Average Error: 0.0 → 0.0
Time: 1.2min
Precision: binary64
Cost: 14528
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
\[\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} \]
(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 (/ (+ Vef (+ EDonor (- mu Ec))) 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((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
}
double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp(((Vef + (EDonor + (mu - Ec))) / KbT)))) + (NaChar / (1.0 + exp(((Ev + (Vef + (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(((vef + (edonor + (mu - ec))) / kbt)))) + (nachar / (1.0d0 + exp(((ev + (vef + (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(((Vef + (EDonor + (mu - Ec))) / 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((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp(((Vef + (EDonor + (mu - Ec))) / KbT)))) + (NaChar / (1.0 + 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(Vef + Float64(EDonor + Float64(mu - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + 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(((Vef + (EDonor + (mu - Ec))) / KbT)))) + (NaChar / (1.0 + exp(((Ev + (Vef + (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[(Vef + N[(EDonor + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $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{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}

Error

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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

    \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}} \]
    Proof
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (+.f64 EDonor (-.f64 mu Ec))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Vef (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 EDonor mu) Ec))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= associate--l+_binary64 (-.f64 (+.f64 Vef (+.f64 EDonor mu)) Ec)) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (+.f64 Vef (+.f64 EDonor mu)) (neg.f64 Ec))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (+.f64 (+.f64 Vef (+.f64 EDonor mu)) (Rewrite=> neg-sub0_binary64 (-.f64 0 Ec))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= +-commutative_binary64 (+.f64 (-.f64 0 Ec) (+.f64 Vef (+.f64 EDonor mu)))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= associate--r-_binary64 (-.f64 0 (-.f64 Ec (+.f64 Vef (+.f64 EDonor mu))))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 0 (Rewrite<= associate--l-_binary64 (-.f64 (-.f64 Ec Vef) (+.f64 EDonor mu)))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (-.f64 0 (Rewrite<= associate--l-_binary64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= neg-sub0_binary64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu))) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (-.f64 EAccept mu))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (+.f64 Ev (+.f64 Vef (Rewrite<= unsub-neg_binary64 (+.f64 EAccept (neg.f64 mu))))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 Ev Vef) (+.f64 EAccept (neg.f64 mu)))) KbT))))): 0 points increase in error, 0 points decrease in error
    (+.f64 (/.f64 NdChar (+.f64 1 (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 1 (exp.f64 (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu))) KbT))))): 0 points increase in error, 0 points decrease in error
  3. Final simplification0.0

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

Alternatives

Alternative 1
Error27.9
Cost15476
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + t_1\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_4 := \frac{Ec - EDonor}{KbT}\\ t_5 := \frac{Vef}{KbT} - t_4\\ t_6 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_7 := t_6 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ t_8 := t_6 + \left(\left(1 + KbT \cdot \frac{NdChar}{Vef}\right) + -1\right)\\ t_9 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;Vef \leq -7.755345101638849 \cdot 10^{+245}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;Vef \leq -1.5009255580379943 \cdot 10^{+169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq -1.137105933765451 \cdot 10^{+114}:\\ \;\;\;\;t_8\\ \mathbf{elif}\;Vef \leq -1.8087442072487722 \cdot 10^{-21}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -6.614790082748894 \cdot 10^{-238}:\\ \;\;\;\;t_6 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{elif}\;Vef \leq 1.1894064205357374 \cdot 10^{-176}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 6.4484660848012094 \cdot 10^{-52}:\\ \;\;\;\;t_3 + t_0\\ \mathbf{elif}\;Vef \leq 1.1634769999902633 \cdot 10^{-18}:\\ \;\;\;\;t_9 + t_0\\ \mathbf{elif}\;Vef \leq 7.53373347921869 \cdot 10^{+30}:\\ \;\;\;\;t_7\\ \mathbf{elif}\;Vef \leq 3.157353046236711 \cdot 10^{+43}:\\ \;\;\;\;t_6 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \frac{1 - t_5 \cdot t_5}{1 + \left(t_4 - \frac{Vef}{KbT}\right)}\right)}\\ \mathbf{elif}\;Vef \leq 1.279817990324452 \cdot 10^{+84}:\\ \;\;\;\;t_3 + t_1\\ \mathbf{elif}\;Vef \leq 7.953140848054757 \cdot 10^{+143}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ \mathbf{elif}\;Vef \leq 2.4848525740653727 \cdot 10^{+149}:\\ \;\;\;\;t_1 + t_9\\ \mathbf{elif}\;Vef \leq 2.0610942571692812 \cdot 10^{+238}:\\ \;\;\;\;t_7\\ \mathbf{else}:\\ \;\;\;\;t_8\\ \end{array} \]
