Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 21.0s

Alternatives: 20

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = 4.184408720623827e+236
  2. Ec = -1.792748367895745e-47
  3. Vef = 7.361874210882777e+273
  4. EDonor = 7.800532708276649e+133
  5. mu = -2.094833324078763e+162
  6. KbT = -8.275680683169116e-196
  7. NaChar = 1.260319811804625e+237
  8. Ev = 3.1928927799052218e+240
  9. EAccept = 1.383557648253586e-55

Specification

Math

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

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))))))

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))));
}

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

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))));
}

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))))

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

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

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]

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

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))))))

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))));
}

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

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))));
}

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))))

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

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

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]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))
  (/ NaChar (+ (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0));
}

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 / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (exp(((vef - ((mu - eaccept) - ev)) / kbt)) + 1.0d0))
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 / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)) + 1.0));
}

Python

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

Julia

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

MATLAB

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 67.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 4.8 \cdot 10^{-199}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 2.3 \cdot 10^{+210}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 4.8e-199)
   (+
    (/ NdChar (+ (exp (/ (+ EDonor (+ mu (- Vef Ec))) KbT)) 1.0))
    (/ NaChar (+ (exp (/ Ev KbT)) 1.0)))
   (if (<= EAccept 2.3e+210)
     (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
     (/ NdChar (+ (exp (/ (- (+ EDonor (+ mu Vef)) Ec) KbT)) 1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 4.8e-199) {
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp((Ev / KbT)) + 1.0));
	} else if (EAccept <= 2.3e+210) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (eaccept <= 4.8d-199) then
        tmp = (ndchar / (exp(((edonor + (mu + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (exp((ev / kbt)) + 1.0d0))
    else if (eaccept <= 2.3d+210) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = ndchar / (exp((((edonor + (mu + vef)) - ec) / kbt)) + 1.0d0)
    end if
    code = tmp
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) {
	double tmp;
	if (EAccept <= 4.8e-199) {
		tmp = (NdChar / (Math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (Math.exp((Ev / KbT)) + 1.0));
	} else if (EAccept <= 2.3e+210) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (Math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 4.8e-199:
		tmp = (NdChar / (math.exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (math.exp((Ev / KbT)) + 1.0))
	elif EAccept <= 2.3e+210:
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = NdChar / (math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 4.8e-199)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(mu + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)));
	elseif (EAccept <= 2.3e+210)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 4.8e-199)
		tmp = (NdChar / (exp(((EDonor + (mu + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp((Ev / KbT)) + 1.0));
	elseif (EAccept <= 2.3e+210)
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 4.8e-199], N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(mu + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 2.3e+210], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(N[Exp[N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 4.79999999999999991e-199

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 73.8%

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

   if 4.79999999999999991e-199 < EAccept < 2.2999999999999999e210

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 81.2%

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

   if 2.2999999999999999e210 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in NdChar around inf 84.9%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 4.8 \cdot 10^{-199}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 2.3 \cdot 10^{+210}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.56 \cdot 10^{-25} \lor \neg \left(NaChar \leq 3.6 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.56e-25) (not (<= NaChar 3.6e-98)))
   (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
   (/ NdChar (+ (exp (/ (- (+ EDonor (+ mu Vef)) Ec) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.56e-25) || !(NaChar <= 3.6e-98)) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((nachar <= (-1.56d-25)) .or. (.not. (nachar <= 3.6d-98))) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = ndchar / (exp((((edonor + (mu + vef)) - ec) / kbt)) + 1.0d0)
    end if
    code = tmp
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) {
	double tmp;
	if ((NaChar <= -1.56e-25) || !(NaChar <= 3.6e-98)) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (Math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.56e-25) or not (NaChar <= 3.6e-98):
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = NdChar / (math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.56e-25) || !(NaChar <= 3.6e-98))
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1.56e-25) || ~((NaChar <= 3.6e-98)))
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.56e-25], N[Not[LessEqual[NaChar, 3.6e-98]], $MachinePrecision]], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(N[Exp[N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.55999999999999995e-25 or 3.6000000000000002e-98 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 74.6%

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

   if -1.55999999999999995e-25 < NaChar < 3.6000000000000002e-98

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 78.4%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{\left(EDonor + \left(Vef + mu\right)\right) - Ec}{KbT}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.56 \cdot 10^{-25} \lor \neg \left(NaChar \leq 3.6 \cdot 10^{-98}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 65.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.35 \cdot 10^{-24} \lor \neg \left(NaChar \leq 1.2 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(mu + Vef\right) - Ec}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.35e-24) (not (<= NaChar 1.2e-100)))
   (/ NaChar (+ (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)) 1.0))
   (/ NdChar (+ (exp (/ (- (+ mu Vef) Ec) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.35e-24) || !(NaChar <= 1.2e-100)) {
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((nachar <= (-1.35d-24)) .or. (.not. (nachar <= 1.2d-100))) then
        tmp = nachar / (exp((((eaccept + (vef + ev)) - mu) / kbt)) + 1.0d0)
    else
        tmp = ndchar / (exp((((mu + vef) - ec) / kbt)) + 1.0d0)
    end if
    code = tmp
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) {
	double tmp;
	if ((NaChar <= -1.35e-24) || !(NaChar <= 1.2e-100)) {
		tmp = NaChar / (Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (Math.exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.35e-24) or not (NaChar <= 1.2e-100):
		tmp = NaChar / (math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0)
	else:
		tmp = NdChar / (math.exp((((mu + Vef) - Ec) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.35e-24) || !(NaChar <= 1.2e-100))
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1.35e-24) || ~((NaChar <= 1.2e-100)))
		tmp = NaChar / (exp((((EAccept + (Vef + Ev)) - mu) / KbT)) + 1.0);
	else
		tmp = NdChar / (exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.35e-24], N[Not[LessEqual[NaChar, 1.2e-100]], $MachinePrecision]], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.35000000000000003e-24 or 1.2000000000000001e-100 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 74.6%

