Bulmash initializePoisson

?

Percentage Accurate: 100.0% → 100.0%
Time: 27.0s
Precision: binary64
Cost: 20928

?

\[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
↓
\[\frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + {e}^{\left(\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}\right)}} \]
(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 (- (+ Vef EDonor) Ec)) KbT))))
  (/ NaChar (+ 1.0 (pow E (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
}
↓
double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp(((mu + ((Vef + EDonor) - Ec)) / KbT)))) + (NaChar / (1.0 + pow(((double) M_E), ((Vef + (Ev + (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((-(((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 + ((Vef + EDonor) - Ec)) / KbT)))) + (NaChar / (1.0 + Math.pow(Math.E, ((Vef + (Ev + (EAccept - mu))) / KbT))));
}

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) + -mu) / KbT))))
↓
def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / (1.0 + math.exp(((mu + ((Vef + EDonor) - Ec)) / KbT)))) + (NaChar / (1.0 + math.pow(math.e, ((Vef + (Ev + (EAccept - mu))) / KbT))))

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) + Float64(-mu)) / KbT)))))
end
↓
function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(Float64(Vef + EDonor) - Ec)) / KbT)))) + Float64(NaChar / Float64(1.0 + (exp(1) ^ Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
end

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) + -mu) / KbT))));
end
↓
function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp(((mu + ((Vef + EDonor) - Ec)) / KbT)))) + (NaChar / (1.0 + (2.71828182845904523536 ^ ((Vef + (Ev + (EAccept - mu))) / KbT))));
end

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] + (-mu)), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
↓
code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(N[(Vef + EDonor), $MachinePrecision] - Ec), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Power[E, N[(N[(Vef + N[(Ev + 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{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + {e}^{\left(\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}\right)}}

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 18 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

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Results

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Derivation?

  1. Initial program 100.0%

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

  2. Simplified100.0%

    \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{mu - \left(Ec - \left(Vef + EDonor\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}} \]
    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-rr100.0%

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

    [Start]100.0%

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

    *-un-lft-identity [=>]100.0%

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

    exp-prod [=>]100.0%

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

    exp-1-e [=>]100.0%

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

    associate--l+ [=>]100.0%

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

    associate--l+ [=>]100.0%

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

  4. Final simplification100.0%

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

Alternatives

Alternative 1
Accuracy100.0%
Cost20928
\[\frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + {e}^{\left(\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}\right)}} \]
Alternative 2
Accuracy71.1%
Cost14673
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}}\\ \mathbf{if}\;Ev \leq -1.82 \cdot 10^{+196}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -7.2 \cdot 10^{+68}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.3 \cdot 10^{-15} \lor \neg \left(Ev \leq 3.5 \cdot 10^{-185}\right):\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
Alternative 3
Accuracy76.7%
Cost14672
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.8 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 2.3 \cdot 10^{-20}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 4.5 \cdot 10^{+47}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.7 \cdot 10^{+87}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(\frac{Ev}{KbT} + \frac{-1}{\frac{EAccept}{KbT} + \left(-1 - \frac{Vef}{KbT}\right)}\right) - \frac{mu}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 4
Accuracy68.1%
Cost14544
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;EDonor \leq -1.65 \cdot 10^{+229}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EDonor \leq -2.8 \cdot 10^{+169}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right)}\\ \mathbf{elif}\;EDonor \leq 1.02 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EDonor \leq 8.2 \cdot 10^{+117}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
Alternative 5
Accuracy77.8%
Cost14540
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.4 \cdot 10^{+36}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq 1.1 \cdot 10^{-115}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.75 \cdot 10^{+95}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]
Alternative 6
Accuracy100.0%
Cost14528
\[\frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} \]
Alternative 7
Accuracy66.5%
Cost14281
\[\begin{array}{l} \mathbf{if}\;NaChar \leq -9 \cdot 10^{+35} \lor \neg \left(NaChar \leq 6.2 \cdot 10^{+17}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right)}\\ \end{array} \]
Alternative 8
Accuracy64.6%
Cost8521
\[\begin{array}{l} t_0 := \frac{Vef}{KbT} + 2\\ \mathbf{if}\;NaChar \leq -5.8 \cdot 10^{-26} \lor \neg \left(NaChar \leq 4 \cdot 10^{-61}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} + \frac{NdChar}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + t_0\right)}\\ \end{array} \]
Alternative 9
Accuracy59.9%
Cost8281
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NdChar \leq -4.5 \cdot 10^{+136}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -4.5 \cdot 10^{-66}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -4.7 \cdot 10^{-132}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + EDonor\right) - Ec}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 6.5 \cdot 10^{-226} \lor \neg \left(NdChar \leq 1.22 \cdot 10^{-166}\right) \land NdChar \leq 4.2 \cdot 10^{-110}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 10
Accuracy62.1%
Cost8272
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{if}\;NdChar \leq -1.26 \cdot 10^{+144}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 2.1 \cdot 10^{-52}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 1.28 \cdot 10^{+20}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 3 \cdot 10^{+116}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(\left(Vef + EDonor\right) - Ec\right)}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
Alternative 11
Accuracy60.9%
Cost7960
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + \left(mu + EDonor\right)\right) - Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;KbT \leq -1.4 \cdot 10^{+240}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq -6 \cdot 10^{+152}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -2.65 \cdot 10^{+121}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.32 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 9.2 \cdot 10^{+84}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq 3 \cdot 10^{+215}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef + EDonor\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \]
Alternative 12
Accuracy55.9%
Cost7896
\[\begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(Vef + EDonor\right) - Ec}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;KbT \leq -1.55 \cdot 10^{+239}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq -8.5 \cdot 10^{+152}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq -7 \cdot 10^{+120}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 9.6 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq 2.1 \cdot 10^{+85}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;KbT \leq 6.7 \cdot 10^{+215}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 13
Accuracy51.1%
Cost7632
\[\begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef + EDonor\right) - Ec}{KbT}}}\\ \mathbf{if}\;NdChar \leq -6 \cdot 10^{+105}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -3.8 \cdot 10^{-63}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq -1.45 \cdot 10^{-177}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 5.8 \cdot 10^{-226}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]
Alternative 14
Accuracy37.6%
Cost7368
\[\begin{array}{l} \mathbf{if}\;EAccept \leq 1.6 \cdot 10^{-228}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;EAccept \leq 3.7 \cdot 10^{+59}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 15
Accuracy37.2%
Cost7236
\[\begin{array}{l} \mathbf{if}\;EAccept \leq 4.4 \cdot 10^{+58}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
Alternative 16
Accuracy37.9%
Cost1348
\[\begin{array}{l} \mathbf{if}\;KbT \leq 5 \cdot 10^{+210}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{\left(\frac{mu}{KbT} + \left(\frac{Vef}{KbT} + 2\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
Alternative 17
Accuracy37.9%
Cost580
\[\begin{array}{l} \mathbf{if}\;KbT \leq 8.5 \cdot 10^{+209}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5 + \frac{NdChar}{2}\\ \end{array} \]
Alternative 18
Accuracy36.0%
Cost320
\[NdChar + NaChar \cdot 0.5 \]

Reproduce?

herbie shell --seed 2023165 
(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))))))