Bulmash initializePoisson

Average Error: 0.0 → 0.0

Time: 54.0s

Precision: binary64

Cost: 14528

Math

\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

↓

\[\frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
  (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))

↓

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ 1.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT))))
  (/ NaChar (+ 1.0 (exp (/ (+ Ev (+ Vef (- EAccept mu))) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
}

↓

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp(((Vef + (mu + (EDonor - Ec))) / KbT)))) + (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT))));
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
end function

↓

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / (1.0d0 + exp(((vef + (mu + (edonor - ec))) / kbt)))) + (nachar / (1.0d0 + exp(((ev + (vef + (eaccept - mu))) / kbt))))
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
}

↓

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT))));
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))

↓

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)))) + (NaChar / (1.0 + math.exp(((Ev + (Vef + (EAccept - mu))) / KbT))))

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
end

↓

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
end

↓

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp(((Vef + (mu + (EDonor - Ec))) / KbT)))) + (NaChar / (1.0 + exp(((Ev + (Vef + (EAccept - mu))) / KbT))));
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 0.0

   \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

2. Simplified 0.0

   \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{Vef + \left(mu - \left(Ec - EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}} \]

3. Final simplification 0.0

   \[\leadsto \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} \]

Alternatives

Alternative 1
Error	15.8
Cost	15660

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_4 := t_2 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{if}\;mu \leq -9.865985231828396 \cdot 10^{+213}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq -1.854410348660515 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -2.6131731822661918 \cdot 10^{-132}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;mu \leq -7.532042825088217 \cdot 10^{-220}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 1.291393842594977 \cdot 10^{-19}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq 1.1321354368332707 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 4.983809944337118 \cdot 10^{+97}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.6568754732875268 \cdot 10^{+175}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 3.0108888357038383 \cdot 10^{+187}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.1314503334124471 \cdot 10^{+199}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev - mu}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;mu \leq 1.0016412976016496 \cdot 10^{+222}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 2
Error	18.5
Cost	15596

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_2 := t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_4 := t_3 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;EDonor \leq -9.295149367336023 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EDonor \leq -2.4183821840089205 \cdot 10^{+60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq -5.178724972646169 \cdot 10^{-203}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;EDonor \leq -8.806791986622148 \cdot 10^{-218}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EDonor \leq -3.435342231359028 \cdot 10^{-241}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;EDonor \leq 3.6400182850655544 \cdot 10^{-294}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EDonor \leq 8.285044879314363 \cdot 10^{-219}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq 4.624295978865799 \cdot 10^{-76}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;EDonor \leq 0.0021384493596341416:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EDonor \leq 1.5738702783839286 \cdot 10^{+95}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev - mu}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;EDonor \leq 1.5835382308112322 \cdot 10^{+250}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]

Alternative 3
Error	25.1
Cost	15408

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_2 := 1 + e^{\frac{Vef}{KbT}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_4 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_5 := t_4 + \frac{NaChar}{1 + \left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev - mu}{KbT}\right)\right)\right)}\\ \mathbf{if}\;mu \leq -1.052585222616147 \cdot 10^{+215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq -2.563175556073649 \cdot 10^{+44}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq -3.3749715140197333 \cdot 10^{-9}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;mu \leq -1.4895609434790124 \cdot 10^{-177}:\\ \;\;\;\;t_4 + \frac{NaChar}{2 + \frac{Vef \cdot \left(1 + \frac{Vef \cdot \left(0.5 + \frac{Vef}{KbT} \cdot 0.16666666666666666\right)}{KbT}\right)}{KbT}}\\ \mathbf{elif}\;mu \leq 2.2882530052984663 \cdot 10^{-269}:\\ \;\;\;\;t_1 + \frac{NdChar}{t_2}\\ \mathbf{elif}\;mu \leq 5.8223092172008684 \cdot 10^{-260}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq 1.3009768820973165 \cdot 10^{-109}:\\ \;\;\;\;t_0 + \frac{NaChar}{t_2}\\ \mathbf{elif}\;mu \leq 3.861892515355851 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t_0\\ \mathbf{elif}\;mu \leq 2.6531402502203126 \cdot 10^{+73}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 4.983809944337118 \cdot 10^{+97}:\\ \;\;\;\;t_4 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;mu \leq 2.7351511473837582 \cdot 10^{+156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 1.0016412976016496 \cdot 10^{+222}:\\ \;\;\;\;t_4 + \frac{NaChar}{2 + \frac{Vef}{KbT} \cdot \left(1 + \frac{0.5}{\frac{KbT}{Vef}}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	24.9
Cost	15144

