Bulmash initializePoisson

Average Error: 0.0 → 0.0

Time: 1.3min

Precision: binary64

Cost: 14592

Math

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

↓

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

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 (- Ec (+ EDonor mu))) KbT))))
  (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ (- mu) (+ Ev EAccept))) 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 - (Ec - (EDonor + mu))) / KbT)))) + (NaChar / (1.0 + exp(((Vef + (-mu + (Ev + EAccept))) / 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 - (ec - (edonor + mu))) / kbt)))) + (nachar / (1.0d0 + exp(((vef + (-mu + (ev + eaccept))) / 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 - (Ec - (EDonor + mu))) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef + (-mu + (Ev + EAccept))) / 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 - (Ec - (EDonor + mu))) / KbT)))) + (NaChar / (1.0 + math.exp(((Vef + (-mu + (Ev + EAccept))) / 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(Ec - Float64(EDonor + mu))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(-mu) + Float64(Ev + EAccept))) / 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 - (Ec - (EDonor + mu))) / KbT)))) + (NaChar / (1.0 + exp(((Vef + (-mu + (Ev + EAccept))) / 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[(Ec - N[(EDonor + mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[((-mu) + N[(Ev + EAccept), $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

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

   [Start] 0.0	\[ \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   rational.json-simplify-12 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{\color{blue}{0 - \left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   rational.json-simplify-45 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{0 - \color{blue}{\left(\left(Ec - Vef\right) - \left(EDonor + mu\right)\right)}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   rational.json-simplify-44 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(EDonor + mu\right) - \left(\left(Ec - Vef\right) - 0\right)}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   rational.json-simplify-5 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{\left(EDonor + mu\right) - \color{blue}{\left(Ec - Vef\right)}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   rational.json-simplify-44 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{\color{blue}{Vef - \left(Ec - \left(EDonor + mu\right)\right)}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   rational.json-simplify-1 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\color{blue}{\left(-mu\right) + \left(\left(Ev + Vef\right) + EAccept\right)}}{KbT}}} \]
   rational.json-simplify-1 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(-mu\right) + \color{blue}{\left(EAccept + \left(Ev + Vef\right)\right)}}{KbT}}} \]
   rational.json-simplify-1 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(-mu\right) + \left(EAccept + \color{blue}{\left(Vef + Ev\right)}\right)}{KbT}}} \]
   rational.json-simplify-41 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(-mu\right) + \color{blue}{\left(Vef + \left(Ev + EAccept\right)\right)}}{KbT}}} \]
   rational.json-simplify-41 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\color{blue}{Vef + \left(\left(Ev + EAccept\right) + \left(-mu\right)\right)}}{KbT}}} \]
   rational.json-simplify-1 [=>] 0.0	\[ \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \color{blue}{\left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}}{KbT}}} \]

3. Final simplification 0.0

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

Alternatives

Alternative 1
Error	29.2
Cost	15080

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_2 := \frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\\ t_3 := \frac{mu}{KbT} - \left(\frac{Ec}{KbT} - t_2\right)\\ t_4 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_5 := t_1 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ \mathbf{if}\;mu \leq -7.6 \cdot 10^{+252}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT}} + t_0\\ \mathbf{elif}\;mu \leq -3.2 \cdot 10^{+181}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -4.8 \cdot 10^{+146}:\\ \;\;\;\;\left(\left(0 - \left(-1 - \frac{NdChar \cdot KbT}{Vef}\right)\right) - 1\right) + t_0\\ \mathbf{elif}\;mu \leq -3.5 \cdot 10^{+46}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + \left(\left(\frac{Vef}{KbT} + \left(\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right) + 1\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -2.7 \cdot 10^{-57}:\\ \;\;\;\;\frac{NdChar}{\frac{1}{\frac{mu}{KbT} - -2} \cdot \left(t_3 \cdot t_3\right)} + t_0\\ \mathbf{elif}\;mu \leq -1.3 \cdot 10^{-214}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq 2.8 \cdot 10^{-249}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_4\\ \mathbf{elif}\;mu \leq 7.6 \cdot 10^{-122}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq 3.5 \cdot 10^{+52}:\\ \;\;\;\;\frac{NdChar}{\left(\frac{mu}{KbT} + t_2\right) - \frac{Ec}{KbT}} + t_0\\ \mathbf{elif}\;mu \leq 4.8 \cdot 10^{+118}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_4\\ \end{array} \]

