Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 50.2s

Precision: binary64

Cost: 27392

• Unsound rule application detected in e-graph. Results may not be sound.

• could not determine a ground truth

  1. NdChar = -2.511181702100737e+52
  2. Ec = 1.9877105744429173e-271
  3. Vef = -6.492094605876802e+78
  4. EDonor = 1.640212665304471e-150
  5. mu = 8.944089752808333e+110
  6. KbT = -2.2085618975529367e-206
  7. NaChar = 5.124850939139175e+51
  8. Ev = 7.497121528062419e-212
  9. EAccept = 1.321498490643293e+197

Math

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

↓

\[\frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + {\left(\sqrt{e^{\frac{Vef + \left(\left(Ev + EAccept\right) - mu\right)}{KbT}}}\right)}^{2}} \]

FPCore

(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 (- Ec (+ Vef EDonor))) KbT))))
  (/
   NaChar
   (+ 1.0 (pow (sqrt (exp (/ (+ Vef (- (+ Ev EAccept) mu)) KbT))) 2.0)))))

C

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 - (Ec - (Vef + EDonor))) / KbT)))) + (NaChar / (1.0 + pow(sqrt(exp(((Vef + ((Ev + EAccept) - mu)) / KbT))), 2.0)));
}

Fortran

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 - (ec - (vef + edonor))) / kbt)))) + (nachar / (1.0d0 + (sqrt(exp(((vef + ((ev + eaccept) - mu)) / kbt))) ** 2.0d0)))
end function

Java

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 - (Ec - (Vef + EDonor))) / KbT)))) + (NaChar / (1.0 + Math.pow(Math.sqrt(Math.exp(((Vef + ((Ev + EAccept) - mu)) / KbT))), 2.0)));
}

Python

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 - (Ec - (Vef + EDonor))) / KbT)))) + (NaChar / (1.0 + math.pow(math.sqrt(math.exp(((Vef + ((Ev + EAccept) - mu)) / KbT))), 2.0)))

Julia

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(Ec - Float64(Vef + EDonor))) / KbT)))) + Float64(NaChar / Float64(1.0 + (sqrt(exp(Float64(Float64(Vef + Float64(Float64(Ev + EAccept) - mu)) / KbT))) ^ 2.0))))
end

MATLAB

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 - (Ec - (Vef + EDonor))) / KbT)))) + (NaChar / (1.0 + (sqrt(exp(((Vef + ((Ev + EAccept) - mu)) / KbT))) ^ 2.0)));
end

Wolfram

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[(Ec - N[(Vef + EDonor), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Power[N[Sqrt[N[Exp[N[(N[(Vef + N[(N[(Ev + EAccept), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

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. Simplified 100.0%

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

   [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%	\[ \frac{NdChar}{1 + e^{\frac{\color{blue}{mu + \left(0 - \left(\left(Ec - Vef\right) - EDonor\right)\right)}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   neg-sub0 [<=] 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%	\[ \frac{NdChar}{1 + e^{\frac{mu - \color{blue}{\left(Ec - \left(Vef + EDonor\right)\right)}}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   unsub-neg [=>] 100.0%	\[ \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\color{blue}{\left(\left(Ev + Vef\right) + EAccept\right) - mu}}{KbT}}} \]
   +-commutative [=>] 100.0%	\[ \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\color{blue}{\left(Vef + Ev\right)} + EAccept\right) - mu}{KbT}}} \]
   associate-+l+ [=>] 100.0%	\[ \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\color{blue}{\left(Vef + \left(Ev + EAccept\right)\right)} - mu}{KbT}}} \]

3. Applied egg-rr 100.0%

   \[\leadsto \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{{\left(\sqrt{e^{\frac{Vef + \left(\left(Ev + EAccept\right) - mu\right)}{KbT}}}\right)}^{2}}} \]
   Step-by-step derivation

   [Start] 100.0%	\[ \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} \]
   add-sqr-sqrt [=>] 100.0%	\[ \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{\sqrt{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} \cdot \sqrt{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}}} \]
   pow2 [=>] 100.0%	\[ \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + \color{blue}{{\left(\sqrt{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\right)}^{2}}} \]
   associate--l+ [=>] 100.0%	\[ \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + {\left(\sqrt{e^{\frac{\color{blue}{Vef + \left(\left(Ev + EAccept\right) - mu\right)}}{KbT}}}\right)}^{2}} \]

4. Final simplification 100.0%

   \[\leadsto \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + {\left(\sqrt{e^{\frac{Vef + \left(\left(Ev + EAccept\right) - mu\right)}{KbT}}}\right)}^{2}} \]

Alternatives

Alternative 1
Accuracy	100.0%
Cost	27392

\[\frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + {\left(\sqrt{e^{\frac{Vef + \left(\left(Ev + EAccept\right) - mu\right)}{KbT}}}\right)}^{2}} \]

Alternative 2
Accuracy	100.0%
Cost	14528

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

Alternative 3
Accuracy	74.6%
Cost	14409

\[\begin{array}{l} \mathbf{if}\;mu \leq -1 \cdot 10^{+169} \lor \neg \left(mu \leq 2.05 \cdot 10^{+82}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 4
Accuracy	78.2%
Cost	14409

\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;mu \leq -350000 \lor \neg \left(mu \leq 6.8 \cdot 10^{+75}\right):\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]

