Average Error: 0.0 → 0.0
Time: 52.5s
Precision: binary64
Cost: 14656
\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
\[\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{1}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} \cdot NaChar \]
(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 (/ (+ Vef (+ EDonor (- mu Ec))) KbT))))
  (* (/ 1.0 (+ 1.0 (exp (/ (+ Ev (+ Vef (- 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(((Vef + (EDonor + (mu - Ec))) / KbT)))) + ((1.0 / (1.0 + exp(((Ev + (Vef + (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(((vef + (edonor + (mu - ec))) / kbt)))) + ((1.0d0 / (1.0d0 + exp(((ev + (vef + (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(((Vef + (EDonor + (mu - Ec))) / KbT)))) + ((1.0 / (1.0 + Math.exp(((Ev + (Vef + (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(((Vef + (EDonor + (mu - Ec))) / KbT)))) + ((1.0 / (1.0 + math.exp(((Ev + (Vef + (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(Vef + Float64(EDonor + Float64(mu - Ec))) / KbT)))) + Float64(Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Ev + Float64(Vef + Float64(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(((Vef + (EDonor + (mu - Ec))) / KbT)))) + ((1.0 / (1.0 + exp(((Ev + (Vef + (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[(Vef + N[(EDonor + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / N[(1.0 + N[Exp[N[(N[(Ev + N[(Vef + N[(EAccept - mu), $MachinePrecision]), $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{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{1}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} \cdot NaChar

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. Applied egg-rr0.0

    \[\leadsto \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \color{blue}{\frac{1}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} \cdot NaChar} \]
  4. Final simplification0.0

