Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 24.1s

Alternatives: 26

Speedup: 1.0×

• could not determine a ground truth

  1. branch3914 = -2.4964581626863026e-123
  2. NdChar = 1.9108629617118788e-50
  3. Ec = -2.193736845378214e-279
  4. Vef = 9.93364369698154e+244
  5. EDonor = -3.366460436352403e-290
  6. mu = 1.9175144496338898e+189
  7. KbT = -2.3129727200367476e-248
  8. NaChar = 5.84214470427292e-123
  9. Ev = -1.1855441547554696e-96
  10. EAccept = -3.589301733461895e-255

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

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
  (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev 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(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - 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(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - 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(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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%

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

4. Final simplification 99.9%

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

Alternative 2: 69.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;Ec \leq -7.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + t_2\\ \mathbf{elif}\;Ec \leq 8.2 \cdot 10^{-79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ec \leq 7.2 \cdot 10^{-32}:\\ \;\;\;\;t_1 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ec \leq 3.25 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))))
   (if (<= Ec -7.8e-96)
     (+ (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))) t_2)
     (if (<= Ec 8.2e-79)
       t_0
       (if (<= Ec 7.2e-32)
         (+ t_1 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
         (if (<= Ec 3.25e+72) t_0 (+ t_1 t_2)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	double t_1 = NaChar / (1.0 + exp((Ev / KbT)));
	double t_2 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (Ec <= -7.8e-96) {
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + t_2;
	} else if (Ec <= 8.2e-79) {
		tmp = t_0;
	} else if (Ec <= 7.2e-32) {
		tmp = t_1 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (Ec <= 3.25e+72) {
		tmp = t_0;
	} else {
		tmp = t_1 + t_2;
	}
	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) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    t_1 = nachar / (1.0d0 + exp((ev / kbt)))
    t_2 = ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))
    if (ec <= (-7.8d-96)) then
        tmp = (nachar / (1.0d0 + exp((-mu / kbt)))) + t_2
    else if (ec <= 8.2d-79) then
        tmp = t_0
    else if (ec <= 7.2d-32) then
        tmp = t_1 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (ec <= 3.25d+72) then
        tmp = t_0
    else
        tmp = t_1 + t_2
    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 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp((Ev / KbT)));
	double t_2 = NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (Ec <= -7.8e-96) {
		tmp = (NaChar / (1.0 + Math.exp((-mu / KbT)))) + t_2;
	} else if (Ec <= 8.2e-79) {
		tmp = t_0;
	} else if (Ec <= 7.2e-32) {
		tmp = t_1 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (Ec <= 3.25e+72) {
		tmp = t_0;
	} else {
		tmp = t_1 + t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	t_1 = NaChar / (1.0 + math.exp((Ev / KbT)))
	t_2 = NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))
	tmp = 0
	if Ec <= -7.8e-96:
		tmp = (NaChar / (1.0 + math.exp((-mu / KbT)))) + t_2
	elif Ec <= 8.2e-79:
		tmp = t_0
	elif Ec <= 7.2e-32:
		tmp = t_1 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif Ec <= 3.25e+72:
		tmp = t_0
	else:
		tmp = t_1 + t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT))))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))))
	tmp = 0.0
	if (Ec <= -7.8e-96)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))) + t_2);
	elseif (Ec <= 8.2e-79)
		tmp = t_0;
	elseif (Ec <= 7.2e-32)
		tmp = Float64(t_1 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (Ec <= 3.25e+72)
		tmp = t_0;
	else
		tmp = Float64(t_1 + t_2);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	t_1 = NaChar / (1.0 + exp((Ev / KbT)));
	t_2 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	tmp = 0.0;
	if (Ec <= -7.8e-96)
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + t_2;
	elseif (Ec <= 8.2e-79)
		tmp = t_0;
	elseif (Ec <= 7.2e-32)
		tmp = t_1 + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (Ec <= 3.25e+72)
		tmp = t_0;
	else
		tmp = t_1 + t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ec, -7.8e-96], N[(N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision], If[LessEqual[Ec, 8.2e-79], t$95$0, If[LessEqual[Ec, 7.2e-32], N[(t$95$1 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ec, 3.25e+72], t$95$0, N[(t$95$1 + t$95$2), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ec < -7.7999999999999997e-96

   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%

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

   4. Taylor expanded in mu around inf 78.2%

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

      1. associate-*r/ 78.2%

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

      2. mul-1-neg 78.2%

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

   6. Simplified 78.2%

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

   7. Taylor expanded in EDonor around 0 73.6%

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

   if -7.7999999999999997e-96 < Ec < 8.19999999999999987e-79 or 7.19999999999999986e-32 < Ec < 3.2500000000000001e72

   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%

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

   4. Taylor expanded in mu around inf 78.6%

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

   if 8.19999999999999987e-79 < Ec < 7.19999999999999986e-32

   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%

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

   4. Taylor expanded in Ev around inf 87.8%

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

   5. Taylor expanded in EDonor around inf 87.8%

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

   if 3.2500000000000001e72 < Ec

   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%

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

   4. Taylor expanded in Ev around inf 77.2%

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

   5. Taylor expanded in EDonor around 0 73.4%

      \[\leadsto \frac{NdChar}{1 + \color{blue}{e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq -7.8 \cdot 10^{-96}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Ec \leq 8.2 \cdot 10^{-79}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ec \leq 7.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Ec \leq 3.25 \cdot 10^{+72}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]