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

   if -1.35000000000000003e-24 < NaChar < 1.2000000000000001e-100

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 78.4%

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

   6. Taylor expanded in EDonor around 0 67.3%

      \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.35 \cdot 10^{-24} \lor \neg \left(NaChar \leq 1.2 \cdot 10^{-100}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(mu + Vef\right) - Ec}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 43.4% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{if}\;Vef \leq -6 \cdot 10^{+40}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq -4.9 \cdot 10^{-195}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;Vef \leq 3.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ Vef KbT)) 1.0))))
   (if (<= Vef -6e+40)
     t_0
     (if (<= Vef -4.9e-195)
       (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))
       (if (<= Vef 3.8e+115) (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp((Vef / KbT)) + 1.0);
	double tmp;
	if (Vef <= -6e+40) {
		tmp = t_0;
	} else if (Vef <= -4.9e-195) {
		tmp = NdChar / (exp((EDonor / KbT)) + 1.0);
	} else if (Vef <= 3.8e+115) {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp((vef / kbt)) + 1.0d0)
    if (vef <= (-6d+40)) then
        tmp = t_0
    else if (vef <= (-4.9d-195)) then
        tmp = ndchar / (exp((edonor / kbt)) + 1.0d0)
    else if (vef <= 3.8d+115) then
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
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) {
	double t_0 = NdChar / (Math.exp((Vef / KbT)) + 1.0);
	double tmp;
	if (Vef <= -6e+40) {
		tmp = t_0;
	} else if (Vef <= -4.9e-195) {
		tmp = NdChar / (Math.exp((EDonor / KbT)) + 1.0);
	} else if (Vef <= 3.8e+115) {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp((Vef / KbT)) + 1.0)
	tmp = 0
	if Vef <= -6e+40:
		tmp = t_0
	elif Vef <= -4.9e-195:
		tmp = NdChar / (math.exp((EDonor / KbT)) + 1.0)
	elif Vef <= 3.8e+115:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0))
	tmp = 0.0
	if (Vef <= -6e+40)
		tmp = t_0;
	elseif (Vef <= -4.9e-195)
		tmp = Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0));
	elseif (Vef <= 3.8e+115)
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp((Vef / KbT)) + 1.0);
	tmp = 0.0;
	if (Vef <= -6e+40)
		tmp = t_0;
	elseif (Vef <= -4.9e-195)
		tmp = NdChar / (exp((EDonor / KbT)) + 1.0);
	elseif (Vef <= 3.8e+115)
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -6e+40], t$95$0, If[LessEqual[Vef, -4.9e-195], N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 3.8e+115], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -6.0000000000000004e40 or 3.8000000000000001e115 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 63.4%

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

   6. Taylor expanded in EDonor around 0 59.6%

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

   7. Taylor expanded in Vef around inf 53.2%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{Vef}{KbT}}}} \]

   if -6.0000000000000004e40 < Vef < -4.9000000000000003e-195

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 61.7%

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

   6. Taylor expanded in EDonor around inf 53.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} \]

   if -4.9000000000000003e-195 < Vef < 3.8000000000000001e115

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 63.5%

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

   6. Taylor expanded in EAccept around inf 43.6%

      \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -6 \cdot 10^{+40}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Vef \leq -4.9 \cdot 10^{-195}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;Vef \leq 3.8 \cdot 10^{+115}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -1.186 \cdot 10^{+100}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -3.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -3.1 \cdot 10^{-165}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -1.186e+100)
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
   (if (<= Ev -3.6e-88)
     (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))
     (if (<= Ev -3.1e-165)
       (/ NaChar (+ (exp (/ Vef KbT)) 1.0))
       (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -1.186e+100) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -3.6e-88) {
		tmp = NdChar / (exp((EDonor / KbT)) + 1.0);
	} else if (Ev <= -3.1e-165) {
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (ev <= (-1.186d+100)) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else if (ev <= (-3.6d-88)) then
        tmp = ndchar / (exp((edonor / kbt)) + 1.0d0)
    else if (ev <= (-3.1d-165)) then
        tmp = nachar / (exp((vef / kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
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) {
	double tmp;
	if (Ev <= -1.186e+100) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -3.6e-88) {
		tmp = NdChar / (Math.exp((EDonor / KbT)) + 1.0);
	} else if (Ev <= -3.1e-165) {
		tmp = NaChar / (Math.exp((Vef / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -1.186e+100:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	elif Ev <= -3.6e-88:
		tmp = NdChar / (math.exp((EDonor / KbT)) + 1.0)
	elif Ev <= -3.1e-165:
		tmp = NaChar / (math.exp((Vef / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -1.186e+100)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	elseif (Ev <= -3.6e-88)
		tmp = Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0));
	elseif (Ev <= -3.1e-165)
		tmp = Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -1.186e+100)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	elseif (Ev <= -3.6e-88)
		tmp = NdChar / (exp((EDonor / KbT)) + 1.0);
	elseif (Ev <= -3.1e-165)
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -1.186e+100], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -3.6e-88], N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -3.1e-165], N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -1.1859999999999999e100

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 85.0%

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

   6. Taylor expanded in NdChar around 0 45.2%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}} \]

   if -1.1859999999999999e100 < Ev < -3.5999999999999999e-88

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 72.3%

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

   6. Taylor expanded in EDonor around inf 44.5%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} \]

   if -3.5999999999999999e-88 < Ev < -3.09999999999999996e-165

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 59.8%

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

   6. Taylor expanded in Vef around inf 45.0%

      \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{Vef}{KbT}}}} \]

   if -3.09999999999999996e-165 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 66.1%

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

   6. Taylor expanded in EAccept around inf 38.5%

      \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 41.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.186 \cdot 10^{+100}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -3.6 \cdot 10^{-88}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -3.1 \cdot 10^{-165}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 54.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq 9.2 \cdot 10^{-287} \lor \neg \left(NdChar \leq 1.45 \cdot 10^{-142}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(mu + Vef\right) - Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar 9.2e-287) (not (<= NdChar 1.45e-142)))
   (/ NdChar (+ (exp (/ (- (+ mu Vef) Ec) KbT)) 1.0))
   (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= 9.2e-287) || !(NdChar <= 1.45e-142)) {
		tmp = NdChar / (exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((ndchar <= 9.2d-287) .or. (.not. (ndchar <= 1.45d-142))) then
        tmp = ndchar / (exp((((mu + vef) - ec) / kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
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) {
	double tmp;
	if ((NdChar <= 9.2e-287) || !(NdChar <= 1.45e-142)) {
		tmp = NdChar / (Math.exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= 9.2e-287) or not (NdChar <= 1.45e-142):
		tmp = NdChar / (math.exp((((mu + Vef) - Ec) / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= 9.2e-287) || !(NdChar <= 1.45e-142))
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= 9.2e-287) || ~((NdChar <= 1.45e-142)))
		tmp = NdChar / (exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, 9.2e-287], N[Not[LessEqual[NdChar, 1.45e-142]], $MachinePrecision]], N[(NdChar / N[(N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < 9.19999999999999944e-287 or 1.44999999999999995e-142 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 67.9%

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

   6. Taylor expanded in EDonor around 0 59.6%

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

   if 9.19999999999999944e-287 < NdChar < 1.44999999999999995e-142

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 92.6%

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

   6. Taylor expanded in EAccept around inf 56.1%

      \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq 9.2 \cdot 10^{-287} \lor \neg \left(NdChar \leq 1.45 \cdot 10^{-142}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(mu + Vef\right) - Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 40.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{if}\;KbT \leq -9.2 \cdot 10^{+109}:\\ \;\;\;\;t\_0 - 0.25 \cdot \left(Ev \cdot \frac{NaChar}{KbT}\right)\\ \mathbf{elif}\;KbT \leq 4 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + -0.25 \cdot \left(mu \cdot \frac{NdChar - NaChar}{KbT}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar))))
   (if (<= KbT -9.2e+109)
     (- t_0 (* 0.25 (* Ev (/ NaChar KbT))))
     (if (<= KbT 4e+216)
       (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))
       (+ t_0 (* -0.25 (* mu (/ (- NdChar NaChar) KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -9.2e+109) {
		tmp = t_0 - (0.25 * (Ev * (NaChar / KbT)));
	} else if (KbT <= 4e+216) {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	} else {
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    if (kbt <= (-9.2d+109)) then
        tmp = t_0 - (0.25d0 * (ev * (nachar / kbt)))
    else if (kbt <= 4d+216) then
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    else
        tmp = t_0 + ((-0.25d0) * (mu * ((ndchar - nachar) / kbt)))
    end if
    code = tmp
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) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -9.2e+109) {
		tmp = t_0 - (0.25 * (Ev * (NaChar / KbT)));
	} else if (KbT <= 4e+216) {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	} else {
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	tmp = 0
	if KbT <= -9.2e+109:
		tmp = t_0 - (0.25 * (Ev * (NaChar / KbT)))
	elif KbT <= 4e+216:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	else:
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	tmp = 0.0
	if (KbT <= -9.2e+109)
		tmp = Float64(t_0 - Float64(0.25 * Float64(Ev * Float64(NaChar / KbT))));
	elseif (KbT <= 4e+216)
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	else
		tmp = Float64(t_0 + Float64(-0.25 * Float64(mu * Float64(Float64(NdChar - NaChar) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	tmp = 0.0;
	if (KbT <= -9.2e+109)
		tmp = t_0 - (0.25 * (Ev * (NaChar / KbT)));
	elseif (KbT <= 4e+216)
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	else
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -9.2e+109], N[(t$95$0 - N[(0.25 * N[(Ev * N[(NaChar / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4e+216], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(-0.25 * N[(mu * N[(N[(NdChar - NaChar), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -9.20000000000000042e109