Alternative 2
Error19.3
Cost15332
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{if}\;NdChar \leq -6.752528596258286 \cdot 10^{+61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -1.881764636184228 \cdot 10^{-24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -5.738296699438971 \cdot 10^{-47}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq -5.196845786643373 \cdot 10^{-118}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -3.000114564418447 \cdot 10^{-157}:\\ \;\;\;\;t_2 + \left(\left(1 + KbT \cdot \frac{NdChar}{EDonor}\right) + -1\right)\\ \mathbf{elif}\;NdChar \leq 8.052160679149231 \cdot 10^{-200}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NdChar \leq 2.6326025269241977 \cdot 10^{-132}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 6.182108154255115 \cdot 10^{-107}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NdChar \leq 1.0339801087412951 \cdot 10^{+143}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 3
Error29.8
Cost15212
\[\begin{array}{l} t_0 := \frac{Ec - EDonor}{KbT}\\ t_1 := \frac{Vef}{KbT} - t_0\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_4 := t_3 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \frac{1 - t_1 \cdot t_1}{1 + \left(t_0 - \frac{Vef}{KbT}\right)}\right)}\\ t_5 := t_3 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ t_6 := t_3 + \left(\left(1 + KbT \cdot \frac{NdChar}{Vef}\right) + -1\right)\\ \mathbf{if}\;Vef \leq -7.755345101638849 \cdot 10^{+245}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;Vef \leq -2.366054299008867 \cdot 10^{+166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -2.4916209230801076 \cdot 10^{+101}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;Vef \leq -1.6037758642400488 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -6.614790082748894 \cdot 10^{-238}:\\ \;\;\;\;t_3 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{elif}\;Vef \leq 2.821267472995944 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 6.293105392686424 \cdot 10^{-99}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 5.24401273824079 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 7.53373347921869 \cdot 10^{+30}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq 3.157353046236711 \cdot 10^{+43}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 3.369791146614734 \cdot 10^{+80}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.0610942571692812 \cdot 10^{+238}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]
Alternative 4
Error29.5
Cost15212
\[\begin{array}{l} t_0 := \frac{Ec - EDonor}{KbT}\\ t_1 := \frac{Vef}{KbT} - t_0\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_4 := t_3 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ t_5 := t_3 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \frac{1 - t_1 \cdot t_1}{1 + \left(t_0 - \frac{Vef}{KbT}\right)}\right)}\\ t_6 := t_3 + \left(\left(1 + KbT \cdot \frac{NdChar}{Vef}\right) + -1\right)\\ \mathbf{if}\;Vef \leq -7.755345101638849 \cdot 10^{+245}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;Vef \leq -2.366054299008867 \cdot 10^{+166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -2.4916209230801076 \cdot 10^{+101}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;Vef \leq -1.6037758642400488 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -6.614790082748894 \cdot 10^{-238}:\\ \;\;\;\;t_3 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{elif}\;Vef \leq 2.821267472995944 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.8183316352773222 \cdot 10^{-94}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq 1.1634769999902633 \cdot 10^{-18}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 7.53373347921869 \cdot 10^{+30}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 3.157353046236711 \cdot 10^{+43}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq 3.369791146614734 \cdot 10^{+80}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.0610942571692812 \cdot 10^{+238}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]
Alternative 5
Error19.0
Cost15200
