?

Average Error: 0.0 → 0.0
Time: 35.2s
Precision: binary64
Cost: 27328

?

\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
↓
\[\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \mathsf{expm1}\left(\mathsf{log1p}\left(e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}\right)\right)} \]
(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 (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
  (/
   NaChar
   (+ 1.0 (expm1 (log1p (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((-(((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(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + expm1(log1p(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((-(((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(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.expm1(Math.log1p(Math.exp(((Ev + (Vef + (EAccept - mu))) / KbT))))));
}

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(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.expm1(math.log1p(math.exp(((Ev + (Vef + (EAccept - mu))) / KbT))))))

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(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + expm1(log1p(exp(Float64(Float64(Ev + Float64(Vef + Float64(EAccept - mu))) / KbT)))))))
end

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[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(Exp[N[Log[1 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\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{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \mathsf{expm1}\left(\mathsf{log1p}\left(e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}\right)\right)}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified0.0

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

    [Start]0.0

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

    neg-sub0 [=>]0.0

    \[ \frac{NdChar}{1 + e^{\frac{\color{blue}{0 - \left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

    associate--r- [=>]0.0

    \[ \frac{NdChar}{1 + e^{\frac{\color{blue}{\left(0 - \left(\left(Ec - Vef\right) - EDonor\right)\right) + mu}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

    +-commutative [=>]0.0

    \[ \frac{NdChar}{1 + e^{\frac{\color{blue}{mu + \left(0 - \left(\left(Ec - Vef\right) - EDonor\right)\right)}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

    sub0-neg [=>]0.0

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

    sub-neg [<=]0.0

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

    associate-+l+ [=>]0.0

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

    +-commutative [=>]0.0

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

    unsub-neg [=>]0.0

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

  3. Applied egg-rr0.0

    \[\leadsto \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}\right)\right)}} \]

  4. Final simplification0.0

    \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \mathsf{expm1}\left(\mathsf{log1p}\left(e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}\right)\right)} \]