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 37.3%

      \[\leadsto \color{blue}{-1 \cdot \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)\right) + 0.25 \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)}{KbT} + \left(0.5 \cdot NaChar + 0.5 \cdot NdChar\right)} \]

   7. Simplified 37.3%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right) - \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + Ev\right) + \left(Vef - mu\right)\right) + NdChar \cdot \left(\left(Vef + EDonor\right) + \left(mu - Ec\right)\right)\right)}{KbT}} \]

   8. Taylor expanded in Ev around inf 52.6%

      \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{0.25 \cdot \frac{Ev \cdot NaChar}{KbT}} \]
   9. Step-by-step derivation

      1. associate-/l* 58.4%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - 0.25 \cdot \color{blue}{\left(Ev \cdot \frac{NaChar}{KbT}\right)} \]

   10. Simplified 58.4%

       \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{0.25 \cdot \left(Ev \cdot \frac{NaChar}{KbT}\right)} \]

   if -9.20000000000000042e109 < KbT < 4.0000000000000001e216

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 64.5%

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

   6. Taylor expanded in EAccept around inf 34.8%

      \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]

   if 4.0000000000000001e216 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)\right) + 0.25 \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)}{KbT} + \left(0.5 \cdot NaChar + 0.5 \cdot NdChar\right)} \]

   7. Simplified 45.6%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right) - \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + Ev\right) + \left(Vef - mu\right)\right) + NdChar \cdot \left(\left(Vef + EDonor\right) + \left(mu - Ec\right)\right)\right)}{KbT}} \]

   8. Taylor expanded in mu around -inf 78.2%

      \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{-0.25 \cdot \frac{mu \cdot \left(NaChar + -1 \cdot NdChar\right)}{KbT}} \]
   9. Step-by-step derivation

      1. associate-/l* 78.8%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - -0.25 \cdot \color{blue}{\left(mu \cdot \frac{NaChar + -1 \cdot NdChar}{KbT}\right)} \]

      2. mul-1-neg 78.8%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - -0.25 \cdot \left(mu \cdot \frac{NaChar + \color{blue}{\left(-NdChar\right)}}{KbT}\right) \]

      3. sub-neg 78.8%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - -0.25 \cdot \left(mu \cdot \frac{\color{blue}{NaChar - NdChar}}{KbT}\right) \]

   10. Simplified 78.8%

       \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{-0.25 \cdot \left(mu \cdot \frac{NaChar - NdChar}{KbT}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 41.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -9.2 \cdot 10^{+109}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) - 0.25 \cdot \left(Ev \cdot \frac{NaChar}{KbT}\right)\\ \mathbf{elif}\;KbT \leq 4 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) + -0.25 \cdot \left(mu \cdot \frac{NdChar - NaChar}{KbT}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 40.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 1.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 1.5e+70)
   (/ NaChar (+ (exp (/ Vef KbT)) 1.0))
   (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 1.5e+70) {
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (eaccept <= 1.5d+70) then
        tmp = nachar / (exp((vef / kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
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) {
	double tmp;
	if (EAccept <= 1.5e+70) {
		tmp = NaChar / (Math.exp((Vef / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 1.5e+70:
		tmp = NaChar / (math.exp((Vef / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 1.5e+70)
		tmp = Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 1.5e+70)
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 1.5e+70], N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 1.49999999999999988e70

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 61.5%

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

   6. Taylor expanded in Vef around inf 37.5%

      \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{Vef}{KbT}}}} \]

   if 1.49999999999999988e70 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in NdChar around 0 61.1%

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

   6. Taylor expanded in EAccept around inf 50.7%

      \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 1.5 \cdot 10^{+70}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 38.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 6 \cdot 10^{+69}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 6e+69)
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
   (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 6e+69) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

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
    real(8) :: tmp
    if (eaccept <= 6d+69) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
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) {
	double tmp;
	if (EAccept <= 6e+69) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 6e+69:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 6e+69)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 6e+69)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 6e+69], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 5.99999999999999967e69

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 70.7%

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

   6. Taylor expanded in NdChar around 0 38.5%

      \[\leadsto \color{blue}{\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}} \]

   if 5.99999999999999967e69 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in NdChar around 0 61.1%

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

   6. Taylor expanded in EAccept around inf 50.7%

      \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 40.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 6 \cdot 10^{+69}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 31.2% accurate, 7.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{if}\;KbT \leq -7.5 \cdot 10^{-105}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 4 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{2 + mu \cdot \left(\frac{EAccept + \left(Vef + Ev\right)}{mu \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + -0.25 \cdot \left(mu \cdot \frac{NdChar - NaChar}{KbT}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar))))
   (if (<= KbT -7.5e-105)
     t_0
     (if (<= KbT 4e+216)
       (/
        NaChar
        (+ 2.0 (* mu (+ (/ (+ EAccept (+ Vef Ev)) (* mu KbT)) (/ -1.0 KbT)))))
       (+ t_0 (* -0.25 (* mu (/ (- NdChar NaChar) KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -7.5e-105) {
		tmp = t_0;
	} else if (KbT <= 4e+216) {
		tmp = NaChar / (2.0 + (mu * (((EAccept + (Vef + Ev)) / (mu * KbT)) + (-1.0 / KbT))));
	} else {
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    if (kbt <= (-7.5d-105)) then
        tmp = t_0
    else if (kbt <= 4d+216) then
        tmp = nachar / (2.0d0 + (mu * (((eaccept + (vef + ev)) / (mu * kbt)) + ((-1.0d0) / kbt))))
    else
        tmp = t_0 + ((-0.25d0) * (mu * ((ndchar - nachar) / kbt)))
    end if
    code = tmp
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) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -7.5e-105) {
		tmp = t_0;
	} else if (KbT <= 4e+216) {
		tmp = NaChar / (2.0 + (mu * (((EAccept + (Vef + Ev)) / (mu * KbT)) + (-1.0 / KbT))));
	} else {
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	tmp = 0
	if KbT <= -7.5e-105:
		tmp = t_0
	elif KbT <= 4e+216:
		tmp = NaChar / (2.0 + (mu * (((EAccept + (Vef + Ev)) / (mu * KbT)) + (-1.0 / KbT))))
	else:
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	tmp = 0.0
	if (KbT <= -7.5e-105)
		tmp = t_0;
	elseif (KbT <= 4e+216)
		tmp = Float64(NaChar / Float64(2.0 + Float64(mu * Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) / Float64(mu * KbT)) + Float64(-1.0 / KbT)))));
	else
		tmp = Float64(t_0 + Float64(-0.25 * Float64(mu * Float64(Float64(NdChar - NaChar) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	tmp = 0.0;
	if (KbT <= -7.5e-105)
		tmp = t_0;
	elseif (KbT <= 4e+216)
		tmp = NaChar / (2.0 + (mu * (((EAccept + (Vef + Ev)) / (mu * KbT)) + (-1.0 / KbT))));
	else
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -7.5e-105], t$95$0, If[LessEqual[KbT, 4e+216], N[(NaChar / N[(2.0 + N[(mu * N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / N[(mu * KbT), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(-0.25 * N[(mu * N[(N[(NdChar - NaChar), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -7.5000000000000006e-105