Alternative 2
Error	24.7
Cost	15012

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\\ t_2 := \frac{mu}{KbT} - \left(\frac{Ec}{KbT} - t_1\right)\\ t_3 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_4 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_5 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_6 := t_4 + \frac{NaChar}{1 + e^{-\frac{mu}{KbT}}}\\ t_7 := t_3 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ \mathbf{if}\;mu \leq -1.1 \cdot 10^{+118}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq -2.45 \cdot 10^{-58}:\\ \;\;\;\;\frac{NdChar}{\frac{1}{\frac{mu}{KbT} - -2} \cdot \left(t_2 \cdot t_2\right)} + t_5\\ \mathbf{elif}\;mu \leq -1.15 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}} + t_0\\ \mathbf{elif}\;mu \leq -2.4 \cdot 10^{-215}:\\ \;\;\;\;t_3 + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 3.6 \cdot 10^{-250}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_0\\ \mathbf{elif}\;mu \leq 8.5 \cdot 10^{-122}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq 1.6 \cdot 10^{+52}:\\ \;\;\;\;\frac{NdChar}{\left(\frac{mu}{KbT} + t_1\right) - \frac{Ec}{KbT}} + t_5\\ \mathbf{elif}\;mu \leq 3.2 \cdot 10^{+128}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq 2.5 \cdot 10^{+193}:\\ \;\;\;\;t_4 + t_0\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]

Alternative 3
Error	18.9
Cost	15000

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + e^{-\frac{mu}{KbT}}}\\ t_2 := t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;Ev \leq -3.2 \cdot 10^{+222}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -5.2 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq -1.4 \cdot 10^{-117}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -1.8 \cdot 10^{-176}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq 1.45 \cdot 10^{-239}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq 2.5 \cdot 10^{-119}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 4
Error	23.7
Cost	14940

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{-\frac{mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_1\\ t_3 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}} + 1}\\ t_4 := \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\ \mathbf{if}\;Vef \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -2.2 \cdot 10^{-29}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -2.7 \cdot 10^{-69}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_0\\ \mathbf{elif}\;Vef \leq -2.6 \cdot 10^{-184}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{Vef}{KbT} + \left(\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right) + 1\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;Vef \leq 1.5 \cdot 10^{-205}:\\ \;\;\;\;t_4 + t_1\\ \mathbf{elif}\;Vef \leq 4.8 \cdot 10^{-174}:\\ \;\;\;\;t_4 + t_0\\ \mathbf{elif}\;Vef \leq 9.6 \cdot 10^{+195}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	15.0
Cost	14868

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;Vef \leq -7.5 \cdot 10^{+79}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -3 \cdot 10^{-77}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_0\\ \mathbf{elif}\;Vef \leq 1.3 \cdot 10^{-205}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 2.7 \cdot 10^{-174}:\\ \;\;\;\;\frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}} + \frac{NaChar}{1 + e^{-\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.75 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 6
Error	15.3
Cost	14868

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ t_2 := \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\ \mathbf{if}\;Vef \leq -6.2 \cdot 10^{+80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -6 \cdot 10^{-190}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_0\\ \mathbf{elif}\;Vef \leq 0.0051:\\ \;\;\;\;t_2 + t_0\\ \mathbf{elif}\;Vef \leq 5.7 \cdot 10^{+141}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.5 \cdot 10^{+195}:\\ \;\;\;\;t_2 + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 7
Error	20.5
Cost	14740

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}} + 1}\\ t_1 := \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Vef \leq -4.5 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -9.5 \cdot 10^{-22}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.15 \cdot 10^{-58}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -2.1 \cdot 10^{-185}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{Vef}{KbT} + \left(\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right) + 1\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;Vef \leq 9.6 \cdot 10^{+195}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 8
Error	16.7
Cost	14740

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Vef \leq -2.8 \cdot 10^{+199}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.5 \cdot 10^{-205}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq 6.2 \cdot 10^{-175}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{-\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.55 \cdot 10^{+196}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq 9.2 \cdot 10^{+291}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \end{array} \]