Alternative 3: 72.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;EAccept \leq 1.15 \cdot 10^{-305}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.66 \cdot 10^{-155}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.7 \cdot 10^{+131}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))))
   (if (<= EAccept 1.15e-305)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= EAccept 1.66e-155)
       (+
        (/ NaChar (+ 1.0 (exp (/ (- mu) KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
       (if (<= EAccept 1.5e-83)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         (if (<= EAccept 3.7e+131)
           (+ t_0 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))
           (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept 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 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (EAccept <= 1.15e-305) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (EAccept <= 1.66e-155) {
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else if (EAccept <= 1.5e-83) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (EAccept <= 3.7e+131) {
		tmp = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / 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 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    if (eaccept <= 1.15d-305) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (eaccept <= 1.66d-155) then
        tmp = (nachar / (1.0d0 + exp((-mu / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else if (eaccept <= 1.5d-83) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (eaccept <= 3.7d+131) then
        tmp = t_0 + (nachar / (1.0d0 + exp((vef / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / 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 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (EAccept <= 1.15e-305) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (EAccept <= 1.66e-155) {
		tmp = (NaChar / (1.0 + Math.exp((-mu / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else if (EAccept <= 1.5e-83) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (EAccept <= 3.7e+131) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	tmp = 0
	if EAccept <= 1.15e-305:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif EAccept <= 1.66e-155:
		tmp = (NaChar / (1.0 + math.exp((-mu / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	elif EAccept <= 1.5e-83:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif EAccept <= 3.7e+131:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (EAccept <= 1.15e-305)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (EAccept <= 1.66e-155)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	elseif (EAccept <= 1.5e-83)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (EAccept <= 3.7e+131)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (EAccept <= 1.15e-305)
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (EAccept <= 1.66e-155)
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	elseif (EAccept <= 1.5e-83)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (EAccept <= 3.7e+131)
		tmp = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, 1.15e-305], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.66e-155], N[(N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.5e-83], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.7e+131], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if EAccept < 1.15e-305

   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%

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

   4. Taylor expanded in Ev around inf 71.1%

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

   if 1.15e-305 < EAccept < 1.65999999999999999e-155

   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%

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

   4. Taylor expanded in mu around inf 80.6%

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

      1. associate-*r/ 80.6%

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

      2. mul-1-neg 80.6%

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

   6. Simplified 80.6%

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

   7. Taylor expanded in EDonor around 0 73.6%

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

   if 1.65999999999999999e-155 < EAccept < 1.50000000000000005e-83

   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%

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

   4. Taylor expanded in mu around inf 76.1%

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

   if 1.50000000000000005e-83 < EAccept < 3.69999999999999995e131

   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%

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

   4. Taylor expanded in Vef around inf 86.0%

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

   if 3.69999999999999995e131 < EAccept

   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%

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

   4. Taylor expanded in EAccept around inf 75.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 1.15 \cdot 10^{-305}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.66 \cdot 10^{-155}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.5 \cdot 10^{-83}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.7 \cdot 10^{+131}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 4: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;EAccept \leq 1.1 \cdot 10^{-304}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.65 \cdot 10^{-159}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.42 \cdot 10^{-86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 5.6 \cdot 10^{+131}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))))
   (if (<= EAccept 1.1e-304)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= EAccept 1.65e-159)
       (+ t_0 (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
       (if (<= EAccept 1.42e-86)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         (if (<= EAccept 5.6e+131)
           (+ t_0 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))
           (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept 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 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (EAccept <= 1.1e-304) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (EAccept <= 1.65e-159) {
		tmp = t_0 + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (EAccept <= 1.42e-86) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (EAccept <= 5.6e+131) {
		tmp = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / 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 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    if (eaccept <= 1.1d-304) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (eaccept <= 1.65d-159) then
        tmp = t_0 + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (eaccept <= 1.42d-86) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (eaccept <= 5.6d+131) then
        tmp = t_0 + (nachar / (1.0d0 + exp((vef / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / 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 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (EAccept <= 1.1e-304) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (EAccept <= 1.65e-159) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (EAccept <= 1.42e-86) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (EAccept <= 5.6e+131) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	tmp = 0
	if EAccept <= 1.1e-304:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif EAccept <= 1.65e-159:
		tmp = t_0 + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif EAccept <= 1.42e-86:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif EAccept <= 5.6e+131:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (EAccept <= 1.1e-304)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (EAccept <= 1.65e-159)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (EAccept <= 1.42e-86)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (EAccept <= 5.6e+131)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (EAccept <= 1.1e-304)
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (EAccept <= 1.65e-159)
		tmp = t_0 + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (EAccept <= 1.42e-86)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (EAccept <= 5.6e+131)
		tmp = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, 1.1e-304], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.65e-159], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.42e-86], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 5.6e+131], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if EAccept < 1.1e-304