Alternatives

Alternative 1
Error24.3
Cost15804
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ t_2 := t_0 + NaChar\\ t_3 := Vef + \left(Ev + EAccept\right)\\ t_4 := t_0 + \frac{KbT \cdot NaChar}{t_3 \cdot t_3 - mu \cdot mu} \cdot \left(Vef + \left(EAccept + \left(mu + Ev\right)\right)\right)\\ t_5 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_6 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{-\frac{mu}{KbT}}}\\ t_7 := t_5 + \frac{NdChar}{1 + \left(1 + \frac{Ec}{KbT} \cdot \left(-1 + \frac{Ec \cdot 0.5}{KbT}\right)\right)}\\ \mathbf{if}\;mu \leq -1.15 \cdot 10^{+223}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq -7.5 \cdot 10^{+145}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq -2.8 \cdot 10^{+111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq -2.5 \cdot 10^{+66}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq -1.62 \cdot 10^{-24}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq -5.5 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -1.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;mu \leq -2.9 \cdot 10^{-151}:\\ \;\;\;\;t_5 + \frac{NdChar}{1 + \left(\left(\frac{mu}{KbT} + \left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -1.46 \cdot 10^{-177}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq 3.3 \cdot 10^{-217}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 1.55 \cdot 10^{-120}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 1.05 \cdot 10^{-86}:\\ \;\;\;\;t_5 + \frac{NdChar}{1 + \left(1 + \frac{EDonor}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 8.7 \cdot 10^{-51}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq 450000:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq 2.3 \cdot 10^{+147}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]
Alternative 2
Error24.1
Cost15408
\[\begin{array}{l} t_0 := Vef + \left(Ev + EAccept\right)\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{KbT \cdot NaChar}{t_0 \cdot t_0 - mu \cdot mu} \cdot \left(Vef + \left(EAccept + \left(mu + Ev\right)\right)\right)\\ t_4 := t_2 + NaChar\\ t_5 := t_2 + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ t_6 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{-\frac{mu}{KbT}}}\\ t_7 := t_1 + \frac{NdChar}{1 + \left(1 + \frac{Ec}{KbT} \cdot \left(-1 + \frac{Ec \cdot 0.5}{KbT}\right)\right)}\\ \mathbf{if}\;mu \leq -1.15 \cdot 10^{+223}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;mu \leq -1.2 \cdot 10^{+138}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq -2.95 \cdot 10^{+111}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq -6.5 \cdot 10^{+66}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq -5 \cdot 10^{-151}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq -5.1 \cdot 10^{-180}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 9.9 \cdot 10^{-216}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq 4.8 \cdot 10^{-122}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq 9.5 \cdot 10^{-87}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \left(1 + \frac{EDonor}{KbT}\right)}\\ \mathbf{elif}\;mu \leq 1.05 \cdot 10^{-51}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 2300000:\\ \;\;\;\;t_7\\ \mathbf{elif}\;mu \leq 5 \cdot 10^{+147}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]
Alternative 3
Error18.1
Cost15201
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + NaChar\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;NaChar \leq -6.4 \cdot 10^{+56}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NaChar \leq -38:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -3 \cdot 10^{-39}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \left(1 + \frac{Ec}{KbT} \cdot \left(-1 + \frac{Ec \cdot 0.5}{KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq -7 \cdot 10^{-132}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-262}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 7 \cdot 10^{-55}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 2.35 \cdot 10^{+44} \lor \neg \left(NaChar \leq 1.6 \cdot 10^{+271}\right):\\ \;\;\;\;t_2 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 4
Error18.2
Cost15200
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + NaChar\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.7 \cdot 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NaChar \leq -86:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -1.6 \cdot 10^{-35}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \left(1 + \frac{Ec}{KbT} \cdot \left(-1 + \frac{Ec \cdot 0.5}{KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq -1.45 \cdot 10^{-130}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NaChar \leq -1.95 \cdot 10^{-265}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 8 \cdot 10^{-54}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 1.02 \cdot 10^{+74}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 6.8 \cdot 10^{+271}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
Alternative 5
Error15.4
Cost15000
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_2 := t_0 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{if}\;Ec \leq -5.2 \cdot 10^{+33}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ec \leq -1.7 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -1.35 \cdot 10^{-297}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;Ec \leq 5.5 \cdot 10^{-86}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ec \leq 4.6 \cdot 10^{-12}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 2.75 \cdot 10^{+54}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 6
Error18.5
Cost14936
