Bulmash initializePoisson

Average Error: 0.0 → 0.0

Time: 51.4s

Precision: binary64

Cost: 27264

Math

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

↓

\[e^{-\mathsf{log1p}\left(e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}\right)} \cdot NdChar + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \]

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
 (+
  (* (exp (- (log1p (exp (/ (- mu (- Ec (+ Vef EDonor))) KbT))))) NdChar)
  (/ 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 (exp(-log1p(exp(((mu - (Ec - (Vef + EDonor))) / KbT)))) * NdChar) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
}

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 (Math.exp(-Math.log1p(Math.exp(((mu - (Ec - (Vef + EDonor))) / KbT)))) * NdChar) + (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 (math.exp(-math.log1p(math.exp(((mu - (Ec - (Vef + EDonor))) / KbT)))) * NdChar) + (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(exp(Float64(-log1p(exp(Float64(Float64(mu - Float64(Ec - Float64(Vef + EDonor))) / KbT))))) * NdChar) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(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[(N[Exp[(-N[Log[1 + N[Exp[N[(N[(mu - N[(Ec - N[(Vef + EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]], $MachinePrecision])], $MachinePrecision] * NdChar), $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]

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

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

3. Applied egg-rr 0.0

   \[\leadsto \color{blue}{e^{-\mathsf{log1p}\left(e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}\right)} \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \]

Alternatives

Alternative 1
Error	0.0
Cost	27200

\[\frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \]

Alternative 2
Error	17.2
Cost	15204

\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(mu + EDonor\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_1\\ t_4 := \frac{NdChar}{t_0} + \frac{NaChar}{t_0}\\ \mathbf{if}\;Vef \leq -2.1 \cdot 10^{+161}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -1350000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -5.8 \cdot 10^{-124}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -8.6 \cdot 10^{-249}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -1.35 \cdot 10^{-281}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_1\\ \mathbf{elif}\;Vef \leq 1.55 \cdot 10^{-287}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 6.8 \cdot 10^{-106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 6.4 \cdot 10^{-59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 7 \cdot 10^{+158}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 3
Error	16.9
Cost	14936

\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}\\ t_2 := t_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_3 := \frac{NdChar}{t_0} + \frac{NaChar}{t_0}\\ t_4 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;Vef \leq -2.15 \cdot 10^{+164}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -14500000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -1.6 \cdot 10^{-195}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 1.66 \cdot 10^{-105}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 6 \cdot 10^{-59}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 7.8 \cdot 10^{+213}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 4
Error	14.9
Cost	14936

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}\\ t_2 := t_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_3 := t_1 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -3 \cdot 10^{+162}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -34000000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -1 \cdot 10^{-194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq 3.45 \cdot 10^{-105}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 7.3 \cdot 10^{-59}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq 8.2 \cdot 10^{+113}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 5
Error	17.5
Cost	14808

\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(mu + EDonor\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ t_3 := \frac{NdChar}{t_0} + \frac{NaChar}{t_0}\\ \mathbf{if}\;Vef \leq -2.4 \cdot 10^{+163}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -4800000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -7 \cdot 10^{-195}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 6.5 \cdot 10^{-106}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 9 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 6
Error	3.3
Cost	14664

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -2.85 \cdot 10^{+200}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq 1.3 \cdot 10^{+135}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + EDonor\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 7
Error	17.3
Cost	14544

\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(mu + EDonor\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := \frac{NdChar}{t_0} + \frac{NaChar}{t_0}\\ \mathbf{if}\;Vef \leq -3.5 \cdot 10^{+161}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -0.00012:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -7 \cdot 10^{-173}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.05 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 8
Error	0.0
Cost	14528

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

Alternative 9
Error	26.2
Cost	14420

\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{t_0}\\ t_2 := 2 + \frac{-1}{KbT}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}\\ t_4 := \frac{NdChar}{t_0} + t_1\\ \mathbf{if}\;Vef \leq -9.5 \cdot 10^{+90}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -90000000000:\\ \;\;\;\;t_3 + \frac{NaChar}{1 + \left(1 + \frac{1}{KbT}\right)}\\ \mathbf{elif}\;Vef \leq -3.6:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_1\\ \mathbf{elif}\;Vef \leq -1.86 \cdot 10^{-221}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;NdChar \ne 0:\\ \;\;\;\;\frac{1}{\frac{t_2}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{t_2}\\ \end{array} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 6.8 \cdot 10^{+151}:\\ \;\;\;\;t_3 + \frac{NaChar}{1 + \left(1 - \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]

Alternative 10
Error	17.0
Cost	14280

\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{t_0} + \frac{NaChar}{t_0}\\ \mathbf{if}\;Vef \leq -5 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 6.4 \cdot 10^{+150}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + EDonor\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 11
Error	25.8
Cost	8136

\[\begin{array}{l} t_0 := 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -3.2 \cdot 10^{-20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 10^{-39}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Error	25.8
Cost	8136

\[\begin{array}{l} t_0 := 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -4.6 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 9.2 \cdot 10^{-38}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 - \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Error	25.0
Cost	8136

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + \left(1 + \frac{1}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -7.2 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 2.2 \cdot 10^{-40}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 - \frac{1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 14
Error	25.0
Cost	8136

\[\begin{array}{l} t_0 := 1 + \left(1 - \frac{1}{KbT}\right)\\ t_1 := \frac{NdChar}{t_0} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -7.2 \cdot 10^{-23}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 1.75 \cdot 10^{-38}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{t_0}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 15
Error	25.0
Cost	8136

\[\begin{array}{l} t_0 := 1 + \left(1 - \frac{1}{KbT}\right)\\ t_1 := 2 + \frac{-1}{KbT}\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -8.4 \cdot 10^{-20}:\\ \;\;\;\;\begin{array}{l} \mathbf{if}\;NdChar \ne 0:\\ \;\;\;\;\frac{1}{\frac{t_1}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{t_1}\\ \end{array} + t_2\\ \mathbf{elif}\;NaChar \leq 1.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{t_0} + t_2\\ \end{array} \]

Alternative 16
Error	26.7
Cost	8008

\[\begin{array}{l} t_0 := 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -850000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 4.5 \cdot 10^{-37}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + Ev\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 17
Error	27.5
Cost	7752

\[\begin{array}{l} t_0 := 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -5.1 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 9.2 \cdot 10^{-42}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + 0.5 \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 18
Error	34.0
Cost	7488

\[0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \]

Alternative 19
Error	39.0
Cost	7368

\[\begin{array}{l} t_0 := 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;Ev \leq -1.12 \cdot 10^{+52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ev \leq 2 \cdot 10^{+83}:\\ \;\;\;\;0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 20
Error	41.0
Cost	7104

\[0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

Alternative 21
Error	46.0
Cost	320

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

Alternative 22
Error	52.2
Cost	192

\[0.5 \cdot NdChar \]

Reproduce

herbie shell --seed 2023010 
(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))))))