   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%

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

   4. Taylor expanded in Ev around inf 71.1%

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

   if 1.1e-304 < EAccept < 1.6500000000000001e-159

   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%

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

   4. Taylor expanded in mu around inf 79.1%

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

      1. associate-*r/ 79.1%

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

      2. mul-1-neg 79.1%

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

   6. Simplified 79.1%

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

   if 1.6500000000000001e-159 < EAccept < 1.42000000000000001e-86

   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%

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

   4. Taylor expanded in mu around inf 78.4%

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

   if 1.42000000000000001e-86 < EAccept < 5.6000000000000001e131

   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%

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

   4. Taylor expanded in Vef around inf 86.0%

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

   if 5.6000000000000001e131 < EAccept

   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%

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

   4. Taylor expanded in EAccept around inf 75.0%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 1.1 \cdot 10^{-304}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.65 \cdot 10^{-159}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.42 \cdot 10^{-86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 5.6 \cdot 10^{+131}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 5: 73.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;Ev \leq -8 \cdot 10^{+126} \lor \neg \left(Ev \leq -7 \cdot 10^{+82}\right) \land Ev \leq -3.7 \cdot 10^{+23}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))))
   (if (or (<= Ev -8e+126) (and (not (<= Ev -7e+82)) (<= Ev -3.7e+23)))
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept 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 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if ((Ev <= -8e+126) || (!(Ev <= -7e+82) && (Ev <= -3.7e+23))) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / 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 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    if ((ev <= (-8d+126)) .or. (.not. (ev <= (-7d+82))) .and. (ev <= (-3.7d+23))) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / 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 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if ((Ev <= -8e+126) || (!(Ev <= -7e+82) && (Ev <= -3.7e+23))) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	tmp = 0
	if (Ev <= -8e+126) or (not (Ev <= -7e+82) and (Ev <= -3.7e+23)):
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if ((Ev <= -8e+126) || (!(Ev <= -7e+82) && (Ev <= -3.7e+23)))
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if ((Ev <= -8e+126) || (~((Ev <= -7e+82)) && (Ev <= -3.7e+23)))
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[Ev, -8e+126], And[N[Not[LessEqual[Ev, -7e+82]], $MachinePrecision], LessEqual[Ev, -3.7e+23]]], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if Ev < -7.9999999999999994e126 or -7.0000000000000001e82 < Ev < -3.70000000000000013e23

   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%

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

   4. Taylor expanded in Ev around inf 91.5%

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

   if -7.9999999999999994e126 < Ev < -7.0000000000000001e82 or -3.70000000000000013e23 < Ev

   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%

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

   4. Taylor expanded in EAccept around inf 69.7%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -8 \cdot 10^{+126} \lor \neg \left(Ev \leq -7 \cdot 10^{+82}\right) \land Ev \leq -3.7 \cdot 10^{+23}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 6: 69.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq -1.6 \cdot 10^{-235}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept -1.6e-235)
   (+
    (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
    (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
   (if (<= EAccept 1.2e-66)
     (+
      (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
      (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
      (/ NaChar (+ 1.0 (exp (/ EAccept 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 (EAccept <= -1.6e-235) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else if (EAccept <= 1.2e-66) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((EAccept / 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 (eaccept <= (-1.6d-235)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else if (eaccept <= 1.2d-66) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / 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 (EAccept <= -1.6e-235) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else if (EAccept <= 1.2e-66) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= -1.6e-235:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	elif EAccept <= 1.2e-66:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= -1.6e-235)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	elseif (EAccept <= 1.2e-66)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= -1.6e-235)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	elseif (EAccept <= 1.2e-66)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, -1.6e-235], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.2e-66], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < -1.6000000000000001e-235

   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%

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

   4. Taylor expanded in Ev around inf 72.0%

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

   5. Taylor expanded in EDonor around 0 66.8%

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

   if -1.6000000000000001e-235 < EAccept < 1.20000000000000013e-66

   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%

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

   4. Taylor expanded in mu around inf 65.9%

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

   if 1.20000000000000013e-66 < EAccept

   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%

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

   4. Taylor expanded in EAccept around inf 71.8%

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

4. Final simplification 68.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -1.6 \cdot 10^{-235}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.2 \cdot 10^{-66}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 7: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;Ev \leq -1.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t_0\\ \mathbf{elif}\;Ev \leq 1.75 \cdot 10^{-89}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))))
   (if (<= Ev -1.2e+131)
     (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_0)
     (if (<= Ev 1.75e-89)
       (+ (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))) t_0)
       (+
        (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
        (/ NdChar (+ 1.0 (exp (/ EDonor 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 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (Ev <= -1.2e+131) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	} else if (Ev <= 1.75e-89) {
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + t_0;
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((EDonor / 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 = ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))
    if (ev <= (-1.2d+131)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + t_0
    else if (ev <= 1.75d-89) then
        tmp = (nachar / (1.0d0 + exp((-mu / kbt)))) + t_0
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / (1.0d0 + exp((edonor / 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 = NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)));
	double tmp;
	if (Ev <= -1.2e+131) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + t_0;
	} else if (Ev <= 1.75e-89) {
		tmp = (NaChar / (1.0 + Math.exp((-mu / KbT)))) + t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))
	tmp = 0
	if Ev <= -1.2e+131:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + t_0
	elif Ev <= 1.75e-89:
		tmp = (NaChar / (1.0 + math.exp((-mu / KbT)))) + t_0
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT))))
	tmp = 0.0
	if (Ev <= -1.2e+131)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + t_0);
	elseif (Ev <= 1.75e-89)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))) + t_0);
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)));
	tmp = 0.0;
	if (Ev <= -1.2e+131)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	elseif (Ev <= 1.75e-89)
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + t_0;
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -1.2e+131], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[Ev, 1.75e-89], N[(N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -1.2e131

   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%

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

   4. Taylor expanded in Ev around inf 92.7%

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

   5. Taylor expanded in EDonor around 0 83.0%

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

   if -1.2e131 < Ev < 1.74999999999999985e-89

   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%

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

   4. Taylor expanded in mu around inf 75.2%

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

      1. associate-*r/ 75.2%

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

      2. mul-1-neg 75.2%

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

   6. Simplified 75.2%

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

   7. Taylor expanded in EDonor around 0 70.7%

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

   if 1.74999999999999985e-89 < 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%

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

   4. Taylor expanded in EAccept around inf 65.6%

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

   5. Taylor expanded in EDonor around inf 49.3%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.2 \cdot 10^{+131}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Ev \leq 1.75 \cdot 10^{-89}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]

