?

Average Error: 0.05% → 0.05%
Time: 38.4s
Precision: binary64
Cost: 14656

?

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

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(((mu + (edonor + (vef - ec))) / kbt)))) + ((1.0d0 / (1.0d0 + exp(((vef + ((ev + eaccept) - mu)) / kbt)))) * nachar)
end function

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)))) + ((1.0 / (1.0 + Math.exp(((Vef + ((Ev + EAccept) - mu)) / KbT)))) * NaChar);
}

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)))) + ((1.0 / (1.0 + math.exp(((Vef + ((Ev + EAccept) - mu)) / KbT)))) * NaChar)

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(Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(Ev + EAccept) - mu)) / KbT)))) * NaChar))
end

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(((mu + (EDonor + (Vef - Ec))) / KbT)))) + ((1.0 / (1.0 + exp(((Vef + ((Ev + EAccept) - mu)) / KbT)))) * NaChar);
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[(N[(1.0 / N[(1.0 + N[Exp[N[(N[(Vef + N[(N[(Ev + EAccept), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * NaChar), $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{1}{1 + e^{\frac{Vef + \left(\left(Ev + EAccept\right) - mu\right)}{KbT}}} \cdot NaChar

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.05

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

  2. Simplified0.05

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

    [Start]0.05

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

    neg-sub0 [=>]0.05

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

    associate--r- [=>]0.05

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

    +-commutative [=>]0.05

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

    sub0-neg [=>]0.05

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

    sub-neg [<=]0.05

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

    associate-+l+ [=>]0.05

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

    +-commutative [=>]0.05

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

    unsub-neg [=>]0.05

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

  3. Applied egg-rr0.05

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

  4. Final simplification0.05

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

Alternatives

Alternative 1
Error27.15%
Cost14804
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_2 := t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;Ev \leq -6.5 \cdot 10^{+105}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.05 \cdot 10^{-89}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq -1.9 \cdot 10^{-298}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq 7.4 \cdot 10^{-169}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq 8 \cdot 10^{-143}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 2
Error28.75%
Cost14672
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := 1 + e^{\frac{Vef}{KbT}}\\ \mathbf{if}\;Ev \leq -5 \cdot 10^{+74}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -4.5 \cdot 10^{-58}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \frac{1}{1 + \frac{mu}{KbT}}}\\ \mathbf{elif}\;Ev \leq -3.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{NaChar}{t_1} + \frac{NdChar}{t_1}\\ \mathbf{elif}\;Ev \leq -8.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
Alternative 3
Error33.77%
Cost14540
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;Ev \leq -4.1 \cdot 10^{-58}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + \frac{1}{1 + \frac{mu}{KbT}}}\\ \mathbf{elif}\;Ev \leq -8.5 \cdot 10^{-89}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{t_0}\\ \mathbf{elif}\;Ev \leq -3.6 \cdot 10^{-100}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
Alternative 4
Error27.21%
Cost14540
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;Ev \leq -2.75 \cdot 10^{+83}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.18 \cdot 10^{-36}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.85 \cdot 10^{-89}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
Alternative 5
Error0.05%
Cost14528
\[\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} \]
Alternative 6
Error37.61%
Cost14412
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ \mathbf{if}\;Ev \leq -8.2 \cdot 10^{-59}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \frac{1}{1 + \frac{mu}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.15 \cdot 10^{-88}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{t_0}\\ \mathbf{elif}\;Ev \leq -5.5 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]
Alternative 7
Error31.07%
Cost14288
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \frac{1}{1 + \frac{mu}{KbT}}}\\ t_2 := \frac{NaChar}{t_0} + \frac{NdChar}{t_0}\\ \mathbf{if}\;Vef \leq -8 \cdot 10^{+174}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 8.8 \cdot 10^{+15}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 6.8 \cdot 10^{+55}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 5 \cdot 10^{+89}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 8
Error30.83%
Cost14025
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ \mathbf{if}\;Vef \leq -2.3 \cdot 10^{+176} \lor \neg \left(Vef \leq 7.8 \cdot 10^{+89}\right):\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \frac{1}{1 + \frac{mu}{KbT}}}\\ \end{array} \]
Alternative 9
Error38.14%
Cost8529
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -7.5 \cdot 10^{+175}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq -2.95 \cdot 10^{+138}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{\left(\frac{mu}{KbT} + \left(2 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq -7 \cdot 10^{+100} \lor \neg \left(NaChar \leq 2.4 \cdot 10^{+66}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \frac{1}{1 + \frac{mu}{KbT}}}\\ \end{array} \]
Alternative 10
Error61.61%
Cost8292
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ t_2 := \frac{NdChar}{t_0}\\ t_3 := t_2 + t_1\\ t_4 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;Vef \leq -1.2 \cdot 10^{+173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -4.8 \cdot 10^{-34}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -2 \cdot 10^{-144}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -5.7 \cdot 10^{-201}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.95 \cdot 10^{-287}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + \frac{1}{e^{\frac{mu}{KbT}}}}\\ \mathbf{elif}\;Vef \leq 1.05 \cdot 10^{-107}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 700000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 5.4 \cdot 10^{+95}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 4.6 \cdot 10^{+247}:\\ \;\;\;\;t_2 + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 11
Error61.16%
Cost8292
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ t_2 := \frac{NdChar}{t_0}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;Vef \leq -8.5 \cdot 10^{+172}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;Vef \leq -1.8 \cdot 10^{-28}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -4 \cdot 10^{-108}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_1\\ \mathbf{elif}\;Vef \leq -2.5 \cdot 10^{-117}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -8.6 \cdot 10^{-205}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.2 \cdot 10^{+16}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 7.4 \cdot 10^{+115}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 1.55 \cdot 10^{+156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 4.1 \cdot 10^{+248}:\\ \;\;\;\;t_2 + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 12
Error34.33%
Cost8265
\[\begin{array}{l} \mathbf{if}\;NdChar \leq -2.6 \cdot 10^{-215} \lor \neg \left(NdChar \leq 6.5 \cdot 10^{-113}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \frac{1}{1 + \frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + e^{\frac{Vef + \left(\left(Ev + EAccept\right) - mu\right)}{KbT}}} \cdot NaChar + NdChar \cdot 0.5\\ \end{array} \]
Alternative 13
Error62.03%
Cost8160
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ t_3 := \frac{NdChar}{t_0} + NaChar \cdot 0.5\\ \mathbf{if}\;Vef \leq -1.95 \cdot 10^{+173}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -8.5 \cdot 10^{-115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -1.65 \cdot 10^{-287}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 5 \cdot 10^{-111}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 9 \cdot 10^{+20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 1.4 \cdot 10^{+114}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 1.66 \cdot 10^{+156}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 2.3 \cdot 10^{+248}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 14
Error62.09%
Cost8160
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ t_2 := \frac{NdChar}{t_0} + NaChar \cdot 0.5\\ \mathbf{if}\;Vef \leq -7.5 \cdot 10^{+172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -1 \cdot 10^{-115}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -1.5 \cdot 10^{-287}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + \frac{1}{e^{\frac{mu}{KbT}}}}\\ \mathbf{elif}\;Vef \leq 1.8 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 310:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 1.65 \cdot 10^{+114}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 2 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 5.6 \cdot 10^{+247}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 15
Error61.76%
Cost8028
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ t_2 := \frac{NdChar}{t_0} + NaChar \cdot 0.5\\ \mathbf{if}\;Vef \leq -1.1 \cdot 10^{+173}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -2.65 \cdot 10^{-29}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -8.6 \cdot 10^{-205}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1700000000:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 7 \cdot 10^{+115}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 1.52 \cdot 10^{+156}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 1.4 \cdot 10^{+248}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 16
Error60.95%
Cost8028
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ t_2 := \frac{NdChar}{t_0}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;Vef \leq -9.8 \cdot 10^{+172}:\\ \;\;\;\;t_2 + t_1\\ \mathbf{elif}\;Vef \leq -4.3 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -8.6 \cdot 10^{-205}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.8 \cdot 10^{+15}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 6 \cdot 10^{+115}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 1.65 \cdot 10^{+156}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 2.6 \cdot 10^{+248}:\\ \;\;\;\;t_2 + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 17
Error40.87%
Cost8008
\[\begin{array}{l} \mathbf{if}\;NaChar \leq -1.6 \cdot 10^{-55}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 10^{-95}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + e^{\frac{Vef + \left(\left(Ev + EAccept\right) - mu\right)}{KbT}}} \cdot NaChar + NdChar \cdot 0.5\\ \end{array} \]
Alternative 18
Error43.9%
Cost7880
\[\begin{array}{l} \mathbf{if}\;NaChar \leq -2.1 \cdot 10^{-56}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{-106}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + e^{\frac{Vef + \left(\left(Ev + EAccept\right) - mu\right)}{KbT}}} \cdot NaChar + NdChar \cdot 0.5\\ \end{array} \]
Alternative 19
Error49.67%
Cost7753
\[\begin{array}{l} \mathbf{if}\;NaChar \leq -1.4 \cdot 10^{-139} \lor \neg \left(NaChar \leq 1.7 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \]
Alternative 20
Error43.91%
Cost7753
\[\begin{array}{l} \mathbf{if}\;NaChar \leq -1.36 \cdot 10^{-56} \lor \neg \left(NaChar \leq 2.4 \cdot 10^{-107}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
Alternative 21
Error62.18%
Cost7632
\[\begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{t_0} + NaChar \cdot 0.5\\ \mathbf{if}\;Vef \leq -1.15 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -7.6 \cdot 10^{-168}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 1.65 \cdot 10^{+89}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 2.7 \cdot 10^{+247}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 22
Error63.51%
Cost7500
\[\begin{array}{l} \mathbf{if}\;EAccept \leq 1.9 \cdot 10^{-187}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;EAccept \leq 9.8 \cdot 10^{+145}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;EAccept \leq 3.6 \cdot 10^{+183}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
Alternative 23
Error64.69%
Cost7236
\[\begin{array}{l} \mathbf{if}\;KbT \leq -9.2 \cdot 10^{-296}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
Alternative 24
Error64.41%
Cost7104
\[\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5 \]
Alternative 25
Error72.19%
Cost448
\[NdChar \cdot 0.5 + \frac{NaChar}{2} \]

Error

Reproduce?

herbie shell --seed 2023121 
(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))))))