np
     return 2 * envelope.real / np.sqrt(2 * units.epsilon0 * units.c * n * A_eff)
 
 
+def c_to_a_factor(A_eff_arr: np.ndarray) -> np.ndarray:
+    return (A_eff_arr / A_eff_arr[0]) ** (1 / 4)
+
+
 def conform_pulse_params(
     shape: Literal["gaussian", "sech"],
     width: float = None,
diff --git a/src/scgenerator/physics/simulate.py b/src/scgenerator/physics/simulate.py
index 160d732..57211af 100644
--- a/src/scgenerator/physics/simulate.py
+++ b/src/scgenerator/physics/simulate.py
@@ -85,12 +85,6 @@ class RK4IP:
         self.z_targets.sort()
         self.store_num = len(self.z_targets)
 
-        # Setup initial values for every physical quantity that we want to track
-        if self.params.A_eff_arr is not None:
-            C_to_A_factor = (self.params.A_eff_arr / self.params.A_eff_arr[0]) ** (1 / 4)
-        else:
-            C_to_A_factor = 1.0
-
         # Initial step size
         if self.params.adapt_step_size:
             initial_h = (self.z_targets[1] - self.z_targets[0]) / 2
@@ -100,11 +94,10 @@ class RK4IP:
             length=self.params.length,
             z=self.z_targets.pop(0),
             current_step_size=initial_h,
-            previous_step_size=0.0,
-            step=1,
-            C_to_A_factor=C_to_A_factor,
+            step=0,
+            C_to_A_factor=self.params.c_to_a_factor,
             converter=self.params.ifft,
-            solution=self.params.spec_0.copy() / C_to_A_factor,
+            solution=self.params.spec_0.copy() / self.params.c_to_a_factor,
         )
         self.stored_spectra = self.params.recovery_last_stored * [None] + [
             self.init_state.solution.spectrum.copy()
@@ -170,12 +163,18 @@ class RK4IP:
         store = False
         state = self.init_state.copy()
         yield len(self.stored_spectra) - 1, state
-        integrator = solver.RK4IPSD(
-            state,
-            self.params.linear_operator,
-            self.params.nonlinear_operator,
-            self.params.tolerated_error,
-        )
+        if self.params.adapt_step_size:
+            integrator = solver.ConservedQuantityIntegrator(
+                self.init_state,
+                self.params.linear_operator,
+                self.params.nonlinear_operator,
+                self.params.tolerated_error,
+                self.params.conserved_quantity,
+            )
+        else:
+            integrator = solver.ConstantStepIntegrator(
+                self.init_state, self.params.linear_operator, self.params.nonlinear_operator
+            )
         for state in integrator:
 
             new_tracked_values = integrator.all_values()
diff --git a/src/scgenerator/solver.py b/src/scgenerator/solver.py
index d973f3c..076a3db 100644
--- a/src/scgenerator/solver.py
+++ b/src/scgenerator/solver.py
@@ -1,5 +1,8 @@
+from __future__ import annotations
+
+import logging
 from abc import abstractmethod
-from typing import Iterator
+from typing import Iterator, Type
 
 import numpy as np
 
@@ -13,106 +16,6 @@ from .operators import (
     ValueTracker,
 )
 