Alternative 8: 63.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5.5 \cdot 10^{-63} \lor \neg \left(NaChar \leq 9.2 \cdot 10^{-172}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -5.5e-63) (not (<= NaChar 9.2e-172)))
   (+
    (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
    (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT)))) (/ 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 ((NaChar <= -5.5e-63) || !(NaChar <= 9.2e-172)) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (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 ((nachar <= (-5.5d-63)) .or. (.not. (nachar <= 9.2d-172))) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (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 ((NaChar <= -5.5e-63) || !(NaChar <= 9.2e-172)) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -5.5e-63) or not (NaChar <= 9.2e-172):
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -5.5e-63) || !(NaChar <= 9.2e-172))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -5.5e-63) || ~((NaChar <= 9.2e-172)))
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -5.5e-63], N[Not[LessEqual[NaChar, 9.2e-172]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -5.50000000000000043e-63 or 9.1999999999999998e-172 < 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%

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

   4. Taylor expanded in Ev around inf 72.5%

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

   5. Taylor expanded in EDonor around 0 67.1%

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

   if -5.50000000000000043e-63 < NaChar < 9.1999999999999998e-172

   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%

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

   4. Taylor expanded in KbT around inf 72.9%

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

4. Final simplification 68.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.5 \cdot 10^{-63} \lor \neg \left(NaChar \leq 9.2 \cdot 10^{-172}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \]

Alternative 9: 62.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -7.8 \cdot 10^{+99}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -4.7 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -1.05 \cdot 10^{-115}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 3 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))))
   (if (<= NdChar -7.8e+99)
     (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))
     (if (<= NdChar -4.7e-91)
       (+
        (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
        (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
       (if (<= NdChar -1.05e-115)
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
          (/ NaChar (+ (/ Ev KbT) 2.0)))
         (if (<= NdChar 3e-52)
           (+
            (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
            (/ NdChar (+ 1.0 (+ 1.0 (/ mu KbT)))))
           (+
            t_0
            (/
             NaChar
             (-
              (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))))
              (/ mu 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 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -7.8e+99) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -4.7e-91) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else if (NdChar <= -1.05e-115) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= 3e-52) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	} else {
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (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) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    if (ndchar <= (-7.8d+99)) then
        tmp = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= (-4.7d-91)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else if (ndchar <= (-1.05d-115)) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / ((ev / kbt) + 2.0d0))
    else if (ndchar <= 3d-52) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + (1.0d0 + (mu / kbt))))
    else
        tmp = t_0 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (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 t_0 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -7.8e+99) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= -4.7e-91) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else if (NdChar <= -1.05e-115) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= 3e-52) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	} else {
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -7.8e+99:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= -4.7e-91:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	elif NdChar <= -1.05e-115:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0))
	elif NdChar <= 3e-52:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))))
	else:
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -7.8e+99)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= -4.7e-91)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	elseif (NdChar <= -1.05e-115)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (NdChar <= 3e-52)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(mu / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -7.8e+99)
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= -4.7e-91)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	elseif (NdChar <= -1.05e-115)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	elseif (NdChar <= 3e-52)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	else
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -7.8e+99], N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -4.7e-91], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -1.05e-115], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3e-52], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -7.79999999999999989e99

   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%

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

   4. Taylor expanded in EAccept around inf 81.3%

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

   5. Taylor expanded in EAccept around 0 74.6%

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

   if -7.79999999999999989e99 < NdChar < -4.70000000000000006e-91

   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%

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

   4. Taylor expanded in EAccept around inf 71.8%

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

   5. Taylor expanded in EDonor around inf 60.4%

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

   if -4.70000000000000006e-91 < NdChar < -1.05000000000000001e-115

   1. Initial program 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in Ev around inf 80.2%

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

   5. Taylor expanded in EDonor around 0 80.2%

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

   6. Taylor expanded in Ev around 0 99.7%

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

   if -1.05000000000000001e-115 < NdChar < 3e-52

   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%

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

   4. Taylor expanded in mu around inf 65.4%

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

   5. Taylor expanded in mu around 0 64.6%

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

   if 3e-52 < NdChar

   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%

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

   4. Taylor expanded in KbT around inf 65.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -7.8 \cdot 10^{+99}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -4.7 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -1.05 \cdot 10^{-115}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 3 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \]

Alternative 10: 62.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -5.2 \cdot 10^{-128}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 3.9 \cdot 10^{-53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))))
   (if (<= NdChar -5.2e-128)
     (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))
     (if (<= NdChar 3.9e-53)
       (+
        (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
        (/ NdChar (+ 1.0 (+ 1.0 (/ mu KbT)))))
       (+
        t_0
        (/
         NaChar
         (-
          (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT))))
          (/ mu 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 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -5.2e-128) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 3.9e-53) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	} else {
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (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) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    if (ndchar <= (-5.2d-128)) then
        tmp = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (ndchar <= 3.9d-53) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + (1.0d0 + (mu / kbt))))
    else
        tmp = t_0 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (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 t_0 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (NdChar <= -5.2e-128) {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (NdChar <= 3.9e-53) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	} else {
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	tmp = 0
	if NdChar <= -5.2e-128:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	elif NdChar <= 3.9e-53:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))))
	else:
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (NdChar <= -5.2e-128)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (NdChar <= 3.9e-53)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(mu / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (NdChar <= -5.2e-128)
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (NdChar <= 3.9e-53)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	else
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -5.2e-128], N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.9e-53], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -5.19999999999999961e-128