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

Alternatives

Alternative 1
Error26.9
Cost15608
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_0\\ \mathbf{if}\;Ev \leq -2.5253578845540803 \cdot 10^{+254}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -1.9142640881551954 \cdot 10^{+202}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ev \leq -5.3441296859597826 \cdot 10^{+159}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -1.1951397451701453 \cdot 10^{+149}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Ev \leq -8.666245459620702 \cdot 10^{+143}:\\ \;\;\;\;t_0 + \frac{NdChar}{\left(\frac{mu}{KbT} + \left(2 + \left(\frac{EDonor}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;Ev \leq -6.660239934720514 \cdot 10^{+139}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq -1.6447006651430581 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -1.6103432823464268 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq -1.0010071993728402 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -4.102558704020135 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq -2.846168741517895 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -1.1849748526322428 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq 1.1658266982322661 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq 9.337379423688537 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]
Alternative 2
Error20.0
Cost15332
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_3 := t_1 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;KbT \leq -4.1421327986367515 \cdot 10^{+142}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq -1.0009212938986133 \cdot 10^{-48}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;KbT \leq -1.7946756011032962 \cdot 10^{-192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 4.801883602777152 \cdot 10^{-205}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;KbT \leq 1.471425858190477 \cdot 10^{-69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 1.0383313800166919 \cdot 10^{-45}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq 50049399515282570:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 8.001569872945355 \cdot 10^{+157}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;KbT \leq 1.6219622436245508 \cdot 10^{+179}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]
Alternative 3
Error20.0
Cost15332
\[\begin{array}{l} t_0 := 1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_3 := \frac{NaChar}{t_0}\\ t_4 := t_3 + t_1\\ t_5 := t_3 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;KbT \leq -4.1421327986367515 \cdot 10^{+142}:\\ \;\;\;\;\frac{1}{t_0} \cdot NaChar + t_1\\ \mathbf{elif}\;KbT \leq -1.0009212938986133 \cdot 10^{-48}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;KbT \leq -1.7946756011032962 \cdot 10^{-192}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq 4.801883602777152 \cdot 10^{-205}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;KbT \leq 1.471425858190477 \cdot 10^{-69}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq 1.0383313800166919 \cdot 10^{-45}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;KbT \leq 50049399515282570:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq 8.001569872945355 \cdot 10^{+157}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;KbT \leq 1.6219622436245508 \cdot 10^{+179}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 4
Error17.8
Cost15200
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}}\\ t_4 := t_3 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_5 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;Ev \leq -6.759867485119508 \cdot 10^{+147}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;Ev \leq -5.862703115383937 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq -1.5421266302702414 \cdot 10^{-12}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -8.443314910930683 \cdot 10^{-50}:\\ \;\;\;\;t_5\\ \mathbf{elif}\;Ev \leq -1.1760951842936771 \cdot 10^{-121}:\\ \;\;\;\;t_3 + \frac{NaChar}{\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(2 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Ev \leq -7.14692297904579 \cdot 10^{-299}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq 1.1658266982322661 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq 3.196523513655435 \cdot 10^{-32}:\\ \;\;\;\;t_5\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \]
Alternative 5
Error27.4
Cost15080
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{if}\;Ec \leq -2.008109426120241 \cdot 10^{+193}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq -6.389440482657923 \cdot 10^{+146}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ec \leq -2.4842796286031215 \cdot 10^{+142}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq -6.333281963882108 \cdot 10^{+45}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq -1.5423842194749919 \cdot 10^{-37}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq -1.575580147426964 \cdot 10^{-87}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq 1.0249051300970838 \cdot 10^{-109}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 2.8235969480321333 \cdot 10^{-65}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq 5.942780821844238 \cdot 10^{-36}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 6.668973051373406 \cdot 10^{+66}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Ec \leq 3.757236416585762 \cdot 10^{+148}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(\frac{Ev}{KbT} + \left(\frac{EAccept}{KbT} + \left(2 + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;Ec \leq 1.4858159242141954 \cdot 10^{+162}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq 7.122123597480291 \cdot 10^{+174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 1.9765830327519866 \cdot 10^{+201}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;Ec \leq 2.9009108594831588 \cdot 10^{+243}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{NdChar}{2}\\ \end{array} \]
Alternative 6
Error27.0
Cost14948
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{if}\;Ev \leq -1.9142640881551954 \cdot 10^{+202}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t_0\\ \mathbf{elif}\;Ev \leq -1.6447006651430581 \cdot 10^{+115}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -1.6103432823464268 \cdot 10^{+70}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq -1.0010071993728402 \cdot 10^{-44}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -4.102558704020135 \cdot 10^{-59}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq -2.846168741517895 \cdot 10^{-160}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -1.1849748526322428 \cdot 10^{-204}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Ev \leq 1.1658266982322661 \cdot 10^{-135}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq 9.337379423688537 \cdot 10^{-17}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + t_0\\ \end{array} \]
Alternative 7
Error17.1
Cost14804
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{if}\;mu \leq -6.403953203786087 \cdot 10^{+150}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -3.2398605178416968 \cdot 10^{+63}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;mu \leq -4.9804456001574836 \cdot 10^{+57}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;mu \leq -7.582363398534028 \cdot 10^{-62}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;mu \leq 2.8906324314055416 \cdot 10^{+80}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 8
Error0.0
Cost14528
\[\frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} \]
Alternative 9
Error16.8
Cost14408
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{if}\;mu \leq -9.842167355317472 \cdot 10^{+182}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq 2.8906324314055416 \cdot 10^{+80}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 10
Error22.6
Cost14352
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{if}\;mu \leq -6.403953203786087 \cdot 10^{+150}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq 1.8531076984100464 \cdot 10^{-297}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 2.2218892256973844 \cdot 10^{-100}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;mu \leq 7.994506858244885 \cdot 10^{+41}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 11
Error26.7
Cost9192
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{if}\;Ev \leq -7.784759065251386 \cdot 10^{+244}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ev \leq -1.9142640881551954 \cdot 10^{+202}:\\ \;\;\;\;t_1 + \frac{NdChar}{2}\\ \mathbf{elif}\;Ev \leq -1.6447006651430581 \cdot 10^{+115}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ev \leq -1.6103432823464268 \cdot 10^{+70}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -1.0010071993728402 \cdot 10^{-44}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ev \leq -4.102558704020135 \cdot 10^{-59}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -2.846168741517895 \cdot 10^{-160}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ev \leq -1.1849748526322428 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq 1.1658266982322661 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ev \leq 4.7447938695192987 \cdot 10^{+86}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 12
Error22.0
Cost7752
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;KbT \leq -9.144004139714917 \cdot 10^{+174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 2.0242532396916883 \cdot 10^{+112}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 13
Error22.0
Cost7752
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;KbT \leq -9.144004139714917 \cdot 10^{+174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 3.634395247270723 \cdot 10^{+99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 14
Error22.0
Cost7752
\[\begin{array}{l} t_0 := 1 + e^{\frac{Ev + \left(Vef + \left(EAccept - mu\right)\right)}{KbT}}\\ \mathbf{if}\;KbT \leq -9.144004139714917 \cdot 10^{+174}:\\ \;\;\;\;\frac{1}{t_0} \cdot NaChar + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 3.634395247270723 \cdot 10^{+99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 15
Error38.3
Cost7632
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;KbT \leq -9.144004139714917 \cdot 10^{+174}:\\ \;\;\;\;t_0 + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -5.397913484682112 \cdot 10^{-276}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 1.4164935813967256 \cdot 10^{-235}:\\ \;\;\;\;t_1 + \frac{NdChar \cdot KbT}{EDonor}\\ \mathbf{elif}\;KbT \leq 1.471425858190477 \cdot 10^{-69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NdChar}{2}\\ \end{array} \]
Alternative 16
Error23.6
Cost7496
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{if}\;KbT \leq -9.144004139714917 \cdot 10^{+174}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 2.0242532396916883 \cdot 10^{+112}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 17
Error23.6
Cost7496
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;KbT \leq -9.144004139714917 \cdot 10^{+174}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 2.0242532396916883 \cdot 10^{+112}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{2}\\ \end{array} \]
Alternative 18
Error38.3
Cost7368
\[\begin{array}{l} \mathbf{if}\;KbT \leq -2.845943405717299 \cdot 10^{+218}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 1.471425858190477 \cdot 10^{-69}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 19
Error38.2
Cost7368
\[\begin{array}{l} \mathbf{if}\;KbT \leq -2.845943405717299 \cdot 10^{+218}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 1.471425858190477 \cdot 10^{-69}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 20
Error37.9
Cost7368
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;KbT \leq -9.144004139714917 \cdot 10^{+174}:\\ \;\;\;\;t_0 + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq 1.471425858190477 \cdot 10^{-69}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 21
Error38.6
Cost7112
\[\begin{array}{l} \mathbf{if}\;KbT \leq -2.845943405717299 \cdot 10^{+218}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 2.1374618322583593 \cdot 10^{+41}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
Alternative 22
Error46.0
Cost836
\[\begin{array}{l} t_0 := \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{if}\;KbT \leq -1.7766188501617062 \cdot 10^{-130}:\\ \;\;\;\;\frac{NdChar}{2} + t_0\\ \mathbf{elif}\;KbT \leq 1.1111209460632905 \cdot 10^{-227}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
Alternative 23
Error45.8
Cost712
\[\begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{if}\;KbT \leq -2.872329735581475 \cdot 10^{-129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 1.1111209460632905 \cdot 10^{-227}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 24
Error46.3
Cost320
\[0.5 \cdot \left(NdChar + NaChar\right) \]

Error

Reproduce

herbie shell --seed 2022317 
(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))))))