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;Ec \leq -1.788118437593309 \cdot 10^{+180}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq -1.824807110321803 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq -2.1247894868356202 \cdot 10^{+64}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq -50.904001211403596:\\ \;\;\;\;t_2 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{elif}\;Ec \leq -3.458129502324799 \cdot 10^{-86}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 1.2764037090003886 \cdot 10^{-290}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq 4.3078061864383816 \cdot 10^{-213}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ec \leq 1.5123258783780028 \cdot 10^{+35}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 6
Error18.0
Cost15200
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}}\\ t_4 := t_3 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;EAccept \leq -8.713759512668322 \cdot 10^{-269}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;EAccept \leq 3.333533855206734 \cdot 10^{-267}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 4.675010695918497 \cdot 10^{-208}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;EAccept \leq 8.782813512413263 \cdot 10^{-19}:\\ \;\;\;\;t_3 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 6.78829431339186 \cdot 10^{+155}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 2.0772356982949407 \cdot 10^{+166}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EAccept \leq 4.243989876785908 \cdot 10^{+179}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;EAccept \leq 9.718098480092225 \cdot 10^{+203}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 7
Error14.3
Cost15200
\[\begin{array}{l} t_0 := \frac{Ec - EDonor}{KbT}\\ t_1 := \frac{Vef}{KbT} - t_0\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_4 := t_2 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_5 := t_2 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.137105933765451 \cdot 10^{+114}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Vef \leq -1.055035442378501 \cdot 10^{-8}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -6.605987562700901 \cdot 10^{-111}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -4.655937196029758 \cdot 10^{-192}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -4.258762211585754 \cdot 10^{-207}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \frac{1 - t_1 \cdot t_1}{1 + \left(t_0 - \frac{Vef}{KbT}\right)}\right)}\\ \mathbf{elif}\;Vef \leq -2.830672671918967 \cdot 10^{-244}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq 4.377203521808053 \cdot 10^{-148}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 1.279817990324452 \cdot 10^{+84}:\\ \;\;\;\;t_4\\ \mathbf{else}:\\ \;\;\;\;t_5\\ \end{array} \]
Alternative 8
Error21.4
Cost15072
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ t_3 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;NdChar \leq -5.738296699438971 \cdot 10^{-47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -5.196845786643373 \cdot 10^{-118}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -1.182308656849495 \cdot 10^{-130}:\\ \;\;\;\;t_1 + \left(\left(1 + KbT \cdot \frac{NdChar}{EDonor}\right) + -1\right)\\ \mathbf{elif}\;NdChar \leq -4.903104360992393 \cdot 10^{-133}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NdChar \leq -3.000114564418447 \cdot 10^{-157}:\\ \;\;\;\;t_1 + \left(\left(1 + KbT \cdot \frac{NdChar}{Vef}\right) + -1\right)\\ \mathbf{elif}\;NdChar \leq 8.052160679149231 \cdot 10^{-200}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq 2.6326025269241977 \cdot 10^{-132}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NdChar \leq 6.182108154255115 \cdot 10^{-107}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 9
Error17.2
Cost14936
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;EAccept \leq -8.713759512668322 \cdot 10^{-269}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 3.333533855206734 \cdot 10^{-267}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EAccept \leq 4.675010695918497 \cdot 10^{-208}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 8.200349346496759 \cdot 10^{-149}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor - Ec\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.7070573429034397 \cdot 10^{-84}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 2.030908834223498 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
Alternative 10
Error28.3
Cost14816