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 37.1%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   6. Step-by-step derivation

      1. distribute-lft-out 37.1%

         \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   7. Simplified 37.1%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   if -7.5000000000000006e-105 < KbT < 4.0000000000000001e216

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 64.6%

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

   6. Taylor expanded in KbT around inf 20.5%

      \[\leadsto \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   7. Taylor expanded in KbT around -inf 23.2%

      \[\leadsto \frac{NaChar}{\color{blue}{2 + -1 \cdot \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 23.2%

         \[\leadsto \frac{NaChar}{2 + \color{blue}{\left(-\frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}\right)}} \]

      2. unsub-neg 23.2%

         \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]

      3. sub-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) + \left(--1 \cdot mu\right)}}{KbT}} \]

      4. associate-+r+ 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + -1 \cdot Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      5. mul-1-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + \color{blue}{\left(-Vef\right)}\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      6. unsub-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) - Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      7. mul-1-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + \color{blue}{\left(-Ev\right)}\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      8. unsub-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\color{blue}{\left(-1 \cdot EAccept - Ev\right)} - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      9. mul-1-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\color{blue}{\left(-EAccept\right)} - Ev\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      10. mul-1-neg 23.2%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \left(-\color{blue}{\left(-mu\right)}\right)}{KbT}} \]

      11. remove-double-neg 23.2%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \color{blue}{mu}}{KbT}} \]

   9. Simplified 23.2%

      \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + mu}{KbT}}} \]

   10. Taylor expanded in mu around inf 27.1%

       \[\leadsto \frac{NaChar}{2 - \color{blue}{mu \cdot \left(-1 \cdot \frac{EAccept + \left(Ev + Vef\right)}{KbT \cdot mu} + \frac{1}{KbT}\right)}} \]
   11. Step-by-step derivation

       1. +-commutative 27.1%

          \[\leadsto \frac{NaChar}{2 - mu \cdot \color{blue}{\left(\frac{1}{KbT} + -1 \cdot \frac{EAccept + \left(Ev + Vef\right)}{KbT \cdot mu}\right)}} \]

       2. mul-1-neg 27.1%

          \[\leadsto \frac{NaChar}{2 - mu \cdot \left(\frac{1}{KbT} + \color{blue}{\left(-\frac{EAccept + \left(Ev + Vef\right)}{KbT \cdot mu}\right)}\right)} \]

       3. unsub-neg 27.1%

          \[\leadsto \frac{NaChar}{2 - mu \cdot \color{blue}{\left(\frac{1}{KbT} - \frac{EAccept + \left(Ev + Vef\right)}{KbT \cdot mu}\right)}} \]

   12. Simplified 27.1%

       \[\leadsto \frac{NaChar}{2 - \color{blue}{mu \cdot \left(\frac{1}{KbT} - \frac{EAccept + \left(Ev + Vef\right)}{KbT \cdot mu}\right)}} \]

   if 4.0000000000000001e216 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)\right) + 0.25 \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)}{KbT} + \left(0.5 \cdot NaChar + 0.5 \cdot NdChar\right)} \]

   7. Simplified 45.6%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right) - \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + Ev\right) + \left(Vef - mu\right)\right) + NdChar \cdot \left(\left(Vef + EDonor\right) + \left(mu - Ec\right)\right)\right)}{KbT}} \]

   8. Taylor expanded in mu around -inf 78.2%

      \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{-0.25 \cdot \frac{mu \cdot \left(NaChar + -1 \cdot NdChar\right)}{KbT}} \]
   9. Step-by-step derivation

      1. associate-/l* 78.8%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - -0.25 \cdot \color{blue}{\left(mu \cdot \frac{NaChar + -1 \cdot NdChar}{KbT}\right)} \]

      2. mul-1-neg 78.8%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - -0.25 \cdot \left(mu \cdot \frac{NaChar + \color{blue}{\left(-NdChar\right)}}{KbT}\right) \]

      3. sub-neg 78.8%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - -0.25 \cdot \left(mu \cdot \frac{\color{blue}{NaChar - NdChar}}{KbT}\right) \]

   10. Simplified 78.8%

       \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{-0.25 \cdot \left(mu \cdot \frac{NaChar - NdChar}{KbT}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 33.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -7.5 \cdot 10^{-105}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;KbT \leq 4 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{2 + mu \cdot \left(\frac{EAccept + \left(Vef + Ev\right)}{mu \cdot KbT} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) + -0.25 \cdot \left(mu \cdot \frac{NdChar - NaChar}{KbT}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 32.7% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{if}\;KbT \leq -1.85 \cdot 10^{+74}:\\ \;\;\;\;t\_0 - 0.25 \cdot \left(Ev \cdot \frac{NaChar}{KbT}\right)\\ \mathbf{elif}\;KbT \leq 7.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev \cdot \left(\frac{\left(Vef + EAccept\right) - mu}{Ev} + 1\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar))))
   (if (<= KbT -1.85e+74)
     (- t_0 (* 0.25 (* Ev (/ NaChar KbT))))
     (if (<= KbT 7.2e-31)
       (/ NaChar (+ 2.0 (/ (* Ev (+ (/ (- (+ Vef EAccept) mu) Ev) 1.0)) KbT)))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -1.85e+74) {
		tmp = t_0 - (0.25 * (Ev * (NaChar / KbT)));
	} else if (KbT <= 7.2e-31) {
		tmp = NaChar / (2.0 + ((Ev * ((((Vef + EAccept) - mu) / Ev) + 1.0)) / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    if (kbt <= (-1.85d+74)) then
        tmp = t_0 - (0.25d0 * (ev * (nachar / kbt)))
    else if (kbt <= 7.2d-31) then
        tmp = nachar / (2.0d0 + ((ev * ((((vef + eaccept) - mu) / ev) + 1.0d0)) / kbt))
    else
        tmp = t_0
    end if
    code = tmp
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) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -1.85e+74) {
		tmp = t_0 - (0.25 * (Ev * (NaChar / KbT)));
	} else if (KbT <= 7.2e-31) {
		tmp = NaChar / (2.0 + ((Ev * ((((Vef + EAccept) - mu) / Ev) + 1.0)) / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	tmp = 0
	if KbT <= -1.85e+74:
		tmp = t_0 - (0.25 * (Ev * (NaChar / KbT)))
	elif KbT <= 7.2e-31:
		tmp = NaChar / (2.0 + ((Ev * ((((Vef + EAccept) - mu) / Ev) + 1.0)) / KbT))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	tmp = 0.0
	if (KbT <= -1.85e+74)
		tmp = Float64(t_0 - Float64(0.25 * Float64(Ev * Float64(NaChar / KbT))));
	elseif (KbT <= 7.2e-31)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(Ev * Float64(Float64(Float64(Float64(Vef + EAccept) - mu) / Ev) + 1.0)) / KbT)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	tmp = 0.0;
	if (KbT <= -1.85e+74)
		tmp = t_0 - (0.25 * (Ev * (NaChar / KbT)));
	elseif (KbT <= 7.2e-31)
		tmp = NaChar / (2.0 + ((Ev * ((((Vef + EAccept) - mu) / Ev) + 1.0)) / KbT));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -1.85e+74], N[(t$95$0 - N[(0.25 * N[(Ev * N[(NaChar / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 7.2e-31], N[(NaChar / N[(2.0 + N[(N[(Ev * N[(N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / Ev), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.8500000000000001e74