   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%

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

   4. Taylor expanded in EAccept around inf 78.6%

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

   5. Taylor expanded in EAccept around 0 64.2%

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

   if -5.19999999999999961e-128 < NdChar < 3.9000000000000002e-53

   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%

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

   4. Taylor expanded in mu around inf 65.4%

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

   5. Taylor expanded in mu around 0 64.6%

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

   if 3.9000000000000002e-53 < NdChar

   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%

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

   4. Taylor expanded in KbT around inf 65.9%

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

4. Final simplification 64.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -5.2 \cdot 10^{-128}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 3.9 \cdot 10^{-53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \]

Alternative 11: 61.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{if}\;NdChar \leq -4 \cdot 10^{-116}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 2.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 4.5 \cdot 10^{+25}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 6.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))))
   (if (<= NdChar -4e-116)
     t_1
     (if (<= NdChar 2.5e-55)
       (+
        (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
        (/ NdChar (+ 1.0 (+ 1.0 (/ mu KbT)))))
       (if (<= NdChar 4.5e+25)
         t_1
         (if (<= NdChar 6.8e+53)
           (+
            (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
            (/
             NdChar
             (-
              (+ 2.0 (+ (/ EDonor KbT) (+ (/ mu KbT) (/ Vef KbT))))
              (/ Ec KbT))))
           (+ t_0 (/ NaChar (+ (/ Ev 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 t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	double tmp;
	if (NdChar <= -4e-116) {
		tmp = t_1;
	} else if (NdChar <= 2.5e-55) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	} else if (NdChar <= 4.5e+25) {
		tmp = t_1;
	} else if (NdChar <= 6.8e+53) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((mu / KbT) + (Vef / KbT)))) - (Ec / KbT)));
	} else {
		tmp = t_0 + (NaChar / ((Ev / 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_1 = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    if (ndchar <= (-4d-116)) then
        tmp = t_1
    else if (ndchar <= 2.5d-55) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + (1.0d0 + (mu / kbt))))
    else if (ndchar <= 4.5d+25) then
        tmp = t_1
    else if (ndchar <= 6.8d+53) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / ((2.0d0 + ((edonor / kbt) + ((mu / kbt) + (vef / kbt)))) - (ec / kbt)))
    else
        tmp = t_0 + (nachar / ((ev / 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 t_0 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	double tmp;
	if (NdChar <= -4e-116) {
		tmp = t_1;
	} else if (NdChar <= 2.5e-55) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	} else if (NdChar <= 4.5e+25) {
		tmp = t_1;
	} else if (NdChar <= 6.8e+53) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((mu / KbT) + (Vef / KbT)))) - (Ec / KbT)));
	} else {
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_1 = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	tmp = 0
	if NdChar <= -4e-116:
		tmp = t_1
	elif NdChar <= 2.5e-55:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))))
	elif NdChar <= 4.5e+25:
		tmp = t_1
	elif NdChar <= 6.8e+53:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((mu / KbT) + (Vef / KbT)))) - (Ec / KbT)))
	else:
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)))
	tmp = 0.0
	if (NdChar <= -4e-116)
		tmp = t_1;
	elseif (NdChar <= 2.5e-55)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(mu / KbT)))));
	elseif (NdChar <= 4.5e+25)
		tmp = t_1;
	elseif (NdChar <= 6.8e+53)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(mu / KbT) + Float64(Vef / KbT)))) - Float64(Ec / KbT))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_1 = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	tmp = 0.0;
	if (NdChar <= -4e-116)
		tmp = t_1;
	elseif (NdChar <= 2.5e-55)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	elseif (NdChar <= 4.5e+25)
		tmp = t_1;
	elseif (NdChar <= 6.8e+53)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / ((2.0 + ((EDonor / KbT) + ((mu / KbT) + (Vef / KbT)))) - (Ec / KbT)));
	else
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -4e-116], t$95$1, If[LessEqual[NdChar, 2.5e-55], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 4.5e+25], t$95$1, If[LessEqual[NdChar, 6.8e+53], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(mu / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -4e-116 or 2.5000000000000001e-55 < NdChar < 4.5000000000000003e25

   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%

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

   4. Taylor expanded in EAccept around inf 78.7%

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

   5. Taylor expanded in EAccept around 0 65.4%

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

   if -4e-116 < NdChar < 2.5000000000000001e-55

   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%

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

   4. Taylor expanded in mu around inf 65.4%

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

   5. Taylor expanded in mu around 0 64.6%

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

   if 4.5000000000000003e25 < NdChar < 6.79999999999999995e53

   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%

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

   4. Taylor expanded in Ev around inf 99.8%

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

   5. Taylor expanded in KbT around inf 80.4%

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

   if 6.79999999999999995e53 < NdChar

   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%

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

   4. Taylor expanded in Ev around inf 75.1%

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

   5. Taylor expanded in Ev around 0 65.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Ev}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 65.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4 \cdot 10^{-116}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 2.5 \cdot 10^{-55}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 4.5 \cdot 10^{+25}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 6.8 \cdot 10^{+53}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{mu}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \]