-##################################################
-################### STEP-TAKER ###################
-##################################################
-
-
-class StepTaker(ValueTracker):
-    linear_operator: LinearOperator
-    nonlinear_operator: NonLinearOperator
-    _tracked_values: dict[str, float]
-
-    def __init__(self, linear_operator: LinearOperator, nonlinear_operator: NonLinearOperator):
-        self.linear_operator = linear_operator
-        self.nonlinear_operator = nonlinear_operator
-        self._tracked_values = {}
-
-    @abstractmethod
-    def __call__(self, state: CurrentState, step_size: float) -> np.ndarray:
-        ...
-
-    def all_values(self) -> dict[str, float]:
-        """override ValueTracker.all_values to account for the fact that operators are called
-        multiple times per step, sometimes with different state, so we use value recorded
-        earlier. Please call self.recorde_tracked_values() one time only just after calling
-        the linear and nonlinear operators in your StepTaker.
-
-        Returns
-        -------
-        dict[str, float]
-            tracked values
-        """
-        return self.values() | self._tracked_values
-
-    def record_tracked_values(self):
-        self._tracked_values = super().all_values()
-
-
-class RK4IPStepTaker(StepTaker):
-    c2 = 1 / 2
-    c3 = 1 / 3
-    c6 = 1 / 6
-    _cached_values: tuple[np.ndarray, np.ndarray]
-    _cached_key: float
-    _cache_hits: int
-    _cache_misses: int
-
-    def __init__(self, linear_operator: LinearOperator, nonlinear_operator: NonLinearOperator):
-        super().__init__(linear_operator, nonlinear_operator)
-        self._cached_key = None
-        self._cached_values = None
-        self._cache_hits = 0
-        self._cache_misses = 0
-
-    def __call__(self, state: CurrentState, step_size: float) -> np.ndarray:
-        h = step_size
-        l0, nl0 = self.cached_values(state)
-        expD = np.exp(h * self.c2 * l0)
-
-        A_I = expD * state.solution
-        k1 = expD * (h * nl0)
-        k2 = h * self.nonlinear_operator(state.replace(A_I + k1 * self.c2))
-        k3 = h * self.nonlinear_operator(state.replace(A_I + k2 * self.c2))
-        k4 = h * self.nonlinear_operator(state.replace(expD * (A_I + k3)))
-
-        return expD * (A_I + k1 * self.c6 + k2 * self.c3 + k3 * self.c3) + k4 * self.c6
-
-    def cached_values(self, state: CurrentState) -> tuple[np.ndarray, np.ndarray]:
-        """the evaluation of the linear and nonlinear operators at the start of the step don't
-        depend on the step size, so we cache them in case we need them more than once (which
-        can happen depending on the adaptive step size controller)
-
-
-        Parameters
-        ----------
-        state : CurrentState
-            current state of the simulation. state.z is used as the key for the cache
-
-        Returns
-        -------
-        np.ndarray
-            result of the linear operator
-        np.ndarray
-            result of the nonlinear operator
-        """
-        if self._cached_key != state.z:
-            self._cache_misses += 1
-            self._cached_key = state.z
-            self._cached_values = self.linear_operator(state), self.nonlinear_operator(state)
-            self.record_tracked_values()
-        else:
-            self._cache_hits += 1
-        return self._cached_values
-
-    def values(self) -> dict[str, float]:
-        return dict(RK4IP_cache_hits=self._cache_hits, RK4IP_cache_misses=self._cache_misses)
-
-
-##################################################
-################### INTEGRATOR ###################
-##################################################
-
 
 class Integrator(ValueTracker):
     linear_operator: LinearOperator
@@ -120,6 +23,8 @@ class Integrator(ValueTracker):
     state: CurrentState
     tolerated_error: float
     _tracked_values: dict[str, float]
+    logger: logging.Logger
+    __registry: dict[str, Type[Integrator]] = {}
 
     def __init__(
         self,
@@ -133,11 +38,19 @@ class Integrator(ValueTracker):
         self.nonlinear_operator = nonlinear_operator
         self.tolerated_error = tolerated_error
         self._tracked_values = {}
+        self.logger = get_logger(self.__class__.__name__)
+
+    def __init_subclass__(cls):
+        cls.__registry[cls.__name__] = cls
+
+    @classmethod
+    def get(cls, integr: str) -> Type[Integrator]:
+        return cls.__registry[integr]
 
     @abstractmethod
     def __iter__(self) -> Iterator[CurrentState]:
         """propagate the state with a step size of state.current_step_size
-        and yield a new state with updated z and previous_step_size attributes"""
+        and yield a new state with updated z and step attributes"""
         ...
 
     def all_values(self) -> dict[str, float]:
@@ -151,7 +64,7 @@ class Integrator(ValueTracker):
         dict[str, float]
             tracked values
         """
-        return self.values() | self._tracked_values
+        return self.values() | self._tracked_values | dict(z=self.state.z, step=self.state.step)
 
     def record_tracked_values(self):
         self._tracked_values = super().all_values()
@@ -161,85 +74,104 @@ class Integrator(ValueTracker):
 
 
 class ConstantStepIntegrator(Integrator):
-    def __call__(self, state: CurrentState) -> CurrentState:
-        new_state = state.replace(self.step_taker(state, state.current_step_size))
-        new_state.z += new_state.current_step_size
-        new_state.previous_step_size = new_state.current_step_size
-        return new_state
+    def __init__(
+        self,
+        init_state: CurrentState,
+        linear_operator: LinearOperator,
+        nonlinear_operator: NonLinearOperator,
+    ):
+        super().__init__(init_state, linear_operator, nonlinear_operator, 0.0)
 