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_1 := \frac{Ec - EDonor}{KbT}\\ t_2 := \frac{Vef}{KbT} - t_1\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_4 := t_3 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ t_5 := t_3 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \frac{1 - t_2 \cdot t_2}{1 + \left(t_1 - \frac{Vef}{KbT}\right)}\right)}\\ t_6 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ \mathbf{if}\;KbT \leq -1.4288473703042102 \cdot 10^{-34}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;KbT \leq -1.0751906404660036 \cdot 10^{-231}:\\ \;\;\;\;t_6\\ \mathbf{elif}\;KbT \leq -1.884250487191135 \cdot 10^{-274}:\\ \;\;\;\;t_3 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{elif}\;KbT \leq -1.3151942451149122 \cdot 10^{-303}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t_0\\ \mathbf{elif}\;KbT \leq 1.3293310986589823 \cdot 10^{-145}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;KbT \leq 2.0034949983089744 \cdot 10^{-67}:\\ \;\;\;\;t_3 + \frac{NdChar \cdot KbT}{\left(Vef + \left(EDonor + mu\right)\right) - Ec}\\ \mathbf{elif}\;KbT \leq 1.1579600390534722 \cdot 10^{-7}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;KbT \leq 7.643178086097125 \cdot 10^{+179}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_6\\ \end{array} \]
Alternative 11
Error17.3
Cost14412
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -2.822750606867609 \cdot 10^{+129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq -3.021130197927675 \cdot 10^{+22}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{elif}\;mu \leq 7.689605222232073 \cdot 10^{+130}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor - Ec\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 12
Error23.6
Cost14352
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -2.822750606867609 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -3.2973628691664313 \cdot 10^{-153}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{elif}\;mu \leq 1.618415096109228 \cdot 10^{-186}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.117688099195073 \cdot 10^{+38}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 13
Error23.9
Cost14352
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -2.822750606867609 \cdot 10^{+129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq -3.2973628691664313 \cdot 10^{-153}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{elif}\;mu \leq 1.618415096109228 \cdot 10^{-186}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 2.995561190733629 \cdot 10^{+51}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 14
Error29.7
Cost10844
\[\begin{array}{l} t_0 := \frac{Ec - EDonor}{KbT}\\ t_1 := \frac{Vef}{KbT} - t_0\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ t_3 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_4 := t_3 + \left(\left(1 + KbT \cdot \frac{NdChar}{Vef}\right) + -1\right)\\ \mathbf{if}\;Vef \leq -7.755345101638849 \cdot 10^{+245}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -2.366054299008867 \cdot 10^{+166}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -2.4916209230801076 \cdot 10^{+101}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Vef \leq -1.6037758642400488 \cdot 10^{+78}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -6.614790082748894 \cdot 10^{-238}:\\ \;\;\;\;t_3 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ \mathbf{elif}\;Vef \leq 2.821267472995944 \cdot 10^{-162}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 6.293105392686424 \cdot 10^{-99}:\\ \;\;\;\;t_3 + \frac{NdChar}{1 + \left(\frac{mu}{KbT} + \frac{1 - t_1 \cdot t_1}{1 + \left(t_0 - \frac{Vef}{KbT}\right)}\right)}\\ \mathbf{elif}\;Vef \leq 5.24401273824079 \cdot 10^{-22}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 2.0610942571692812 \cdot 10^{+238}:\\ \;\;\;\;t_3 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 15
Error29.4
Cost9308
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + \frac{mu - Ec}{KbT}\right)\right)}\\ t_3 := t_1 + \left(\left(1 + KbT \cdot \frac{NdChar}{Vef}\right) + -1\right)\\ \mathbf{if}\;Vef \leq -7.755345101638849 \cdot 10^{+245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -2.366054299008867 \cdot 10^{+166}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -2.4916209230801076 \cdot 10^{+101}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -1.6037758642400488 \cdot 10^{+78}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -6.614790082748894 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.767256031693766 \cdot 10^{-173}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq 6.293105392686424 \cdot 10^{-99}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 5.24401273824079 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq 2.0610942571692812 \cdot 10^{+238}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 16
Error31.2
Cost8664