Alternative 12: 52.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{KbT}{\frac{mu}{NdChar}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{if}\;KbT \leq 5.5 \cdot 10^{-257}:\\ \;\;\;\;t_2 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 1.8 \cdot 10^{-200}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq 4.4 \cdot 10^{-122}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;KbT \leq 2 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;KbT \leq 5.5 \cdot 10^{+49}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1 (+ t_0 (/ KbT (/ mu NdChar))))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_3 (+ t_2 (/ NaChar (+ (/ EAccept KbT) 2.0)))))
   (if (<= KbT 5.5e-257)
     (+ t_2 (/ NaChar (+ (/ Ev KbT) 2.0)))
     (if (<= KbT 1.8e-200)
       t_1
       (if (<= KbT 4.4e-122)
         t_3
         (if (<= KbT 2e-56)
           t_1
           (if (<= KbT 5.5e+49) t_3 (+ t_0 (/ NdChar 2.0)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (KbT / (mu / NdChar));
	double t_2 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_3 = t_2 + (NaChar / ((EAccept / KbT) + 2.0));
	double tmp;
	if (KbT <= 5.5e-257) {
		tmp = t_2 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= 1.8e-200) {
		tmp = t_1;
	} else if (KbT <= 4.4e-122) {
		tmp = t_3;
	} else if (KbT <= 2e-56) {
		tmp = t_1;
	} else if (KbT <= 5.5e+49) {
		tmp = t_3;
	} else {
		tmp = t_0 + (NdChar / 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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = t_0 + (kbt / (mu / ndchar))
    t_2 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_3 = t_2 + (nachar / ((eaccept / kbt) + 2.0d0))
    if (kbt <= 5.5d-257) then
        tmp = t_2 + (nachar / ((ev / kbt) + 2.0d0))
    else if (kbt <= 1.8d-200) then
        tmp = t_1
    else if (kbt <= 4.4d-122) then
        tmp = t_3
    else if (kbt <= 2d-56) then
        tmp = t_1
    else if (kbt <= 5.5d+49) then
        tmp = t_3
    else
        tmp = t_0 + (ndchar / 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 t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (KbT / (mu / NdChar));
	double t_2 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_3 = t_2 + (NaChar / ((EAccept / KbT) + 2.0));
	double tmp;
	if (KbT <= 5.5e-257) {
		tmp = t_2 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (KbT <= 1.8e-200) {
		tmp = t_1;
	} else if (KbT <= 4.4e-122) {
		tmp = t_3;
	} else if (KbT <= 2e-56) {
		tmp = t_1;
	} else if (KbT <= 5.5e+49) {
		tmp = t_3;
	} else {
		tmp = t_0 + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = t_0 + (KbT / (mu / NdChar))
	t_2 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_3 = t_2 + (NaChar / ((EAccept / KbT) + 2.0))
	tmp = 0
	if KbT <= 5.5e-257:
		tmp = t_2 + (NaChar / ((Ev / KbT) + 2.0))
	elif KbT <= 1.8e-200:
		tmp = t_1
	elif KbT <= 4.4e-122:
		tmp = t_3
	elif KbT <= 2e-56:
		tmp = t_1
	elif KbT <= 5.5e+49:
		tmp = t_3
	else:
		tmp = t_0 + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(KbT / Float64(mu / NdChar)))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_3 = Float64(t_2 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)))
	tmp = 0.0
	if (KbT <= 5.5e-257)
		tmp = Float64(t_2 + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (KbT <= 1.8e-200)
		tmp = t_1;
	elseif (KbT <= 4.4e-122)
		tmp = t_3;
	elseif (KbT <= 2e-56)
		tmp = t_1;
	elseif (KbT <= 5.5e+49)
		tmp = t_3;
	else
		tmp = Float64(t_0 + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = t_0 + (KbT / (mu / NdChar));
	t_2 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_3 = t_2 + (NaChar / ((EAccept / KbT) + 2.0));
	tmp = 0.0;
	if (KbT <= 5.5e-257)
		tmp = t_2 + (NaChar / ((Ev / KbT) + 2.0));
	elseif (KbT <= 1.8e-200)
		tmp = t_1;
	elseif (KbT <= 4.4e-122)
		tmp = t_3;
	elseif (KbT <= 2e-56)
		tmp = t_1;
	elseif (KbT <= 5.5e+49)
		tmp = t_3;
	else
		tmp = t_0 + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(KbT / N[(mu / NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, 5.5e-257], N[(t$95$2 + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.8e-200], t$95$1, If[LessEqual[KbT, 4.4e-122], t$95$3, If[LessEqual[KbT, 2e-56], t$95$1, If[LessEqual[KbT, 5.5e+49], t$95$3, N[(t$95$0 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < 5.50000000000000025e-257

   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%

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

   4. Taylor expanded in Ev around inf 75.9%

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

   5. Taylor expanded in Ev around 0 59.7%

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

   if 5.50000000000000025e-257 < KbT < 1.8000000000000001e-200 or 4.4e-122 < KbT < 2.0000000000000001e-56

   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%

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

   4. Taylor expanded in mu around inf 71.2%

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

   5. Taylor expanded in mu around 0 63.8%

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

   6. Taylor expanded in mu around inf 66.7%

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

      1. associate-/l* 62.9%

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

   8. Simplified 62.9%

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

   if 1.8000000000000001e-200 < KbT < 4.4e-122 or 2.0000000000000001e-56 < KbT < 5.50000000000000042e49

   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%

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

   4. Taylor expanded in EAccept around inf 63.2%

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

   5. Taylor expanded in EAccept around 0 53.8%

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

   if 5.50000000000000042e49 < 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%