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.7%

      \[\leadsto \color{blue}{-1 \cdot \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)\right) + 0.25 \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)}{KbT} + \left(0.5 \cdot NaChar + 0.5 \cdot NdChar\right)} \]

   7. Simplified 31.7%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right) - \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + Ev\right) + \left(Vef - mu\right)\right) + NdChar \cdot \left(\left(Vef + EDonor\right) + \left(mu - Ec\right)\right)\right)}{KbT}} \]

   8. Taylor expanded in Ev around inf 45.1%

      \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{0.25 \cdot \frac{Ev \cdot NaChar}{KbT}} \]
   9. Step-by-step derivation

      1. associate-/l* 49.9%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - 0.25 \cdot \color{blue}{\left(Ev \cdot \frac{NaChar}{KbT}\right)} \]

   10. Simplified 49.9%

       \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{0.25 \cdot \left(Ev \cdot \frac{NaChar}{KbT}\right)} \]

   if -1.8500000000000001e74 < KbT < 7.20000000000000007e-31

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 65.8%

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

   6. Taylor expanded in KbT around inf 19.2%

      \[\leadsto \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   7. Taylor expanded in KbT around -inf 22.3%

      \[\leadsto \frac{NaChar}{\color{blue}{2 + -1 \cdot \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 22.3%

         \[\leadsto \frac{NaChar}{2 + \color{blue}{\left(-\frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}\right)}} \]

      2. unsub-neg 22.3%

         \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]

      3. sub-neg 22.3%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) + \left(--1 \cdot mu\right)}}{KbT}} \]

      4. associate-+r+ 22.3%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + -1 \cdot Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      5. mul-1-neg 22.3%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + \color{blue}{\left(-Vef\right)}\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      6. unsub-neg 22.3%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) - Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      7. mul-1-neg 22.3%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + \color{blue}{\left(-Ev\right)}\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      8. unsub-neg 22.3%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\color{blue}{\left(-1 \cdot EAccept - Ev\right)} - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      9. mul-1-neg 22.3%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\color{blue}{\left(-EAccept\right)} - Ev\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      10. mul-1-neg 22.3%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \left(-\color{blue}{\left(-mu\right)}\right)}{KbT}} \]

      11. remove-double-neg 22.3%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \color{blue}{mu}}{KbT}} \]

   9. Simplified 22.3%

      \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + mu}{KbT}}} \]

   10. Taylor expanded in Ev around -inf 24.3%

       \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{-1 \cdot \left(Ev \cdot \left(1 + -1 \cdot \frac{mu - \left(EAccept + Vef\right)}{Ev}\right)\right)}}{KbT}} \]
   11. Step-by-step derivation

       1. associate-*r* 24.3%

          \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(-1 \cdot Ev\right) \cdot \left(1 + -1 \cdot \frac{mu - \left(EAccept + Vef\right)}{Ev}\right)}}{KbT}} \]

       2. mul-1-neg 24.3%

          \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(-Ev\right)} \cdot \left(1 + -1 \cdot \frac{mu - \left(EAccept + Vef\right)}{Ev}\right)}{KbT}} \]

       3. mul-1-neg 24.3%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(-Ev\right) \cdot \left(1 + \color{blue}{\left(-\frac{mu - \left(EAccept + Vef\right)}{Ev}\right)}\right)}{KbT}} \]

       4. unsub-neg 24.3%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(-Ev\right) \cdot \color{blue}{\left(1 - \frac{mu - \left(EAccept + Vef\right)}{Ev}\right)}}{KbT}} \]

       5. +-commutative 24.3%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(-Ev\right) \cdot \left(1 - \frac{mu - \color{blue}{\left(Vef + EAccept\right)}}{Ev}\right)}{KbT}} \]

   12. Simplified 24.3%

       \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(-Ev\right) \cdot \left(1 - \frac{mu - \left(Vef + EAccept\right)}{Ev}\right)}}{KbT}} \]

   if 7.20000000000000007e-31 < KbT

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 33.9%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   6. Step-by-step derivation

      1. distribute-lft-out 33.9%

         \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   7. Simplified 33.9%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.85 \cdot 10^{+74}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) - 0.25 \cdot \left(Ev \cdot \frac{NaChar}{KbT}\right)\\ \mathbf{elif}\;KbT \leq 7.2 \cdot 10^{-31}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev \cdot \left(\frac{\left(Vef + EAccept\right) - mu}{Ev} + 1\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 30.7% accurate, 8.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{if}\;KbT \leq -6.5 \cdot 10^{-105}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;KbT \leq 4 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{mu \cdot \left(\frac{EAccept + \left(Vef + Ev\right)}{mu} + -1\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + -0.25 \cdot \left(mu \cdot \frac{NdChar - NaChar}{KbT}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar))))
   (if (<= KbT -6.5e-105)
     t_0
     (if (<= KbT 4e+216)
       (/ NaChar (+ 2.0 (/ (* mu (+ (/ (+ EAccept (+ Vef Ev)) mu) -1.0)) KbT)))
       (+ t_0 (* -0.25 (* mu (/ (- NdChar NaChar) KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -6.5e-105) {
		tmp = t_0;
	} else if (KbT <= 4e+216) {
		tmp = NaChar / (2.0 + ((mu * (((EAccept + (Vef + Ev)) / mu) + -1.0)) / KbT));
	} else {
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)));
	}
	return tmp;
}