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + NaChar\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1 \cdot 10^{+57}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NaChar \leq -48:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -5 \cdot 10^{-42}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \left(1 + \frac{Ec}{KbT} \cdot \left(-1 + \frac{Ec \cdot 0.5}{KbT}\right)\right)}\\ \mathbf{elif}\;NaChar \leq -1.7 \cdot 10^{-130}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NaChar \leq -4 \cdot 10^{-260}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 6800000000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 7
Error0.0
Cost14528
\[\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} \]
Alternative 8
Error21.5
Cost9176
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + \frac{EAccept}{KbT}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Ec}{KbT} \cdot \left(-1 + \frac{Ec \cdot 0.5}{KbT}\right)\right)}\\ \mathbf{if}\;NaChar \leq -3 \cdot 10^{+68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq -1300000000000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -3.1 \cdot 10^{-46}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq -1.35 \cdot 10^{-88}:\\ \;\;\;\;t_0 + \frac{KbT}{\frac{Vef + \left(EAccept - mu\right)}{NaChar}}\\ \mathbf{elif}\;NaChar \leq -2 \cdot 10^{-265}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 5.8 \cdot 10^{+104}:\\ \;\;\;\;t_0 + NaChar\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 9
Error21.4
Cost9168
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{Ec}{KbT} \cdot \left(-1 + \frac{Ec \cdot 0.5}{KbT}\right)\right)}\\ \mathbf{if}\;NaChar \leq -2.9 \cdot 10^{+69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -80000000000000:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \frac{EAccept}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2.1 \cdot 10^{-46}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -4.2 \cdot 10^{-261}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 5.6 \cdot 10^{+104}:\\ \;\;\;\;t_0 + NaChar\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 10
Error20.5
Cost8401
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + NaChar\\ \mathbf{if}\;NdChar \leq -3.8 \cdot 10^{+165}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -1.2 \cdot 10^{+129}:\\ \;\;\;\;t_0 + \frac{KbT}{\frac{Vef + \left(EAccept - mu\right)}{NaChar}}\\ \mathbf{elif}\;NdChar \leq -1.7 \cdot 10^{-145} \lor \neg \left(NdChar \leq 1.3 \cdot 10^{-49}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{EDonor}{KbT}\right)}\\ \end{array} \]
Alternative 11
Error21.5
Cost7752
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;KbT \leq -7.7 \cdot 10^{+135}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 9.5 \cdot 10^{+167}:\\ \;\;\;\;t_0 + NaChar\\ \mathbf{else}:\\ \;\;\;\;t_0 + NaChar \cdot 0.5\\ \end{array} \]
Alternative 12
Error22.7
Cost7624
\[\begin{array}{l} \mathbf{if}\;KbT \leq -9.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{NaChar}{1 + e^{-\frac{mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 6.3 \cdot 10^{+209}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
Alternative 13
Error21.8
Cost7624
\[\begin{array}{l} \mathbf{if}\;KbT \leq -7.7 \cdot 10^{+135}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 3 \cdot 10^{+209}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
Alternative 14
Error31.8
Cost7369
\[\begin{array}{l} \mathbf{if}\;KbT \leq -8.6 \cdot 10^{+102} \lor \neg \left(KbT \leq 1.45 \cdot 10^{+171}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NaChar + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \]
Alternative 15
Error32.0
Cost7304
\[\begin{array}{l} \mathbf{if}\;KbT \leq -8.5 \cdot 10^{+135}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{EDonor}{KbT} \cdot \left(-1 + \frac{EDonor \cdot -0.5}{KbT}\right)} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 1.05 \cdot 10^{+210}:\\ \;\;\;\;NaChar + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)} + NdChar \cdot 0.5\\ \end{array} \]
Alternative 16
Error31.7
Cost7304
\[\begin{array}{l} \mathbf{if}\;KbT \leq -6.2 \cdot 10^{+135}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.8 \cdot 10^{+209}:\\ \;\;\;\;NaChar + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)} + NdChar \cdot 0.5\\ \end{array} \]
Alternative 17
Error39.0
Cost1864
\[\begin{array}{l} \mathbf{if}\;KbT \leq -3.8 \cdot 10^{+103}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{EDonor}{KbT} \cdot \left(-1 + \frac{EDonor \cdot -0.5}{KbT}\right)} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 1.45 \cdot 10^{+168}:\\ \;\;\;\;NaChar + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(1 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)} + NdChar \cdot 0.5\\ \end{array} \]
Alternative 18
Error39.0
Cost1348
\[\begin{array}{l} \mathbf{if}\;KbT \leq -7.6 \cdot 10^{+103}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{EDonor}{KbT} \cdot \left(-1 + \frac{EDonor \cdot -0.5}{KbT}\right)} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 1.3 \cdot 10^{+168}:\\ \;\;\;\;NaChar + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \]
Alternative 19
Error38.9
Cost1097
\[\begin{array}{l} \mathbf{if}\;KbT \leq -2.35 \cdot 10^{+132} \lor \neg \left(KbT \leq 2.2 \cdot 10^{+168}\right):\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;NaChar + NdChar \cdot 0.5\\ \end{array} \]
Alternative 20
Error39.0
Cost1096
\[\begin{array}{l} \mathbf{if}\;KbT \leq -2.8 \cdot 10^{+104}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 1.6 \cdot 10^{+168}:\\ \;\;\;\;NaChar + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \end{array} \]
Alternative 21
Error38.9
Cost713
\[\begin{array}{l} \mathbf{if}\;KbT \leq -9.2 \cdot 10^{+135} \lor \neg \left(KbT \leq 2 \cdot 10^{+168}\right):\\ \;\;\;\;NdChar \cdot 0.5 + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NaChar + NdChar \cdot 0.5\\ \end{array} \]
Alternative 22
Error41.0
Cost320
\[NaChar + NdChar \cdot 0.5 \]
Alternative 23
Error52.5
Cost192
\[NdChar \cdot 0.5 \]

Error

Reproduce?

herbie shell --seed 2023034 
(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))))))