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

   4. Taylor expanded in mu around inf 80.0%

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

   5. Taylor expanded in mu around 0 74.7%

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

   6. Taylor expanded in mu around 0 75.3%

      \[\leadsto \frac{NdChar}{\color{blue}{2}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 62.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 5.5 \cdot 10^{-257}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 1.8 \cdot 10^{-200}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{KbT}{\frac{mu}{NdChar}}\\ \mathbf{elif}\;KbT \leq 4.4 \cdot 10^{-122}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;KbT \leq 2 \cdot 10^{-56}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{KbT}{\frac{mu}{NdChar}}\\ \mathbf{elif}\;KbT \leq 5.5 \cdot 10^{+49}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 13: 55.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NdChar \leq -1.45 \cdot 10^{-131}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 10^{-52}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 9000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar 2.0))))
   (if (<= NdChar -1.45e-131)
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
      (/ NaChar 2.0))
     (if (<= NdChar 1e-52)
       t_0
       (if (<= NdChar 9000.0)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (- 1.0 (/ mu KbT)))))
         (if (<= NdChar 1.1e+34)
           t_0
           (+
            (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
            (/ NaChar (+ (/ Ev 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 t_0 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= -1.45e-131) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else if (NdChar <= 1e-52) {
		tmp = t_0;
	} else if (NdChar <= 9000.0) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + (1.0 - (mu / KbT))));
	} else if (NdChar <= 1.1e+34) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / 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) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / 2.0d0)
    if (ndchar <= (-1.45d-131)) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    else if (ndchar <= 1d-52) then
        tmp = t_0
    else if (ndchar <= 9000.0d0) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + (1.0d0 - (mu / kbt))))
    else if (ndchar <= 1.1d+34) then
        tmp = t_0
    else
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / ((ev / 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 t_0 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NdChar <= -1.45e-131) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else if (NdChar <= 1e-52) {
		tmp = t_0;
	} else if (NdChar <= 9000.0) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + (1.0 - (mu / KbT))));
	} else if (NdChar <= 1.1e+34) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NdChar <= -1.45e-131:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	elif NdChar <= 1e-52:
		tmp = t_0
	elif NdChar <= 9000.0:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + (1.0 - (mu / KbT))))
	elif NdChar <= 1.1e+34:
		tmp = t_0
	else:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NdChar <= -1.45e-131)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0));
	elseif (NdChar <= 1e-52)
		tmp = t_0;
	elseif (NdChar <= 9000.0)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 - Float64(mu / KbT)))));
	elseif (NdChar <= 1.1e+34)
		tmp = t_0;
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -1.45e-131)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	elseif (NdChar <= 1e-52)
		tmp = t_0;
	elseif (NdChar <= 9000.0)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + (1.0 - (mu / KbT))));
	elseif (NdChar <= 1.1e+34)
		tmp = t_0;
	else
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.45e-131], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1e-52], t$95$0, If[LessEqual[NdChar, 9000.0], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.1e+34], t$95$0, N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -1.4500000000000001e-131

   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%

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

   4. Taylor expanded in KbT around inf 57.8%

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

   if -1.4500000000000001e-131 < NdChar < 1e-52 or 9e3 < NdChar < 1.1000000000000001e34

   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%

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

   4. Taylor expanded in mu around inf 67.2%

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

   5. Taylor expanded in mu around 0 65.4%

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

   6. Taylor expanded in mu around 0 58.8%

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

   if 1e-52 < NdChar < 9e3

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in mu around inf 89.1%

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

      1. associate-*r/ 89.1%

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

      2. mul-1-neg 89.1%

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

   6. Simplified 89.1%

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

   7. Taylor expanded in mu around inf 89.5%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} \]

   8. Taylor expanded in mu around 0 89.5%

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

      1. mul-1-neg 89.5%

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

      2. unsub-neg 89.5%

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

   10. Simplified 89.5%

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

   if 1.1000000000000001e34 < NdChar

   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%

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

   4. Taylor expanded in Ev around inf 76.7%

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

   5. Taylor expanded in EDonor around 0 72.3%

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

   6. Taylor expanded in Ev around 0 60.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{\left(Vef + mu\right) - Ec}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Ev}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.45 \cdot 10^{-131}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 10^{-52}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NdChar \leq 9000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + \left(1 - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \]

Alternative 14: 62.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -1.7 \cdot 10^{-123} \lor \neg \left(NdChar \leq 3 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -1.7e-123) (not (<= NdChar 3e-52)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ EAccept KbT) 2.0)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar (+ 1.0 (+ 1.0 (/ 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 ((NdChar <= -1.7e-123) || !(NdChar <= 3e-52)) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (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 ((ndchar <= (-1.7d-123)) .or. (.not. (ndchar <= 3d-52))) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + (1.0d0 + (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 ((NdChar <= -1.7e-123) || !(NdChar <= 3e-52)) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -1.7e-123) or not (NdChar <= 3e-52):
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -1.7e-123) || !(NdChar <= 3e-52))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(1.0 + Float64(mu / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -1.7e-123) || ~((NdChar <= 3e-52)))
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + (1.0 + (mu / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -1.7e-123], N[Not[LessEqual[NdChar, 3e-52]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(1.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -1.7e-123 or 3e-52 < NdChar

   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%

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

   4. Taylor expanded in EAccept around inf 75.7%

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

   5. Taylor expanded in EAccept around 0 63.4%

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

   if -1.7e-123 < NdChar < 3e-52

   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%

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

   4. Taylor expanded in mu around inf 65.4%

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

   5. Taylor expanded in mu around 0 64.6%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.7 \cdot 10^{-123} \lor \neg \left(NdChar \leq 3 \cdot 10^{-52}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(1 + \frac{mu}{KbT}\right)}\\ \end{array} \]

Alternative 15: 59.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -9 \cdot 10^{-119} \lor \neg \left(NdChar \leq 3.1 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -9e-119) (not (<= NdChar 3.1e-55)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ EAccept KbT) 2.0)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar 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 ((NdChar <= -9e-119) || !(NdChar <= 3.1e-55)) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 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 ((ndchar <= (-9d-119)) .or. (.not. (ndchar <= 3.1d-55))) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / 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 ((NdChar <= -9e-119) || !(NdChar <= 3.1e-55)) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -9e-119) or not (NdChar <= 3.1e-55):
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -9e-119) || !(NdChar <= 3.1e-55))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -9e-119) || ~((NdChar <= 3.1e-55)))
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -9e-119], N[Not[LessEqual[NdChar, 3.1e-55]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -9.0000000000000005e-119 or 3.09999999999999997e-55 < NdChar