-    def values(self) -> dict[str, float]:
-        return dict(h=self.last_step)
+    def __iter__(self) -> Iterator[CurrentState]:
+        while True:
+            lin = self.linear_operator(self.state)
+            nonlin = self.nonlinear_operator(self.state)
+            self.record_tracked_values()
+            new_spec = RK4IP_step(
+                self.nonlinear_operator,
+                self.state,
+                self.state.solution.spectrum,
+                self.state.current_step_size,
+                lin,
+                nonlin,
+            )
+
+            self.state.z += self.state.current_step_size
+            self.state.step += 1
+            self.state.solution = new_spec
+            yield self.state
 
 
 class ConservedQuantityIntegrator(Integrator):
-    step_taker: StepTaker
+    last_qty: float
     conserved_quantity: AbstractConservedQuantity
-    last_quantity_value: float
-    tolerated_error: float
-    local_error: float = 0.0
+    current_error: float = 0.0
 
     def __init__(
         self,
-        step_taker: StepTaker,
-        conserved_quantity: AbstractConservedQuantity,
+        init_state: CurrentState,
+        linear_operator: LinearOperator,
+        nonlinear_operator: NonLinearOperator,
         tolerated_error: float,
+        conserved_quantity: AbstractConservedQuantity,
     ):
+        super().__init__(init_state, linear_operator, nonlinear_operator, tolerated_error)
         self.conserved_quantity = conserved_quantity
-        self.last_quantity_value = 0
-        self.tolerated_error = tolerated_error
-        self.logger = get_logger(self.__class__.__name__)
-        self.size_fac = 2.0 ** (1.0 / 5.0)
-        self.step_taker = step_taker
+        self.last_qty = self.conserved_quantity(self.state)
 
-    def __call__(self, state: CurrentState) -> CurrentState:
-        keep = False
-        h_next_step = state.current_step_size
-        while not keep:
-            h = h_next_step
+    def __iter__(self) -> Iterator[CurrentState]:
+        h_next_step = self.state.current_step_size
+        size_fac = 2.0 ** (1.0 / 5.0)
+        while True:
+            lin = self.linear_operator(self.state)
+            nonlin = self.nonlinear_operator(self.state)
+            self.record_tracked_values()
+            while True:
+                h = h_next_step
+                new_state = self.state.replace(
+                    RK4IP_step(
+                        self.nonlinear_operator,
+                        self.state,
+                        self.state.solution.spectrum,
+                        h,
+                        lin,
+                        nonlin,
+                    )
+                )
 
-            new_state = state.replace(self.step_taker(state, h))
+                new_qty = self.conserved_quantity(new_state)
+                self.current_error = np.abs(new_qty - self.last_qty) / self.last_qty
 
-            new_qty = self.conserved_quantity(new_state)
-            delta = np.abs(new_qty - self.last_quantity_value) / self.last_quantity_value
-
-            if delta > 2 * self.tolerated_error:
-                progress_str = f"step {state.step} rejected with h = {h:.4e}, doing over"
-                self.logger.info(progress_str)
-                keep = False
-                h_next_step = h * 0.5
-            elif self.tolerated_error < delta <= 2.0 * self.tolerated_error:
-                keep = True
-                h_next_step = h / self.size_fac
-            elif delta < 0.1 * self.tolerated_error:
-                keep = True
-                h_next_step = h * self.size_fac
-            else:
-                keep = True
-                h_next_step = h
-
-        self.local_error = delta
-        self.last_quantity_value = new_qty
-        new_state.current_step_size = h_next_step
-        new_state.previous_step_size = h
-        new_state.z += h
-        self.last_step = h
-        return new_state
+                if self.current_error > 2 * self.tolerated_error:
+                    h_next_step = h * 0.5
+                elif self.tolerated_error < self.current_error <= 2.0 * self.tolerated_error:
+                    h_next_step = h / size_fac
+                    break
+                elif self.current_error < 0.1 * self.tolerated_error:
+                    h_next_step = h * size_fac
+                    break
+                else:
+                    h_next_step = h
+                    break
+                self.logger.info(
+                    f"step {new_state.step} rejected : {h=}, {self.current_error=}, {h_next_step=}"
+                )
+            self.last_qty = new_qty
+            self.state = new_state
+            self.state.current_step_size = h_next_step
+            self.state.z += h
+            self.state.step += 1
+            yield self.state
 
     def values(self) -> dict[str, float]:
-        return dict(
-            cons_qty=self.last_quantity_value, h=self.last_step, relative_error=self.local_error
-        )
+        return dict(cons_qty=self.last_qty, relative_error=self.current_error)
 
 
 class RK4IPSD(Integrator):
     """Runge-Kutta 4 in Interaction Picture with step doubling"""
 