Alternative 9
Error	29.4
Cost	14684

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_1 := \frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\\ t_2 := \frac{mu}{KbT} - \left(\frac{Ec}{KbT} - t_1\right)\\ t_3 := t_0 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ t_4 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_5 := \frac{NdChar}{\left(\frac{mu}{KbT} + t_1\right) - \frac{Ec}{KbT}} + t_4\\ t_6 := t_0 + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{if}\;mu \leq -1.95 \cdot 10^{+250}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT}} + t_4\\ \mathbf{elif}\;mu \leq -1.15 \cdot 10^{+181}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq -6.8 \cdot 10^{+146}:\\ \;\;\;\;\left(\left(0 - \left(-1 - \frac{NdChar \cdot KbT}{Vef}\right)\right) - 1\right) + t_4\\ \mathbf{elif}\;mu \leq -2.3 \cdot 10^{+48}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\left(\frac{Vef}{KbT} + \left(\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right) + 1\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -5.9 \cdot 10^{-58}:\\ \;\;\;\;\frac{NdChar}{\frac{1}{\frac{mu}{KbT} - -2} \cdot \left(t_2 \cdot t_2\right)} + t_4\\ \mathbf{elif}\;mu \leq -3.6 \cdot 10^{-215}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 1.4 \cdot 10^{-250}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq 8.5 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 1.8 \cdot 10^{+53}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq 4.2 \cdot 10^{+209}:\\ \;\;\;\;t_6\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 10
Error	17.1
Cost	14408

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ \mathbf{if}\;EAccept \leq 2.6 \cdot 10^{-165}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.2 \cdot 10^{+46}:\\ \;\;\;\;\frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 11
Error	28.6
Cost	11164

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_1 := \frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\\ t_2 := \frac{mu}{KbT} - \left(\frac{Ec}{KbT} - t_1\right)\\ t_3 := t_0 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ t_4 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_5 := \frac{NdChar}{\left(\frac{mu}{KbT} + t_1\right) - \frac{Ec}{KbT}} + t_4\\ t_6 := \frac{NdChar}{\frac{1}{\frac{mu}{KbT} - -2} \cdot \left(t_2 \cdot t_2\right)} + t_4\\ t_7 := t_0 + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{if}\;mu \leq -5 \cdot 10^{+251}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT}} + t_4\\ \mathbf{elif}\;mu \leq -8.5 \cdot 10^{+180}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq -1.2 \cdot 10^{+146}:\\ \;\;\;\;\left(\left(0 - \left(-1 - \frac{NdChar \cdot KbT}{Vef}\right)\right) - 1\right) + t_4\\ \mathbf{elif}\;mu \leq -1.05 \cdot 10^{+41}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\left(\frac{Vef}{KbT} + \left(\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right) + 1\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -2.6 \cdot 10^{-58}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq -1.02 \cdot 10^{-226}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 7.1 \cdot 10^{-245}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq 8 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 6 \cdot 10^{+53}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq 4.2 \cdot 10^{+209}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]

Alternative 12
Error	29.5
Cost	10716

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ t_3 := t_1 + \frac{NaChar}{1 + \left(\left(\frac{Vef}{KbT} + \left(\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right) + 1\right)\right) - \frac{mu}{KbT}\right)}\\ t_4 := t_1 + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ t_5 := \frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\\ t_6 := \frac{NdChar}{\frac{1}{\frac{mu}{KbT} - \frac{Ec}{KbT}} \cdot \left(\left(\frac{mu}{KbT} - \left(\frac{Ec}{KbT} - t_5\right)\right) \cdot \left(\frac{mu}{KbT} - \left(-\frac{Vef}{KbT}\right)\right)\right)} + t_0\\ t_7 := \frac{NdChar}{\left(\frac{mu}{KbT} + t_5\right) - \frac{Ec}{KbT}} + t_0\\ \mathbf{if}\;mu \leq -2.75 \cdot 10^{+250}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT}} + t_0\\ \mathbf{elif}\;mu \leq -2.5 \cdot 10^{+182}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq -1.42 \cdot 10^{+147}:\\ \;\;\;\;\left(\left(0 - \left(-1 - \frac{NdChar \cdot KbT}{Vef}\right)\right) - 1\right) + t_0\\ \mathbf{elif}\;mu \leq -3.8 \cdot 10^{+104}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq -9.8 \cdot 10^{+92}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq -2.85 \cdot 10^{-18}:\\ \;\;\;\;t_1 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;mu \leq -3.3 \cdot 10^{-57}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq -2.05 \cdot 10^{-203}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq -1.95 \cdot 10^{-305}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 8.2 \cdot 10^{-244}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq 7.8 \cdot 10^{-122}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 2.4 \cdot 10^{+53}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq 1.3 \cdot 10^{+198}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_7\\ \end{array} \]