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
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    if (kbt <= (-6.5d-105)) then
        tmp = t_0
    else if (kbt <= 4d+216) then
        tmp = nachar / (2.0d0 + ((mu * (((eaccept + (vef + ev)) / mu) + (-1.0d0))) / kbt))
    else
        tmp = t_0 + ((-0.25d0) * (mu * ((ndchar - nachar) / kbt)))
    end if
    code = tmp
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) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double tmp;
	if (KbT <= -6.5e-105) {
		tmp = t_0;
	} else if (KbT <= 4e+216) {
		tmp = NaChar / (2.0 + ((mu * (((EAccept + (Vef + Ev)) / mu) + -1.0)) / KbT));
	} else {
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	tmp = 0
	if KbT <= -6.5e-105:
		tmp = t_0
	elif KbT <= 4e+216:
		tmp = NaChar / (2.0 + ((mu * (((EAccept + (Vef + Ev)) / mu) + -1.0)) / KbT))
	else:
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	tmp = 0.0
	if (KbT <= -6.5e-105)
		tmp = t_0;
	elseif (KbT <= 4e+216)
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(mu * Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) / mu) + -1.0)) / KbT)));
	else
		tmp = Float64(t_0 + Float64(-0.25 * Float64(mu * Float64(Float64(NdChar - NaChar) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	tmp = 0.0;
	if (KbT <= -6.5e-105)
		tmp = t_0;
	elseif (KbT <= 4e+216)
		tmp = NaChar / (2.0 + ((mu * (((EAccept + (Vef + Ev)) / mu) + -1.0)) / KbT));
	else
		tmp = t_0 + (-0.25 * (mu * ((NdChar - NaChar) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -6.5e-105], t$95$0, If[LessEqual[KbT, 4e+216], N[(NaChar / N[(2.0 + N[(N[(mu * N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(-0.25 * N[(mu * N[(N[(NdChar - NaChar), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -6.50000000000000006e-105

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 37.1%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   6. Step-by-step derivation

      1. distribute-lft-out 37.1%

         \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   7. Simplified 37.1%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   if -6.50000000000000006e-105 < KbT < 4.0000000000000001e216

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 64.6%

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

   6. Taylor expanded in KbT around inf 20.5%

      \[\leadsto \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   7. Taylor expanded in KbT around -inf 23.2%

      \[\leadsto \frac{NaChar}{\color{blue}{2 + -1 \cdot \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 23.2%

         \[\leadsto \frac{NaChar}{2 + \color{blue}{\left(-\frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}\right)}} \]

      2. unsub-neg 23.2%

         \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]

      3. sub-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) + \left(--1 \cdot mu\right)}}{KbT}} \]

      4. associate-+r+ 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + -1 \cdot Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      5. mul-1-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + \color{blue}{\left(-Vef\right)}\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      6. unsub-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) - Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      7. mul-1-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + \color{blue}{\left(-Ev\right)}\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      8. unsub-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\color{blue}{\left(-1 \cdot EAccept - Ev\right)} - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      9. mul-1-neg 23.2%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\color{blue}{\left(-EAccept\right)} - Ev\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      10. mul-1-neg 23.2%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \left(-\color{blue}{\left(-mu\right)}\right)}{KbT}} \]

      11. remove-double-neg 23.2%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \color{blue}{mu}}{KbT}} \]

   9. Simplified 23.2%

      \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + mu}{KbT}}} \]

   10. Taylor expanded in mu around inf 25.0%

       \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{mu \cdot \left(1 + -1 \cdot \frac{EAccept + \left(Ev + Vef\right)}{mu}\right)}}{KbT}} \]
   11. Step-by-step derivation

       1. mul-1-neg 25.0%

          \[\leadsto \frac{NaChar}{2 - \frac{mu \cdot \left(1 + \color{blue}{\left(-\frac{EAccept + \left(Ev + Vef\right)}{mu}\right)}\right)}{KbT}} \]

       2. unsub-neg 25.0%

          \[\leadsto \frac{NaChar}{2 - \frac{mu \cdot \color{blue}{\left(1 - \frac{EAccept + \left(Ev + Vef\right)}{mu}\right)}}{KbT}} \]

   12. Simplified 25.0%

       \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{mu \cdot \left(1 - \frac{EAccept + \left(Ev + Vef\right)}{mu}\right)}}{KbT}} \]

   if 4.0000000000000001e216 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 45.6%

      \[\leadsto \color{blue}{-1 \cdot \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)\right) + 0.25 \cdot \left(NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)\right)}{KbT} + \left(0.5 \cdot NaChar + 0.5 \cdot NdChar\right)} \]

   7. Simplified 45.6%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right) - \frac{0.25 \cdot \left(NaChar \cdot \left(\left(EAccept + Ev\right) + \left(Vef - mu\right)\right) + NdChar \cdot \left(\left(Vef + EDonor\right) + \left(mu - Ec\right)\right)\right)}{KbT}} \]

   8. Taylor expanded in mu around -inf 78.2%

      \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{-0.25 \cdot \frac{mu \cdot \left(NaChar + -1 \cdot NdChar\right)}{KbT}} \]
   9. Step-by-step derivation

      1. associate-/l* 78.8%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - -0.25 \cdot \color{blue}{\left(mu \cdot \frac{NaChar + -1 \cdot NdChar}{KbT}\right)} \]

      2. mul-1-neg 78.8%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - -0.25 \cdot \left(mu \cdot \frac{NaChar + \color{blue}{\left(-NdChar\right)}}{KbT}\right) \]

      3. sub-neg 78.8%

         \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - -0.25 \cdot \left(mu \cdot \frac{\color{blue}{NaChar - NdChar}}{KbT}\right) \]

   10. Simplified 78.8%

       \[\leadsto 0.5 \cdot \left(NaChar + NdChar\right) - \color{blue}{-0.25 \cdot \left(mu \cdot \frac{NaChar - NdChar}{KbT}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -6.5 \cdot 10^{-105}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;KbT \leq 4 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{mu \cdot \left(\frac{EAccept + \left(Vef + Ev\right)}{mu} + -1\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) + -0.25 \cdot \left(mu \cdot \frac{NdChar - NaChar}{KbT}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 31.2% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -3.2 \cdot 10^{-109} \lor \neg \left(KbT \leq 7 \cdot 10^{-129}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -3.2e-109) (not (<= KbT 7e-129)))
   (* 0.5 (+ NdChar NaChar))
   (/ NaChar (+ 2.0 (/ (- (+ Vef (+ Ev EAccept)) mu) KbT)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -3.2e-109) || !(KbT <= 7e-129)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (2.0 + (((Vef + (Ev + EAccept)) - mu) / KbT));
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((kbt <= (-3.2d-109)) .or. (.not. (kbt <= 7d-129))) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = nachar / (2.0d0 + (((vef + (ev + eaccept)) - mu) / kbt))
    end if
    code = tmp
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) {
	double tmp;
	if ((KbT <= -3.2e-109) || !(KbT <= 7e-129)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (2.0 + (((Vef + (Ev + EAccept)) - mu) / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -3.2e-109) or not (KbT <= 7e-129):
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NaChar / (2.0 + (((Vef + (Ev + EAccept)) - mu) / KbT))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -3.2e-109) || !(KbT <= 7e-129))
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NaChar / Float64(2.0 + Float64(Float64(Float64(Vef + Float64(Ev + EAccept)) - mu) / KbT)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -3.2e-109) || ~((KbT <= 7e-129)))
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NaChar / (2.0 + (((Vef + (Ev + EAccept)) - mu) / KbT));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -3.2e-109], N[Not[LessEqual[KbT, 7e-129]], $MachinePrecision]], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(2.0 + N[(N[(N[(Vef + N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -3.2000000000000002e-109 or 6.9999999999999995e-129 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.2%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   6. Step-by-step derivation