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ t_3 := t_1 + \left(\left(1 + KbT \cdot \frac{NdChar}{Vef}\right) + -1\right)\\ \mathbf{if}\;Vef \leq -7.755345101638849 \cdot 10^{+245}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -2.366054299008867 \cdot 10^{+166}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -1.71594909915716 \cdot 10^{-10}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -6.614790082748894 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 5.24401273824079 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq 2.0610942571692812 \cdot 10^{+238}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 17
Error27.6
Cost8532
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;NdChar \leq -6.991897027065205 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -6.363883139493094 \cdot 10^{-101}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.4580840191180652 \cdot 10^{-117}:\\ \;\;\;\;t_0 + \left(\left(1 + KbT \cdot \frac{NdChar}{EDonor}\right) + -1\right)\\ \mathbf{elif}\;NdChar \leq 0.044516187741161076:\\ \;\;\;\;t_0 + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 1.0737389149661122 \cdot 10^{+70}:\\ \;\;\;\;t_0 + \left(\left(1 + KbT \cdot \frac{NdChar}{Vef}\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 18
Error26.2
Cost8532
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;NdChar \leq -6.991897027065205 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -6.363883139493094 \cdot 10^{-101}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.4580840191180652 \cdot 10^{-117}:\\ \;\;\;\;t_0 + \frac{NdChar \cdot KbT}{\left(Vef + \left(EDonor + mu\right)\right) - Ec}\\ \mathbf{elif}\;NdChar \leq 0.044516187741161076:\\ \;\;\;\;t_0 + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 1.0737389149661122 \cdot 10^{+70}:\\ \;\;\;\;t_0 + \left(\left(1 + KbT \cdot \frac{NdChar}{Vef}\right) + -1\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 19
Error31.7
Cost8404
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{if}\;Vef \leq -7.755345101638849 \cdot 10^{+245}:\\ \;\;\;\;t_1 + NdChar \cdot \frac{KbT}{Vef}\\ \mathbf{elif}\;Vef \leq -2.3932879978963968 \cdot 10^{+61}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -6.614790082748894 \cdot 10^{-238}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 5.24401273824079 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq 2.0610942571692812 \cdot 10^{+238}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{KbT}{\frac{Vef}{NdChar}}\\ \end{array} \]
Alternative 20
Error38.7
Cost8288
\[\begin{array}{l} t_0 := \frac{KbT}{\frac{Vef}{NdChar}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ \mathbf{if}\;Vef \leq -1.137105933765451 \cdot 10^{+114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -5.728619886978422 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.9032503254691528 \cdot 10^{-292}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Vef \leq 7.95215511609103 \cdot 10^{-255}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 5.2959990716838415 \cdot 10^{+67}:\\ \;\;\;\;t_1 + \frac{NdChar}{2}\\ \mathbf{elif}\;Vef \leq 5.104771715907839 \cdot 10^{+155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 1.2053413000013214 \cdot 10^{+186}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Vef \leq 1.0009609071494721 \cdot 10^{+248}:\\ \;\;\;\;t_1 + t_0\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 21
Error28.8
Cost8280
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{2}\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;NdChar \leq -2.3206080602779207 \cdot 10^{+26}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq -5.1117093940212265 \cdot 10^{-23}:\\ \;\;\;\;t_0 + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;NdChar \leq -5.030570206990777 \cdot 10^{-80}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq -1.5606109647721053 \cdot 10^{-236}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 1.4580840191180652 \cdot 10^{-117}:\\ \;\;\;\;t_0 + \frac{KbT}{\frac{EDonor}{NdChar}}\\ \mathbf{elif}\;NdChar \leq 0.035651524885616806:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 22
Error29.8
Cost8280
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;NdChar \leq -2.3206080602779207 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -5.1117093940212265 \cdot 10^{-23}:\\ \;\;\;\;t_0 + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;NdChar \leq -5.030570206990777 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -5.133934846034706 \cdot 10^{-152}:\\ \;\;\;\;t_0 + NdChar \cdot \frac{KbT}{Vef}\\ \mathbf{elif}\;NdChar \leq 1.4580840191180652 \cdot 10^{-117}:\\ \;\;\;\;t_0 + \frac{NdChar \cdot KbT}{EDonor}\\ \mathbf{elif}\;NdChar \leq 0.035651524885616806:\\ \;\;\;\;t_0 + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 23
Error28.3
Cost8276