Alternative 13
Error	29.5
Cost	9632

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_2 := \frac{NdChar}{\left(\frac{mu}{KbT} + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right)\right) - \frac{Ec}{KbT}} + t_1\\ t_3 := t_0 + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{if}\;mu \leq -1.16 \cdot 10^{+250}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT}} + t_1\\ \mathbf{elif}\;mu \leq -6.3 \cdot 10^{+180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq -2.9 \cdot 10^{+149}:\\ \;\;\;\;\left(\left(0 - \left(-1 - \frac{NdChar \cdot KbT}{Vef}\right)\right) - 1\right) + t_1\\ \mathbf{elif}\;mu \leq -4 \cdot 10^{-304}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;mu \leq 1.02 \cdot 10^{-243}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 7.5 \cdot 10^{-122}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ \mathbf{elif}\;mu \leq 6.5 \cdot 10^{+51}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 1.22 \cdot 10^{+200}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 14
Error	29.0
Cost	9632

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_2 := \frac{NdChar}{\left(\frac{mu}{KbT} + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right)\right) - \frac{Ec}{KbT}} + t_1\\ t_3 := t_0 + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{if}\;mu \leq -4.2 \cdot 10^{+252}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT}} + t_1\\ \mathbf{elif}\;mu \leq -5.5 \cdot 10^{+180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq -2.3 \cdot 10^{+147}:\\ \;\;\;\;\left(\left(0 - \left(-1 - \frac{NdChar \cdot KbT}{Vef}\right)\right) - 1\right) + t_1\\ \mathbf{elif}\;mu \leq -5.6 \cdot 10^{-305}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\left(\frac{Vef}{KbT} + \left(\left(\frac{Ev}{KbT} + \frac{EAccept}{KbT}\right) + 1\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 5.6 \cdot 10^{-245}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 7.8 \cdot 10^{-122}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ \mathbf{elif}\;mu \leq 2 \cdot 10^{+52}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 2.1 \cdot 10^{+201}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 15
Error	32.2
Cost	8988

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{2} + t_0\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ t_4 := \left(\left(0 - \left(-1 - \frac{NdChar \cdot KbT}{Vef}\right)\right) - 1\right) + t_0\\ \mathbf{if}\;Ec \leq -1.4 \cdot 10^{+206}:\\ \;\;\;\;\frac{NdChar}{-\frac{Ec}{KbT}} + t_0\\ \mathbf{elif}\;Ec \leq -6.2 \cdot 10^{+74}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -3.9 \cdot 10^{+40}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Ec \leq -1.02 \cdot 10^{-274}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq 1.3 \cdot 10^{-187}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 5.8 \cdot 10^{-45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq 9 \cdot 10^{+91}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \]

Alternative 16
Error	30.4
Cost	8788

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ t_2 := \frac{NdChar}{\frac{mu}{KbT}} + t_0\\ \mathbf{if}\;mu \leq -2.2 \cdot 10^{+251}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq -5.5 \cdot 10^{+180}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -2.3 \cdot 10^{+149}:\\ \;\;\;\;\left(\left(0 - \left(-1 - \frac{NdChar \cdot KbT}{Vef}\right)\right) - 1\right) + t_0\\ \mathbf{elif}\;mu \leq -5.3 \cdot 10^{-306}:\\ \;\;\;\;t_1 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;mu \leq 7.5 \cdot 10^{-245}:\\ \;\;\;\;\frac{NdChar}{\left(\frac{mu}{KbT} + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq 8.2 \cdot 10^{+226}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 17
Error	31.4
Cost	8668

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_2 := \frac{NdChar}{2} + t_1\\ \mathbf{if}\;Ec \leq -6.5 \cdot 10^{+205}:\\ \;\;\;\;\frac{NdChar}{-\frac{Ec}{KbT}} + t_1\\ \mathbf{elif}\;Ec \leq -5.5 \cdot 10^{+43}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ec \leq -3.9 \cdot 10^{+40}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT}} + t_1\\ \mathbf{elif}\;Ec \leq -3.1 \cdot 10^{-250}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 1.55 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ec \leq 3.1 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 3.1 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 18
Error	30.7
Cost	8268