      1. distribute-lft-out 31.2%

         \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   7. Simplified 31.2%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   if -3.2000000000000002e-109 < KbT < 6.9999999999999995e-129

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 71.8%

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

   6. Taylor expanded in KbT around inf 26.6%

      \[\leadsto \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   7. Taylor expanded in KbT around -inf 30.8%

      \[\leadsto \frac{NaChar}{\color{blue}{2 + -1 \cdot \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 + \color{blue}{\left(-\frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}\right)}} \]

      2. unsub-neg 30.8%

         \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]

      3. sub-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) + \left(--1 \cdot mu\right)}}{KbT}} \]

      4. associate-+r+ 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + -1 \cdot Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      5. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + \color{blue}{\left(-Vef\right)}\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      6. unsub-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) - Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      7. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + \color{blue}{\left(-Ev\right)}\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      8. unsub-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\color{blue}{\left(-1 \cdot EAccept - Ev\right)} - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      9. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\color{blue}{\left(-EAccept\right)} - Ev\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      10. mul-1-neg 30.8%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \left(-\color{blue}{\left(-mu\right)}\right)}{KbT}} \]

      11. remove-double-neg 30.8%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \color{blue}{mu}}{KbT}} \]

   9. Simplified 30.8%

      \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + mu}{KbT}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.2 \cdot 10^{-109} \lor \neg \left(KbT \leq 7 \cdot 10^{-129}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 31.2% accurate, 10.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.2 \cdot 10^{-110} \lor \neg \left(KbT \leq 1.05 \cdot 10^{-128}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -2.2e-110) (not (<= KbT 1.05e-128)))
   (* 0.5 (+ NdChar NaChar))
   (/ NaChar (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -2.2e-110) || !(KbT <= 1.05e-128)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (((EAccept + (Vef + Ev)) - mu) / KbT);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((kbt <= (-2.2d-110)) .or. (.not. (kbt <= 1.05d-128))) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = nachar / (((eaccept + (vef + ev)) - mu) / kbt)
    end if
    code = tmp
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) {
	double tmp;
	if ((KbT <= -2.2e-110) || !(KbT <= 1.05e-128)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (((EAccept + (Vef + Ev)) - mu) / KbT);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -2.2e-110) or not (KbT <= 1.05e-128):
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NaChar / (((EAccept + (Vef + Ev)) - mu) / KbT)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -2.2e-110) || !(KbT <= 1.05e-128))
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NaChar / Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -2.2e-110) || ~((KbT <= 1.05e-128)))
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NaChar / (((EAccept + (Vef + Ev)) - mu) / KbT);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -2.2e-110], N[Not[LessEqual[KbT, 1.05e-128]], $MachinePrecision]], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -2.1999999999999999e-110 or 1.0500000000000001e-128 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.2%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   6. Step-by-step derivation

      1. distribute-lft-out 31.2%

         \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   7. Simplified 31.2%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   if -2.1999999999999999e-110 < KbT < 1.0500000000000001e-128

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 71.8%

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

   6. Taylor expanded in KbT around inf 26.6%

      \[\leadsto \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   7. Taylor expanded in KbT around 0 30.8%

      \[\leadsto \frac{NaChar}{\color{blue}{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 31.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.2 \cdot 10^{-110} \lor \neg \left(KbT \leq 1.05 \cdot 10^{-128}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 29.2% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.4 \cdot 10^{-109} \lor \neg \left(KbT \leq 6.5 \cdot 10^{-130}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -1.4e-109) (not (<= KbT 6.5e-130)))
   (* 0.5 (+ NdChar NaChar))
   (/ NaChar (+ (/ Vef KbT) 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -1.4e-109) || !(KbT <= 6.5e-130)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / ((Vef / KbT) + 2.0);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((kbt <= (-1.4d-109)) .or. (.not. (kbt <= 6.5d-130))) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = nachar / ((vef / kbt) + 2.0d0)
    end if
    code = tmp
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) {
	double tmp;
	if ((KbT <= -1.4e-109) || !(KbT <= 6.5e-130)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / ((Vef / KbT) + 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -1.4e-109) or not (KbT <= 6.5e-130):
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NaChar / ((Vef / KbT) + 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -1.4e-109) || !(KbT <= 6.5e-130))
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -1.4e-109) || ~((KbT <= 6.5e-130)))
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NaChar / ((Vef / KbT) + 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -1.4e-109], N[Not[LessEqual[KbT, 6.5e-130]], $MachinePrecision]], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -1.39999999999999989e-109 or 6.5000000000000002e-130 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.2%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   6. Step-by-step derivation

      1. distribute-lft-out 31.2%

         \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   7. Simplified 31.2%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   if -1.39999999999999989e-109 < KbT < 6.5000000000000002e-130

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 71.8%

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

   6. Taylor expanded in KbT around inf 26.6%

      \[\leadsto \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   7. Taylor expanded in KbT around -inf 30.8%

      \[\leadsto \frac{NaChar}{\color{blue}{2 + -1 \cdot \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 + \color{blue}{\left(-\frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}\right)}} \]

      2. unsub-neg 30.8%

         \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]

      3. sub-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) + \left(--1 \cdot mu\right)}}{KbT}} \]

      4. associate-+r+ 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + -1 \cdot Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      5. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + \color{blue}{\left(-Vef\right)}\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      6. unsub-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) - Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      7. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + \color{blue}{\left(-Ev\right)}\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      8. unsub-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\color{blue}{\left(-1 \cdot EAccept - Ev\right)} - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      9. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\color{blue}{\left(-EAccept\right)} - Ev\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      10. mul-1-neg 30.8%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \left(-\color{blue}{\left(-mu\right)}\right)}{KbT}} \]

      11. remove-double-neg 30.8%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \color{blue}{mu}}{KbT}} \]

   9. Simplified 30.8%

      \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + mu}{KbT}}} \]

   10. Taylor expanded in Vef around inf 24.3%

       \[\leadsto \frac{NaChar}{2 - \color{blue}{-1 \cdot \frac{Vef}{KbT}}} \]
   11. Step-by-step derivation

       1. associate-*r/ 24.3%

          \[\leadsto \frac{NaChar}{2 - \color{blue}{\frac{-1 \cdot Vef}{KbT}}} \]

       2. mul-1-neg 24.3%

          \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{-Vef}}{KbT}} \]

   12. Simplified 24.3%

       \[\leadsto \frac{NaChar}{2 - \color{blue}{\frac{-Vef}{KbT}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.4 \cdot 10^{-109} \lor \neg \left(KbT \leq 6.5 \cdot 10^{-130}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 28.9% accurate, 15.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -9.5 \cdot 10^{-107} \lor \neg \left(KbT \leq 7.1 \cdot 10^{-130}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -9.5e-107) (not (<= KbT 7.1e-130)))
   (* 0.5 (+ NdChar NaChar))
   (/ NaChar (/ Vef KbT))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -9.5e-107) || !(KbT <= 7.1e-130)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (Vef / KbT);
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((kbt <= (-9.5d-107)) .or. (.not. (kbt <= 7.1d-130))) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = nachar / (vef / kbt)
    end if
    code = tmp
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) {
	double tmp;
	if ((KbT <= -9.5e-107) || !(KbT <= 7.1e-130)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (Vef / KbT);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -9.5e-107) or not (KbT <= 7.1e-130):
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NaChar / (Vef / KbT)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -9.5e-107) || !(KbT <= 7.1e-130))
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NaChar / Float64(Vef / KbT));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -9.5e-107) || ~((KbT <= 7.1e-130)))
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NaChar / (Vef / KbT);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -9.5e-107], N[Not[LessEqual[KbT, 7.1e-130]], $MachinePrecision]], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -9.4999999999999999e-107 or 7.1000000000000001e-130 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 31.2%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   6. Step-by-step derivation