Alternative 5
Accuracy	71.5%
Cost	14408

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}}\\ \mathbf{if}\;EAccept \leq 2.4 \cdot 10^{-262}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.85 \cdot 10^{-69}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 6
Accuracy	65.2%
Cost	8788

\[\begin{array}{l} t_0 := \frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}\\ t_1 := \frac{NdChar}{1 + e^{t_0}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ t_3 := t_2 + \frac{NdChar}{1 - \frac{Ec}{KbT}}\\ \mathbf{if}\;NaChar \leq -7.4 \cdot 10^{-10}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{-193}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{-92}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.9 \cdot 10^{+88}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 2.7 \cdot 10^{+129}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + t_0}\\ \mathbf{elif}\;NaChar \leq 1.75 \cdot 10^{+137}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 6.5 \cdot 10^{+225}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \]

Alternative 7
Accuracy	65.1%
Cost	8536

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{if}\;NaChar \leq -5.5 \cdot 10^{+258}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -3.65 \cdot 10^{+242}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq -8.8 \cdot 10^{-8}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 4.9 \cdot 10^{-194}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 5.2 \cdot 10^{-95}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.35 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 8
Accuracy	61.5%
Cost	8412

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ t_2 := t_1 + \frac{NdChar}{2}\\ \mathbf{if}\;KbT \leq -1.55 \cdot 10^{+83}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq -1.95 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq -1.55 \cdot 10^{-142}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -2.8 \cdot 10^{-166}:\\ \;\;\;\;t_1 + \frac{KbT}{\frac{mu}{NdChar}}\\ \mathbf{elif}\;KbT \leq 3.2 \cdot 10^{-240}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 6.5 \cdot 10^{-173}:\\ \;\;\;\;t_1 + \frac{KbT}{\frac{Vef}{NdChar}}\\ \mathbf{elif}\;KbT \leq 5.8 \cdot 10^{+73}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \]

Alternative 9
Accuracy	65.3%
Cost	8272

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1 \cdot 10^{-9}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.3 \cdot 10^{-192}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 5.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.62 \cdot 10^{+91}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \]

Alternative 10
Accuracy	63.0%
Cost	7884

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;NdChar \leq -1.45 \cdot 10^{-133}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 1.6 \cdot 10^{-255}:\\ \;\;\;\;t_1 + \frac{KbT}{\frac{Vef}{NdChar}}\\ \mathbf{elif}\;NdChar \leq 4.2 \cdot 10^{-95}:\\ \;\;\;\;t_1 + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 11
Accuracy	44.3%
Cost	7764

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;Vef \leq -3.5 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -5.4 \cdot 10^{-192}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 5.2 \cdot 10^{-306}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 9 \cdot 10^{-119}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;Vef \leq 2.3 \cdot 10^{+116}:\\ \;\;\;\;t_1 + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 12
Accuracy	58.4%
Cost	7760

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.9 \cdot 10^{+234}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -2.45 \cdot 10^{+184}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -5 \cdot 10^{+64}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq 8.2 \cdot 10^{+73}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]

Alternative 13
Accuracy	64.1%
Cost	7753

\[\begin{array}{l} \mathbf{if}\;NdChar \leq -2.05 \cdot 10^{-134} \lor \neg \left(NdChar \leq 2.9 \cdot 10^{-96}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 14
Accuracy	44.9%
Cost	7632

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.1 \cdot 10^{-15}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -1.2 \cdot 10^{-192}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.1 \cdot 10^{-302}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.7 \cdot 10^{+77}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 15
Accuracy	53.6%
Cost	7632

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;KbT \leq -8.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -1.6 \cdot 10^{+187}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -1.2 \cdot 10^{+64}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq 4.5 \cdot 10^{+58}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]

Alternative 16
Accuracy	53.9%
Cost	7632

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;KbT \leq -8.5 \cdot 10^{+233}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;KbT \leq -2.9 \cdot 10^{+185}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -2.1 \cdot 10^{+62}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq 8 \cdot 10^{+73}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]

Alternative 17
Accuracy	41.3%
Cost	7508

\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;mu \leq -950000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq -3.9 \cdot 10^{-85}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;mu \leq -1.66 \cdot 10^{-289}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq 2.5 \cdot 10^{-191}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq 6.5 \cdot 10^{+76}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 18
Accuracy	39.7%
Cost	7376

\[\begin{array}{l} \mathbf{if}\;KbT \leq -2.5 \cdot 10^{+193}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;KbT \leq -1.35 \cdot 10^{-7}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq -5.4 \cdot 10^{-237}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;KbT \leq 8.2 \cdot 10^{+73}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + \left(\left(\frac{mu}{KbT} + \left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \end{array} \]

Alternative 19
Accuracy	38.6%
Cost	7244

\[\begin{array}{l} \mathbf{if}\;KbT \leq -1.2 \cdot 10^{+194}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;KbT \leq -1.4 \cdot 10^{-7}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+42}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + \left(\left(\frac{mu}{KbT} + \left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right)\right) - \frac{Ec}{KbT}\right)}\\ \end{array} \]

Alternative 20
Accuracy	27.4%
Cost	1224

\[\begin{array}{l} t_0 := \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{if}\;mu \leq -4.4 \cdot 10^{-117}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;mu \leq 5.5 \cdot 10^{-82}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \end{array} \]

Alternative 21
Accuracy	26.7%
Cost	1092

\[\begin{array}{l} \mathbf{if}\;NaChar \leq -1 \cdot 10^{-212}:\\ \;\;\;\;\frac{NdChar}{1 - \frac{Ec}{KbT}} + \frac{NaChar}{2 + \frac{Ev}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]

Alternative 22
Accuracy	27.6%
Cost	320

\[0.5 \cdot \left(NdChar + NaChar\right) \]

Reproduce

herbie shell --seed 2023263 
(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))))))