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -1.052585222616147 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -2.563175556073649 \cdot 10^{+44}:\\ \;\;\;\;t_2 + \frac{NaChar}{1 + \left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev - mu}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;mu \leq -3.3749715140197333 \cdot 10^{-9}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;mu \leq -1.4895609434790124 \cdot 10^{-177}:\\ \;\;\;\;t_2 + \frac{NaChar}{2 + \frac{Vef \cdot \left(1 + \frac{Vef \cdot \left(0.5 + \frac{Vef}{KbT} \cdot 0.16666666666666666\right)}{KbT}\right)}{KbT}}\\ \mathbf{elif}\;mu \leq 2.4216902670489574 \cdot 10^{-211}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;mu \leq 3.861892515355851 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;mu \leq 2.6531402502203126 \cdot 10^{+73}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 4.983809944337118 \cdot 10^{+97}:\\ \;\;\;\;t_2 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;mu \leq 2.7351511473837582 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 1.0016412976016496 \cdot 10^{+222}:\\ \;\;\;\;t_2 + \frac{NaChar}{2 + \frac{Vef}{KbT} \cdot \left(1 + \frac{0.5}{\frac{KbT}{Vef}}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 5
Error	17.2
Cost	14672

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_2 := t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;EAccept \leq -3.966232836694577 \cdot 10^{-190}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 5.739595997648585 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EAccept \leq 3.492838836778822 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 8.029628648026695 \cdot 10^{+77}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 6
Error	25.3
Cost	14616

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;Vef \leq -18301.077462004338:\\ \;\;\;\;t_1 + \frac{NaChar}{2 + \frac{Vef}{KbT} \cdot \left(1 + \frac{0.5}{\frac{KbT}{Vef}}\right)}\\ \mathbf{elif}\;Vef \leq -1.9776926059537455 \cdot 10^{-142}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;Vef \leq -9.379493795148854 \cdot 10^{-257}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_0\\ \mathbf{elif}\;Vef \leq 7.4984667524733025 \cdot 10^{-149}:\\ \;\;\;\;t_1 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;Vef \leq 8.408023648427378 \cdot 10^{-53}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.5492024705495999 \cdot 10^{-24}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NaChar}{2 + \frac{Vef \cdot \left(1 + \frac{Vef \cdot \left(0.5 + \frac{Vef}{KbT} \cdot 0.16666666666666666\right)}{KbT}\right)}{KbT}}\\ \end{array} \]

Alternative 7
Error	25.3
Cost	14616

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;Vef \leq -18301.077462004338:\\ \;\;\;\;t_1 + \frac{NaChar}{2 + \frac{Vef}{KbT} \cdot \left(1 + \frac{0.5}{\frac{KbT}{Vef}}\right)}\\ \mathbf{elif}\;Vef \leq -1.9776926059537455 \cdot 10^{-142}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;Vef \leq -9.379493795148854 \cdot 10^{-257}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_0\\ \mathbf{elif}\;Vef \leq 7.4984667524733025 \cdot 10^{-149}:\\ \;\;\;\;t_1 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;Vef \leq 8.408023648427378 \cdot 10^{-53}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.5492024705495999 \cdot 10^{-24}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NaChar}{2 + \frac{Vef \cdot \left(1 + \frac{Vef \cdot \left(0.5 + \frac{Vef}{KbT} \cdot 0.16666666666666666\right)}{KbT}\right)}{KbT}}\\ \end{array} \]

Alternative 8
Error	16.8
Cost	14540

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{if}\;mu \leq -9.865985231828396 \cdot 10^{+213}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq 1.1321354368332707 \cdot 10^{+89}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.2167357953820753 \cdot 10^{+231}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 9
Error	17.4
Cost	14408

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;mu \leq -9.865985231828396 \cdot 10^{+213}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq 4.983809944337118 \cdot 10^{+97}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq 2.0551569808582595 \cdot 10^{+163}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq 1.0016412976016496 \cdot 10^{+222}:\\ \;\;\;\;t_1 + \frac{NaChar}{2 + \frac{Vef}{KbT} \cdot \left(1 + \frac{0.5}{\frac{KbT}{Vef}}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 10
Error	14.2
Cost	14408

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.7909701489270073 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 2.057208121101086 \cdot 10^{+122}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	22.6
Cost	8908

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{if}\;NaChar \leq -2.5919199914051936 \cdot 10^{+30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -1.0579993473401695 \cdot 10^{-190}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev - mu}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 2477766353002307600:\\ \;\;\;\;t_0 + \frac{NaChar}{2 + \frac{Vef}{KbT} \cdot \left(1 + \frac{Vef}{KbT} \cdot \left(Vef \cdot \frac{0.16666666666666666}{KbT}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 12
Error	22.4
Cost	8904

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{if}\;NaChar \leq -5.927885013479394:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 2477766353002307600:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef \cdot \left(1 + \frac{Vef \cdot \left(0.5 + \frac{Vef}{KbT} \cdot 0.16666666666666666\right)}{KbT}\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Error	22.5
Cost	8776

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{if}\;NaChar \leq -5.927885013479394:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 2477766353002307600:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT} \cdot \left(1 + \frac{Vef}{KbT} \cdot \left(Vef \cdot \frac{0.16666666666666666}{KbT}\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 14
Error	22.8
Cost	8520

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{if}\;NaChar \leq -5.927885013479394:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 2477766353002307600:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT} \cdot \left(1 + \frac{0.5}{\frac{KbT}{Vef}}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 15
Error	23.7
Cost	8136

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{if}\;NaChar \leq -5.927885013479394:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 2477766353002307600:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 16
Error	40.6
Cost	8020

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;EDonor \leq -3.2895470138542523 \cdot 10^{+207}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;EDonor \leq -1.9040572288312595 \cdot 10^{-138}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EDonor \leq 3.150957119707545 \cdot 10^{-232}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;EDonor \leq 2.143767002979761 \cdot 10^{-197}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EDonor \leq 8.600328837152254 \cdot 10^{-158}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 17
Error	37.8
Cost	8016

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ t_1 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Vef}{KbT}\right)}\\ \mathbf{if}\;mu \leq -5.42418697649074 \cdot 10^{-12}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq 1.0788219917678416 \cdot 10^{-167}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 7.359033847964709 \cdot 10^{-41}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;mu \leq 1.2687238345617416 \cdot 10^{+126}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 18
Error	24.8
Cost	8008

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -5.927885013479394:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 9.603642266426127 \cdot 10^{+32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 19
Error	23.3
Cost	8008

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{if}\;NaChar \leq -5.927885013479394:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 2477766353002307600:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 20
Error	39.6
Cost	7884

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{if}\;NaChar \leq -5.424101212515535 \cdot 10^{+24}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq -1.2995985078396505 \cdot 10^{-249}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 85114.62773142384:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 21
Error	32.9
Cost	7884

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -4.78258763582637 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq -1.2995985078396505 \cdot 10^{-249}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.692688255038479 \cdot 10^{+19}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 22
Error	40.8
Cost	7828

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;EDonor \leq -3.2895470138542523 \cdot 10^{+207}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;EDonor \leq -1.9040572288312595 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq 3.150957119707545 \cdot 10^{-232}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EDonor \leq 2.143767002979761 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq 1.4377430616386273 \cdot 10^{-142}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 23
Error	41.5
Cost	7764

\[\begin{array}{l} t_0 := \frac{2 - \frac{Ec}{KbT}}{NdChar}\\ t_1 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;Vef \leq -1164389297864951.8:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -2.5053926180610003 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 1.989209899844876 \cdot 10^{-134}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 2.963991710388141 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 3.8216867978873544 \cdot 10^{+157}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{NaChar} + t_0}{\frac{2}{NaChar} \cdot t_0}\\ \end{array} \]

Alternative 24
Error	42.9
Cost	7764

\[\begin{array}{l} t_0 := \frac{2 - \frac{Ec}{KbT}}{NdChar}\\ t_1 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;Vef \leq -6.742651955539449 \cdot 10^{+37}:\\ \;\;\;\;t_2 + NaChar \cdot \frac{KbT}{Vef}\\ \mathbf{elif}\;Vef \leq -2.5053926180610003 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 5.326057032206818 \cdot 10^{-132}:\\ \;\;\;\;t_2 + NaChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 2.963991710388141 \cdot 10^{+137}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 3.8216867978873544 \cdot 10^{+157}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{2}{NaChar} + t_0}{\frac{2}{NaChar} \cdot t_0}\\ \end{array} \]

Alternative 25
Error	39.6
Cost	7764

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ t_2 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;EDonor \leq -3.2895470138542523 \cdot 10^{+207}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EDonor \leq -1.9040572288312595 \cdot 10^{-138}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq 3.150957119707545 \cdot 10^{-232}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EDonor \leq 2.143767002979761 \cdot 10^{-197}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EDonor \leq 3.3692644833460223 \cdot 10^{+133}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 26
Error	27.5
Cost	7752

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;NaChar \leq -4.78258763582637 \cdot 10^{-19}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 9.603642266426127 \cdot 10^{+32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 27
Error	42.2
Cost	7368

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;KbT \leq -7.858996477780241 \cdot 10^{-178}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 6.069396434383155 \cdot 10^{-204}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 28
Error	42.2
Cost	7368

\[\begin{array}{l} \mathbf{if}\;KbT \leq -7.858996477780241 \cdot 10^{-178}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 3.4640141046265243 \cdot 10^{-233}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]

Alternative 29
Error	45.6
Cost	968

\[\begin{array}{l} t_0 := \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{if}\;KbT \leq -1.873237670241047 \cdot 10^{-162}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;KbT \leq 2.7937688251221427 \cdot 10^{-39}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 + NaChar \cdot 0.5\\ \end{array} \]

Alternative 30
Error	45.5
Cost	712

\[\begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{if}\;KbT \leq -1.873237670241047 \cdot 10^{-162}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 5.5386198387108875 \cdot 10^{-151}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 31
Error	46.5
Cost	320

\[0.5 \cdot \left(NdChar + NaChar\right) \]

Alternative 32
Error	52.7
Cost	192

\[NaChar \cdot 0.5 \]

Reproduce

herbie shell --seed 2022225 
(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
  :name "Bulmash initializePoisson"
  :precision binary64
  (+ (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))) (/ NaChar (+ 1.0 (exp (/ (+ (+ (+ Ev Vef) EAccept) (- mu)) KbT))))))