      1. distribute-lft-out 31.2%

         \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   7. Simplified 31.2%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   if -9.4999999999999999e-107 < KbT < 7.1000000000000001e-130

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 71.8%

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

   6. Taylor expanded in KbT around inf 26.6%

      \[\leadsto \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]

   7. Taylor expanded in KbT around -inf 30.8%

      \[\leadsto \frac{NaChar}{\color{blue}{2 + -1 \cdot \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]
   8. Step-by-step derivation

      1. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 + \color{blue}{\left(-\frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}\right)}} \]

      2. unsub-neg 30.8%

         \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) - -1 \cdot mu}{KbT}}} \]

      3. sub-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(-1 \cdot EAccept + \left(-1 \cdot Ev + -1 \cdot Vef\right)\right) + \left(--1 \cdot mu\right)}}{KbT}} \]

      4. associate-+r+ 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + -1 \cdot Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      5. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) + \color{blue}{\left(-Vef\right)}\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      6. unsub-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\color{blue}{\left(\left(-1 \cdot EAccept + -1 \cdot Ev\right) - Vef\right)} + \left(--1 \cdot mu\right)}{KbT}} \]

      7. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(-1 \cdot EAccept + \color{blue}{\left(-Ev\right)}\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      8. unsub-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\color{blue}{\left(-1 \cdot EAccept - Ev\right)} - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      9. mul-1-neg 30.8%

         \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\color{blue}{\left(-EAccept\right)} - Ev\right) - Vef\right) + \left(--1 \cdot mu\right)}{KbT}} \]

      10. mul-1-neg 30.8%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \left(-\color{blue}{\left(-mu\right)}\right)}{KbT}} \]

      11. remove-double-neg 30.8%

          \[\leadsto \frac{NaChar}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + \color{blue}{mu}}{KbT}} \]

   9. Simplified 30.8%

      \[\leadsto \frac{NaChar}{\color{blue}{2 - \frac{\left(\left(\left(-EAccept\right) - Ev\right) - Vef\right) + mu}{KbT}}} \]

   10. Taylor expanded in Vef around inf 23.8%

       \[\leadsto \frac{NaChar}{\color{blue}{\frac{Vef}{KbT}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 28.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -9.5 \cdot 10^{-107} \lor \neg \left(KbT \leq 7.1 \cdot 10^{-130}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 22.2% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.6 \cdot 10^{-79} \lor \neg \left(NaChar \leq 1.35 \cdot 10^{-96}\right):\\ \;\;\;\;\frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.6e-79) (not (<= NaChar 1.35e-96)))
   (/ NaChar 2.0)
   (* NdChar 0.5)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.6e-79) || !(NaChar <= 1.35e-96)) {
		tmp = NaChar / 2.0;
	} else {
		tmp = NdChar * 0.5;
	}
	return tmp;
}

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
    real(8) :: tmp
    if ((nachar <= (-2.6d-79)) .or. (.not. (nachar <= 1.35d-96))) then
        tmp = nachar / 2.0d0
    else
        tmp = ndchar * 0.5d0
    end if
    code = tmp
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) {
	double tmp;
	if ((NaChar <= -2.6e-79) || !(NaChar <= 1.35e-96)) {
		tmp = NaChar / 2.0;
	} else {
		tmp = NdChar * 0.5;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2.6e-79) or not (NaChar <= 1.35e-96):
		tmp = NaChar / 2.0
	else:
		tmp = NdChar * 0.5
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -2.6e-79) || !(NaChar <= 1.35e-96))
		tmp = Float64(NaChar / 2.0);
	else
		tmp = Float64(NdChar * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -2.6e-79) || ~((NaChar <= 1.35e-96)))
		tmp = NaChar / 2.0;
	else
		tmp = NdChar * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -2.6e-79], N[Not[LessEqual[NaChar, 1.35e-96]], $MachinePrecision]], N[(NaChar / 2.0), $MachinePrecision], N[(NdChar * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.59999999999999994e-79 or 1.35e-96 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 73.4%

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

   6. Taylor expanded in KbT around inf 20.1%

      \[\leadsto \frac{NaChar}{\color{blue}{2}} \]

   if -2.59999999999999994e-79 < NaChar < 1.35e-96

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 27.0%

      \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
   6. Step-by-step derivation

      1. distribute-lft-out 27.0%

         \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   7. Simplified 27.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

   8. Taylor expanded in NaChar around 0 26.0%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} \]
   9. Step-by-step derivation

      1. *-commutative 26.0%

         \[\leadsto \color{blue}{NdChar \cdot 0.5} \]

   10. Simplified 26.0%

       \[\leadsto \color{blue}{NdChar \cdot 0.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 22.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.6 \cdot 10^{-79} \lor \neg \left(NaChar \leq 1.35 \cdot 10^{-96}\right):\\ \;\;\;\;\frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.3% accurate, 45.8× speedup

Math

\[\begin{array}{l} \\ 0.5 \cdot \left(NdChar + NaChar\right) \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (* 0.5 (+ NdChar NaChar)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return 0.5 * (NdChar + NaChar);
}

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 = 0.5d0 * (ndchar + nachar)
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 0.5 * (NdChar + NaChar);
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return 0.5 * (NdChar + NaChar)

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(0.5 * Float64(NdChar + NaChar))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.5 * (NdChar + NaChar);
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 24.5%

   \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
6. Step-by-step derivation

   1. distribute-lft-out 24.5%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

7. Simplified 24.5%

   \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

8. Final simplification 24.5%

   \[\leadsto 0.5 \cdot \left(NdChar + NaChar\right) \]
9. Add Preprocessing

Alternative 20: 18.2% accurate, 76.3× speedup

Math

\[\begin{array}{l} \\ NdChar \cdot 0.5 \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (* NdChar 0.5))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return NdChar * 0.5;
}

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 * 0.5d0
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 * 0.5;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return NdChar * 0.5

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(NdChar * 0.5)
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = NdChar * 0.5;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(NdChar * 0.5), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 24.5%

   \[\leadsto \color{blue}{0.5 \cdot NaChar + 0.5 \cdot NdChar} \]
6. Step-by-step derivation

   1. distribute-lft-out 24.5%

      \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

7. Simplified 24.5%

   \[\leadsto \color{blue}{0.5 \cdot \left(NaChar + NdChar\right)} \]

8. Taylor expanded in NaChar around 0 16.1%

   \[\leadsto \color{blue}{0.5 \cdot NdChar} \]
9. Step-by-step derivation

   1. *-commutative 16.1%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} \]

10. Simplified 16.1%

    \[\leadsto \color{blue}{NdChar \cdot 0.5} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024150 
(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))))))