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.32 \cdot 10^{-34}:\\ \;\;\;\;t_1 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq -3 \cdot 10^{-295}:\\ \;\;\;\;\frac{NdChar}{-\frac{Ec}{KbT}} + t_0\\ \mathbf{elif}\;KbT \leq 1.25 \cdot 10^{+100}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + \left(\frac{EAccept}{KbT} + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + t_0\\ \end{array} \]

Alternative 19
Error	37.3
Cost	8020

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ t_1 := \frac{NdChar}{2} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Ec \leq -5.9 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -2.65 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 2.6 \cdot 10^{-124}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 1.5 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 7 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 20
Error	37.8
Cost	8020

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ t_1 := \frac{NdChar}{2} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Ec \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -3.8 \cdot 10^{-250}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 6.2 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 3.8 \cdot 10^{+28}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 1.65 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 21
Error	32.3
Cost	8012

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -8.5 \cdot 10^{-33}:\\ \;\;\;\;t_1 + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -3.3 \cdot 10^{-295}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT}} + t_0\\ \mathbf{elif}\;KbT \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;t_1 + \frac{NaChar \cdot KbT}{Ev}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + t_0\\ \end{array} \]

Alternative 22
Error	31.9
Cost	8012

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.8 \cdot 10^{-31}:\\ \;\;\;\;t_1 + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -3.3 \cdot 10^{-295}:\\ \;\;\;\;\frac{NdChar}{-\frac{Ec}{KbT}} + t_0\\ \mathbf{elif}\;KbT \leq 3.45 \cdot 10^{+16}:\\ \;\;\;\;t_1 + \frac{NaChar \cdot KbT}{Ev}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + t_0\\ \end{array} \]

Alternative 23
Error	37.9
Cost	7820

\[\begin{array}{l} t_0 := \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ t_1 := \frac{NdChar}{2} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Ec \leq -1.7 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -3.9 \cdot 10^{-250}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ \mathbf{elif}\;Ec \leq 4.3 \cdot 10^{-175}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}} + t_0\\ \end{array} \]

Alternative 24
Error	27.8
Cost	7816

\[\begin{array}{l} t_0 := \frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{Vef + \left(\left(-mu\right) + \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.02 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 5.2 \cdot 10^{+20}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 25
Error	37.1
Cost	7756

\[\begin{array}{l} t_0 := \frac{NdChar}{2} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Ec \leq -2.55 \cdot 10^{+48}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq -6 \cdot 10^{-160}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Ec \leq 3 \cdot 10^{+161}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 26
Error	30.6
Cost	7752

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef - \left(Ec - \left(EDonor + mu\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -1.7 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 3 \cdot 10^{-198}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 27
Error	39.5
Cost	7564

\[\begin{array}{l} \mathbf{if}\;NaChar \leq -4.7 \cdot 10^{-17}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.4 \cdot 10^{-248}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 9.5 \cdot 10^{+128}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{-\frac{mu}{KbT}}}\\ \end{array} \]

Alternative 28
Error	39.3
Cost	7500

\[\begin{array}{l} t_0 := \frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;NaChar \leq -3.3 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-247}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{-30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 29
Error	40.4
Cost	7432

\[\begin{array}{l} \mathbf{if}\;EAccept \leq -1 \cdot 10^{-196}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.85 \cdot 10^{+169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{-\frac{Ec}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 30
Error	40.6
Cost	7368

\[\begin{array}{l} \mathbf{if}\;EAccept \leq -1.16 \cdot 10^{-136}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.8 \cdot 10^{+169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 31
Error	40.8
Cost	7236

\[\begin{array}{l} \mathbf{if}\;Ev \leq -1.62 \cdot 10^{+220}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 32
Error	41.4
Cost	7104

\[\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

Alternative 33
Error	46.8
Cost	1992

\[\begin{array}{l} \mathbf{if}\;Ec \leq 2.25 \cdot 10^{-150}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{2}\\ \mathbf{elif}\;Ec \leq 1.6 \cdot 10^{+268}:\\ \;\;\;\;\frac{NdChar}{\left(\frac{mu}{KbT} + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right)\right) - \frac{Ec}{KbT}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(2 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \]

Alternative 34
Error	46.4
Cost	448

\[\frac{NdChar}{2} + \frac{NaChar}{2} \]

Reproduce

herbie shell --seed 2023077 
(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))))))