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -3.376389485963997 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 3.875246734467789 \cdot 10^{-95}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 8.134041816675625 \cdot 10^{-59}:\\ \;\;\;\;t_0 + NdChar \cdot \frac{KbT}{Vef}\\ \mathbf{elif}\;NaChar \leq 2.5694201075740423 \cdot 10^{-44}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 356.05101700276475:\\ \;\;\;\;t_0 + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 24
Error28.3
Cost8276
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -3.376389485963997 \cdot 10^{-16}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 3.875246734467789 \cdot 10^{-95}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 8.134041816675625 \cdot 10^{-59}:\\ \;\;\;\;t_0 + \frac{KbT}{\frac{Vef}{NdChar}}\\ \mathbf{elif}\;NaChar \leq 2.5694201075740423 \cdot 10^{-44}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{elif}\;NaChar \leq 356.05101700276475:\\ \;\;\;\;t_0 + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 25
Error39.1
Cost8156
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_1 := \frac{KbT}{\frac{Vef}{NdChar}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{2}\\ t_3 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_1\\ \mathbf{if}\;Vef \leq -1.137105933765451 \cdot 10^{+114}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq -5.728619886978422 \cdot 10^{-235}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.1894064205357374 \cdot 10^{-176}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Vef \leq 5.2959990716838415 \cdot 10^{+67}:\\ \;\;\;\;t_0 + \frac{NdChar}{2}\\ \mathbf{elif}\;Vef \leq 5.104771715907839 \cdot 10^{+155}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Vef \leq 1.2053413000013214 \cdot 10^{+186}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq 1.0009609071494721 \cdot 10^{+248}:\\ \;\;\;\;t_0 + t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 26
Error32.8
Cost8016
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;NdChar \leq -6.172376307138025 \cdot 10^{-81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -1.3656156664900812 \cdot 10^{-157}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{KbT}{\frac{Vef}{NdChar}}\\ \mathbf{elif}\;NdChar \leq -1.3516750108485062 \cdot 10^{-287}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NdChar \leq 3.3766760478605693 \cdot 10^{-180}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + KbT \cdot \frac{NdChar}{EDonor}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 27
Error27.8
Cost8016
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{if}\;NdChar \leq -2.3206080602779207 \cdot 10^{+26}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -5.1117093940212265 \cdot 10^{-23}:\\ \;\;\;\;t_0 + NdChar \cdot \frac{KbT}{mu}\\ \mathbf{elif}\;NdChar \leq -5.030570206990777 \cdot 10^{-80}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 0.035651524885616806:\\ \;\;\;\;t_0 + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 28
Error40.9
Cost7760
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.3425159163400758 \cdot 10^{+165}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Vef \leq -5.728619886978422 \cdot 10^{-235}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Vef \leq 1.1894064205357374 \cdot 10^{-176}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Vef \leq 1.8366876112568668 \cdot 10^{+75}:\\ \;\;\;\;t_0 + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{KbT}{\frac{Vef}{NdChar}}\\ \end{array} \]
Alternative 29
Error27.8
Cost7752
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -3.376389485963997 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 7.960847830031042 \cdot 10^{-138}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 30
Error39.0
Cost7500
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -1.2584242556794674:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq -1.3178049462558642 \cdot 10^{-305}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 42463269882.29714:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 31
Error38.6
Cost7368
\[\begin{array}{l} \mathbf{if}\;NaChar \leq -1.2584242556794674:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 277551656611279.6:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 32
Error38.6
Cost7368
\[\begin{array}{l} \mathbf{if}\;NdChar \leq -6.991897027065205 \cdot 10^{+95}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 0.035651524885616806:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
Alternative 33
Error40.2
Cost7236
\[\begin{array}{l} \mathbf{if}\;EDonor \leq -6.901843280472398 \cdot 10^{-6}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
Alternative 34
Error41.1
Cost7104
\[\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2} \]
Alternative 35
Error46.1
Cost448
\[\frac{NdChar}{2} + \frac{NaChar}{2} \]

Error

Reproduce

herbie shell --seed 2022308 
(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))))))