-    linear_operator: LinearOperator
-    nonlinear_operator: NonLinearOperator
-    tolerated_error: float
-    current_error: float
-    next_h_factor = 1.0
-    current_error = 0.0
+    next_h_factor: float = 1.0
+    current_error: float = 0.0
 
     def __iter__(self) -> Iterator[CurrentState]:
         h_next_step = self.state.current_step_size
@@ -274,7 +206,6 @@ class RK4IPSD(Integrator):
                     break
 
             self.state.current_step_size = h_next_step
-            self.state.previous_step_size = h
             self.state.z += h
             self.state.step += 1
             self.state.solution = new_fine
@@ -283,15 +214,7 @@ class RK4IPSD(Integrator):
     def take_step(
         self, h: float, spec: np.ndarray, lin: np.ndarray, nonlin: np.ndarray
     ) -> np.ndarray:
-        expD = np.exp(h * 0.5 * lin)
-        A_I = expD * spec
-
-        k1 = expD * nonlin
-        k2 = self.nl(A_I + k1 * 0.5 * h)
-        k3 = self.nl(A_I + k2 * 0.5 * h)
-        k4 = self.nl(expD * (A_I + h * k3))
-
-        return expD * (A_I + h / 6 * (k1 + 2 * k2 + 2 * k3)) + h / 6 * k4
+        return RK4IP_step(self.nonlinear_operator, self.state, spec, h, lin, nonlin)
 
     def compute_diff(self, coarse_spec: np.ndarray, fine_spec: np.ndarray) -> float:
         return np.sqrt(math.abs2(coarse_spec - fine_spec).sum() / math.abs2(fine_spec).sum())
@@ -358,8 +281,11 @@ class ERK43(Integrator):
                 h_next_step = self.next_h_factor * h
                 if self.current_error <= self.tolerated_error:
                     break
+                self.logger.info(
+                    f"step {self.state.step} rejected : {h=}, {self.current_error=}, {h_next_step=}"
+                )
+
             self.state.current_step_size = h_next_step
-            self.state.previous_step_size = h
             self.state.z += h
             self.state.step += 1
             self.state.solution = new_fine
@@ -377,7 +303,7 @@ class ERK43(Integrator):
 
 class ERK54(ERK43):
     def __iter__(self) -> Iterator[CurrentState]:
-        print("using ERK54")
+        self.logger.info("using ERK54")
         h_next_step = self.state.current_step_size
         k7 = self.nonlinear_operator(self.state)
         while True:
@@ -413,10 +339,51 @@ class ERK54(ERK43):
                 h_next_step = self.next_h_factor * h
                 if self.current_error <= self.tolerated_error:
                     break
+                self.logger.info(
+                    f"step {self.state.step} rejected : {h=}, {self.current_error=}, {h_next_step=}"
+                )
             self.state.current_step_size = h_next_step
-            self.state.previous_step_size = h
             self.state.z += h
             self.state.step += 1
             self.state.solution = new_fine
             k7 = tmp_k7
             yield self.state
+
+
+def RK4IP_step(
+    nonlinear_operator: NonLinearOperator,
+    init_state: CurrentState,
+    spectrum: np.ndarray,
+    h: float,
+    init_linear: np.ndarray,
+    init_nonlinear: np.ndarray,
+) -> np.ndarray:
+    """Take a normal RK4IP step
+
+    Parameters
+    ----------
+    nonlinear_operator : NonLinearOperator
+        non linear operator
+    init_state : CurrentState
+        state at the start of the step
+    h : float
+        step size
+    init_linear : np.ndarray
+        linear operator already applied on the initial state
+    init_nonlinear : np.ndarray
+        nonlinear operator already applied on the initial state
+
+    Returns
+    -------
+    np.ndarray
+        resutling spectrum
+    """
+    expD = np.exp(h * 0.5 * init_linear)
+    A_I = expD * spectrum
+
+    k1 = expD * init_nonlinear
+    k2 = nonlinear_operator(init_state.replace(A_I + k1 * 0.5 * h))
+    k3 = nonlinear_operator(init_state.replace(A_I + k2 * 0.5 * h))
+    k4 = nonlinear_operator(init_state.replace(expD * (A_I + h * k3)))
+
+    return expD * (A_I + h / 6 * (k1 + 2 * k2 + 2 * k3)) + h / 6 * k4
diff --git a/src/scgenerator/utils.py b/src/scgenerator/utils.py
index eb998c7..1c7d38e 100644
--- a/src/scgenerator/utils.py
+++ b/src/scgenerator/utils.py
@@ -315,7 +315,7 @@ def ensure_folder(path: Path, prevent_overwrite: bool = True, mkdir=True) -> Pat
 
 
 def branch_id(branch: Path) -> tuple[int, int]:
-    sim_match = branch.parent.name.split()[0]
+    sim_match = branch.resolve().parent.name.split()[0]
     if sim_match.isdigit():
         s_int = int(sim_match)
     else: