?

Average Error: 100.0% → 100.0%
Time: 1.1min
Precision: binary64
Cost: 14528.00

?

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

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)))) + (nachar / (1.0d0 + exp((((vef + ev) + (eaccept - mu)) / kbt))))
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)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) + (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.exp((((Vef + Ev) + (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 + exp(Float64(Float64(Float64(Vef + Ev) + Float64(EAccept - mu)) / KbT)))))
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)))) + (NaChar / (1.0 + exp((((Vef + Ev) + (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[(N[(N[(Vef + Ev), $MachinePrecision] + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $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 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 100.0

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

  2. Simplified100.0

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

    [Start]100.0

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

    neg-sub0 [=>]100.0

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

    associate--r- [=>]100.0

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

    +-commutative [=>]100.0

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

    sub0-neg [=>]100.0

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

    sub-neg [<=]100.0

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

    associate-+l+ [=>]100.0

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

    +-commutative [=>]100.0

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

    unsub-neg [=>]100.0

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

  3. Final simplification100.0

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

Alternatives

Alternative 1
Error56.4%
Cost15736.00
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{\frac{mu}{KbT}}{KbT}\right)\right)\right)}\\ t_2 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_3 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_4 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_5 := t_3 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{if}\;Ec \leq -7.5 \cdot 10^{+231}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Ec \leq -1.65 \cdot 10^{+150}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Ec \leq -5.9 \cdot 10^{+44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Ec \leq -4.3 \cdot 10^{-15}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{elif}\;Ec \leq -3.2 \cdot 10^{-105}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Ec \leq -9.2 \cdot 10^{-271}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;Ec \leq -9 \cdot 10^{-306}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\frac{EAccept}{KbT} + 2\right) + 0.5 \cdot \frac{EAccept \cdot EAccept}{KbT \cdot KbT}}\\ \mathbf{elif}\;Ec \leq 7.4 \cdot 10^{-211}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_2\\ \mathbf{elif}\;Ec \leq 5.6 \cdot 10^{-180}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Ec \leq 6.8 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 2.2 \cdot 10^{-88}:\\ \;\;\;\;t_3 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ec \leq 7.2 \cdot 10^{-36}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + t_2\\ \mathbf{elif}\;Ec \leq 1.65 \cdot 10^{+34}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Ec \leq 3.25 \cdot 10^{+153}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]
Alternative 2
Error56.6%
Cost15345.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ t_3 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_4 := t_1 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{\frac{mu}{KbT}}{KbT}\right)\right)\right)}\\ \mathbf{if}\;Vef \leq -1.35 \cdot 10^{+288}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -1.46 \cdot 10^{+54}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -3.3 \cdot 10^{-17}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -2.3 \cdot 10^{-139}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -4.5 \cdot 10^{-186}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -1.9 \cdot 10^{-286}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 2.65 \cdot 10^{-285}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + t_0\\ \mathbf{elif}\;Vef \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 1.45 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 4.4 \cdot 10^{+198} \lor \neg \left(Vef \leq 5.8 \cdot 10^{+219}\right):\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ \end{array} \]
Alternative 3
Error56.7%
Cost15345.00
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_3 := t_0 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{\frac{mu}{KbT}}{KbT}\right)\right)\right)}\\ \mathbf{if}\;Vef \leq -3.6 \cdot 10^{+288}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -1.95 \cdot 10^{+59}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -6.2 \cdot 10^{-17}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -2.3 \cdot 10^{-60}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -3.4 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -2.5 \cdot 10^{-185}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -8.5 \cdot 10^{-267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.7 \cdot 10^{-177}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.05 \cdot 10^{-172}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Vef \leq 1.04 \cdot 10^{-44}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 3.3 \cdot 10^{+202} \lor \neg \left(Vef \leq 3 \cdot 10^{+219}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
Alternative 4
Error64.0%
Cost15336.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ t_2 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_4 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{if}\;mu \leq -1.45 \cdot 10^{+165}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq -5.6 \cdot 10^{+119}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq -1.06 \cdot 10^{+66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -5 \cdot 10^{+15}:\\ \;\;\;\;t_2 + t_0\\ \mathbf{elif}\;mu \leq -1.45 \cdot 10^{-186}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 1.86 \cdot 10^{-286}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq 1.5 \cdot 10^{-237}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 5.3 \cdot 10^{-136}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 1.3 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ \mathbf{elif}\;mu \leq 2.6 \cdot 10^{+107}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq 3.5 \cdot 10^{+183}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 5
Error73.2%
Cost15332.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_4 := t_2 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_5 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{if}\;mu \leq -1.02 \cdot 10^{+58}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq -7.2 \cdot 10^{-119}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -1.45 \cdot 10^{-185}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{elif}\;mu \leq -2.7 \cdot 10^{-227}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq 3.4 \cdot 10^{-133}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 1.02 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 195000000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq 6.4 \cdot 10^{+106}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq 3.1 \cdot 10^{+181}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 6
Error75.6%
Cost15332.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_2 := t_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_3 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_4 := t_3 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_5 := t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;Vef \leq -8.8 \cdot 10^{+230}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -0.105:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -4.9 \cdot 10^{-17}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq -8.4 \cdot 10^{-66}:\\ \;\;\;\;t_3 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{elif}\;Vef \leq -5.6 \cdot 10^{-163}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq 1.9 \cdot 10^{-172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 3.8 \cdot 10^{-44}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 3.4 \cdot 10^{+92}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 7.7 \cdot 10^{+126}:\\ \;\;\;\;t_3 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 7
Error56.5%
Cost15212.00
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{\frac{mu}{KbT}}{KbT}\right)\right)\right)}\\ \mathbf{if}\;Ec \leq -7.9 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -3.4 \cdot 10^{-15}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{elif}\;Ec \leq -4.3 \cdot 10^{-106}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -7.2 \cdot 10^{-271}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;Ec \leq -3.8 \cdot 10^{-302}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\frac{EAccept}{KbT} + 2\right) + 0.5 \cdot \frac{EAccept \cdot EAccept}{KbT \cdot KbT}}\\ \mathbf{elif}\;Ec \leq 1.1 \cdot 10^{-279}:\\ \;\;\;\;t_2 + NdChar \cdot 0.5\\ \mathbf{elif}\;Ec \leq 4.4 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 9.5 \cdot 10^{-188}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 1.75 \cdot 10^{-116}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq 2.9 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 0.04:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 4.2 \cdot 10^{+156}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error56.6%
Cost15212.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{\frac{mu}{KbT}}{KbT}\right)\right)\right)}\\ \mathbf{if}\;Ec \leq -5.7 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -5.7 \cdot 10^{-15}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{elif}\;Ec \leq -1.65 \cdot 10^{-105}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -8.5 \cdot 10^{-272}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;Ec \leq -1.65 \cdot 10^{-305}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\frac{EAccept}{KbT} + 2\right) + 0.5 \cdot \frac{EAccept \cdot EAccept}{KbT \cdot KbT}}\\ \mathbf{elif}\;Ec \leq 6.4 \cdot 10^{-280}:\\ \;\;\;\;t_2 + NdChar \cdot 0.5\\ \mathbf{elif}\;Ec \leq 7.5 \cdot 10^{-260}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t_0\\ \mathbf{elif}\;Ec \leq 6 \cdot 10^{-182}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 3.6 \cdot 10^{-118}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq 3.2 \cdot 10^{-88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 0.044:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + t_0\\ \mathbf{elif}\;Ec \leq 8 \cdot 10^{+155}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 9
Error67.8%
Cost15072.00
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_1\\ t_3 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_4 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{if}\;mu \leq -6.5 \cdot 10^{+170}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;mu \leq -4.8 \cdot 10^{+119}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq -1.25 \cdot 10^{+67}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{elif}\;mu \leq -2.7 \cdot 10^{+41}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq 2.3 \cdot 10^{-293}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 3 \cdot 10^{-182}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 7000000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 4 \cdot 10^{+90}:\\ \;\;\;\;t_1 + t_0\\ \mathbf{elif}\;mu \leq 1.45 \cdot 10^{+198}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 10
Error70.7%
Cost15072.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_3 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_4 := t_3 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_5 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{if}\;mu \leq -8.5 \cdot 10^{+166}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;mu \leq -4.8 \cdot 10^{+122}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;mu \leq -8 \cdot 10^{+65}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{elif}\;mu \leq -5.4 \cdot 10^{+15}:\\ \;\;\;\;t_3 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;mu \leq 4.6 \cdot 10^{-132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 4.3 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ \mathbf{elif}\;mu \leq 290000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 3.5 \cdot 10^{+107}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.25 \cdot 10^{+183}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 11
Error74.3%
Cost15068.00
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;NdChar \leq -7.2 \cdot 10^{+209}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -2.4 \cdot 10^{-34}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.2 \cdot 10^{-45}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 3.6 \cdot 10^{-8}:\\ \;\;\;\;t_1 + t_2\\ \mathbf{elif}\;NdChar \leq 30000:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 7 \cdot 10^{+142}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 5.8 \cdot 10^{+162}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
Alternative 12
Error75.2%
Cost14936.00
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.1 \cdot 10^{+231}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -4.6 \cdot 10^{-163}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.8 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 1.3 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.2 \cdot 10^{+91}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 8.5 \cdot 10^{+127}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 13
Error76.2%
Cost14936.00
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;Vef \leq -8 \cdot 10^{+62}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -9 \cdot 10^{-163}:\\ \;\;\;\;t_2 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.75 \cdot 10^{-172}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 5.1 \cdot 10^{-45}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 9.2 \cdot 10^{+89}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 3.1 \cdot 10^{+131}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 14
Error64.4%
Cost14880.00
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ t_1 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{if}\;mu \leq -7.2 \cdot 10^{+161}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -7.1 \cdot 10^{+121}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq -3.1 \cdot 10^{+66}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq -3.5 \cdot 10^{-50}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq -1.75 \cdot 10^{-186}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq 2.9 \cdot 10^{-281}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq 5.5 \cdot 10^{-141}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 4.2 \cdot 10^{+191}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 15
Error62.8%
Cost9832.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{if}\;KbT \leq -1.85 \cdot 10^{+185}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq -2.2 \cdot 10^{+147}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -7.5 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq -1.85 \cdot 10^{-156}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -5 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq -2.05 \cdot 10^{-252}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 2.3 \cdot 10^{-306}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq 4.9 \cdot 10^{-80}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 700000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq 1.4 \cdot 10^{+143}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{\frac{mu}{KbT}}{KbT}\right)\right)\right)}\\ \end{array} \]
Alternative 16
Error62.8%
Cost9832.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{if}\;KbT \leq -6.5 \cdot 10^{+185}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;KbT \leq -4 \cdot 10^{+148}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -1 \cdot 10^{+54}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \frac{mu \cdot mu}{KbT \cdot KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -1.6 \cdot 10^{-156}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -9 \cdot 10^{-211}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq -3.6 \cdot 10^{-253}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 6 \cdot 10^{-305}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq 1.7 \cdot 10^{-72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 550000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq 3.9 \cdot 10^{+143}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{\frac{mu}{KbT}}{KbT}\right)\right)\right)}\\ \end{array} \]
Alternative 17
Error60.9%
Cost9700.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ t_3 := t_1 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \left(1 + 0.5 \cdot \left(mu \cdot \frac{mu}{KbT \cdot KbT}\right)\right)\right)}\\ \mathbf{if}\;KbT \leq -4.3 \cdot 10^{+185}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq -1.5 \cdot 10^{+145}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -3.4 \cdot 10^{+80}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;KbT \leq -6.5 \cdot 10^{-156}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -9.2 \cdot 10^{-211}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;KbT \leq -1.72 \cdot 10^{-252}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 3.6 \cdot 10^{-304}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;KbT \leq 1.2 \cdot 10^{-75}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 1820000:\\ \;\;\;\;t_3\\ \mathbf{elif}\;KbT \leq 2.2 \cdot 10^{+142} \lor \neg \left(KbT \leq 1.35 \cdot 10^{+257}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 18
Error65.5%
Cost8402.00
\[\begin{array}{l} \mathbf{if}\;NdChar \leq -5 \cdot 10^{-57} \lor \neg \left(NdChar \leq 6.4 \cdot 10^{-254}\right) \land \left(NdChar \leq 6.3 \cdot 10^{-223} \lor \neg \left(NdChar \leq 2.9 \cdot 10^{-131}\right)\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \end{array} \]
Alternative 19
Error63.6%
Cost8018.00
\[\begin{array}{l} \mathbf{if}\;NdChar \leq -4.2 \cdot 10^{-68} \lor \neg \left(NdChar \leq 3.1 \cdot 10^{-254} \lor \neg \left(NdChar \leq 5.2 \cdot 10^{-216}\right) \land NdChar \leq 2.6 \cdot 10^{-131}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
Alternative 20
Error38.1%
Cost7828.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;Ec \leq -1.5 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -8 \cdot 10^{-64}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Ec \leq -5 \cdot 10^{-103}:\\ \;\;\;\;t_0 + \frac{KbT \cdot NaChar}{Ev}\\ \mathbf{elif}\;Ec \leq -3.6 \cdot 10^{-155}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Ec \leq 1.22 \cdot 10^{+64}:\\ \;\;\;\;t_0 + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 21
Error34.6%
Cost7632.00
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ t_1 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{if}\;KbT \leq -1.55 \cdot 10^{+32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq -2.05 \cdot 10^{-216}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 2.45 \cdot 10^{-262}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq 1.1 \cdot 10^{-178}:\\ \;\;\;\;\frac{NdChar}{\left(2 - \frac{Ec}{KbT}\right) + \frac{0.5}{KbT} \cdot \frac{Ec \cdot Ec}{KbT}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 22
Error34.7%
Cost7500.00
\[\begin{array}{l} \mathbf{if}\;KbT \leq -5.8 \cdot 10^{+42}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.85 \cdot 10^{-261}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 7.5 \cdot 10^{-178}:\\ \;\;\;\;\frac{NdChar}{\left(2 - \frac{Ec}{KbT}\right) + \frac{0.5}{KbT} \cdot \frac{Ec \cdot Ec}{KbT}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
Alternative 23
Error59.2%
Cost7497.00
\[\begin{array}{l} \mathbf{if}\;NdChar \leq -2.6 \cdot 10^{-131} \lor \neg \left(NdChar \leq -2.7 \cdot 10^{-276}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
Alternative 24
Error30.9%
Cost7236.00
\[\begin{array}{l} \mathbf{if}\;KbT \leq 2.1 \cdot 10^{-282}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{\left(2 - \frac{Ec}{KbT}\right) + \frac{0.5}{KbT} \cdot \frac{Ec \cdot Ec}{KbT}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
Alternative 25
Error27.1%
Cost1732.00
\[\begin{array}{l} \mathbf{if}\;KbT \leq 2.2 \cdot 10^{-285}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} + \frac{NdChar}{2 + \left(0.5 \cdot \left(\frac{Ec}{KbT} \cdot \frac{Ec}{KbT}\right) - \frac{Ec}{KbT}\right)}\\ \end{array} \]
Alternative 26
Error26.5%
Cost1600.00
\[\frac{NdChar}{\left(2 - \frac{Ec}{KbT}\right) + \frac{0.5}{KbT} \cdot \frac{Ec \cdot Ec}{KbT}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2} \]
Alternative 27
Error27.3%
Cost1225.00
\[\begin{array}{l} \mathbf{if}\;Ec \leq -6.8 \cdot 10^{+124} \lor \neg \left(Ec \leq 0.042\right):\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 28
Error27.6%
Cost968.00
\[\begin{array}{l} \mathbf{if}\;KbT \leq -1.8 \cdot 10^{-214}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 3.6 \cdot 10^{-133}:\\ \;\;\;\;-\frac{KbT}{mu} \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{EAccept}{KbT} + 2} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 29
Error28.0%
Cost713.00
\[\begin{array}{l} \mathbf{if}\;KbT \leq -8.8 \cdot 10^{-215} \lor \neg \left(KbT \leq 1.5 \cdot 10^{-202}\right):\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;-\frac{KbT}{mu} \cdot NaChar\\ \end{array} \]
Alternative 30
Error6.4%
Cost384.00
\[-\frac{KbT}{mu} \cdot NaChar \]
Alternative 31
Error6.1%
Cost384.00
\[\left(-KbT\right) \cdot \frac{NaChar}{mu} \]

Error

Reproduce?

herbie shell --seed 2023093 
(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))))))