   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%

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

   4. Taylor expanded in EAccept around inf 75.7%

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

   5. Taylor expanded in EAccept around 0 63.4%

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

   if -9.0000000000000005e-119 < NdChar < 3.09999999999999997e-55

   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%

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

   4. Taylor expanded in mu around inf 65.4%

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

   5. Taylor expanded in mu around 0 64.6%

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

   6. Taylor expanded in mu around 0 56.4%

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

4. Final simplification 60.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -9 \cdot 10^{-119} \lor \neg \left(NdChar \leq 3.1 \cdot 10^{-55}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 16: 53.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5 \cdot 10^{+32} \lor \neg \left(NaChar \leq 3.5 \cdot 10^{-113}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -5e+32) (not (<= NaChar 3.5e-113)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar 2.0))
   (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (/ NaChar 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 ((NaChar <= -5e+32) || !(NaChar <= 3.5e-113)) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 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 ((nachar <= (-5d+32)) .or. (.not. (nachar <= 3.5d-113))) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / 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 ((NaChar <= -5e+32) || !(NaChar <= 3.5e-113)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -5e+32) or not (NaChar <= 3.5e-113):
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -5e+32) || !(NaChar <= 3.5e-113))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -5e+32) || ~((NaChar <= 3.5e-113)))
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -5e+32], N[Not[LessEqual[NaChar, 3.5e-113]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.9999999999999997e32 or 3.50000000000000029e-113 < NaChar

   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%

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

   4. Taylor expanded in mu around inf 73.7%

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

   5. Taylor expanded in mu around 0 59.1%

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

   6. Taylor expanded in mu around 0 56.0%

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

   if -4.9999999999999997e32 < NaChar < 3.50000000000000029e-113

   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%

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

   4. Taylor expanded in KbT around inf 56.0%

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

   5. Taylor expanded in EDonor around 0 49.4%

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

4. Final simplification 53.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5 \cdot 10^{+32} \lor \neg \left(NaChar \leq 3.5 \cdot 10^{-113}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 17: 56.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -1.45 \cdot 10^{-131} \lor \neg \left(NdChar \leq 6.5 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -1.45e-131) (not (<= NdChar 6.5e-54)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ NaChar 2.0))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar 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 ((NdChar <= -1.45e-131) || !(NdChar <= 6.5e-54)) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 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 ((ndchar <= (-1.45d-131)) .or. (.not. (ndchar <= 6.5d-54))) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / 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 ((NdChar <= -1.45e-131) || !(NdChar <= 6.5e-54)) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -1.45e-131) or not (NdChar <= 6.5e-54):
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -1.45e-131) || !(NdChar <= 6.5e-54))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -1.45e-131) || ~((NdChar <= 6.5e-54)))
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -1.45e-131], N[Not[LessEqual[NdChar, 6.5e-54]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -1.4500000000000001e-131 or 6.49999999999999991e-54 < NdChar

   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%

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

   4. Taylor expanded in KbT around inf 56.2%

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

   if -1.4500000000000001e-131 < NdChar < 6.49999999999999991e-54

   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%

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

   4. Taylor expanded in mu around inf 66.8%

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

   5. Taylor expanded in mu around 0 64.8%

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

   6. Taylor expanded in mu around 0 57.6%

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

4. Final simplification 56.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.45 \cdot 10^{-131} \lor \neg \left(NdChar \leq 6.5 \cdot 10^{-54}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 18: 45.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -3.5 \cdot 10^{+122} \lor \neg \left(NaChar \leq 3.1 \cdot 10^{+207}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -3.5e+122) (not (<= NaChar 3.1e+207)))
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (/ NaChar 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 ((NaChar <= -3.5e+122) || !(NaChar <= 3.1e+207)) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 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 ((nachar <= (-3.5d+122)) .or. (.not. (nachar <= 3.1d+207))) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / 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 ((NaChar <= -3.5e+122) || !(NaChar <= 3.1e+207)) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -3.5e+122) or not (NaChar <= 3.1e+207):
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -3.5e+122) || !(NaChar <= 3.1e+207))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -3.5e+122) || ~((NaChar <= 3.1e+207)))
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -3.5e+122], N[Not[LessEqual[NaChar, 3.1e+207]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -3.50000000000000014e122 or 3.1000000000000003e207 < NaChar

   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%

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

   4. Taylor expanded in Ev around inf 67.6%

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

   5. Taylor expanded in KbT around inf 52.2%

      \[\leadsto \frac{NdChar}{\color{blue}{2}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -3.50000000000000014e122 < NaChar < 3.1000000000000003e207

   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%

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

   4. Taylor expanded in KbT around inf 51.3%

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

   5. Taylor expanded in EDonor around 0 47.1%

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

4. Final simplification 48.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.5 \cdot 10^{+122} \lor \neg \left(NaChar \leq 3.1 \cdot 10^{+207}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 19: 37.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -2.55 \cdot 10^{+129}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Ev \leq -9.8 \cdot 10^{-139}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Ev \leq 7.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -2.55e+129)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (if (<= Ev -9.8e-139)
     (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (/ NaChar 2.0))
     (if (<= Ev 7.5e-108)
       (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
       (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* 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 (Ev <= -2.55e+129) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (Ev <= -9.8e-139) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / 2.0);
	} else if (Ev <= 7.5e-108) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (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 (ev <= (-2.55d+129)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else if (ev <= (-9.8d-139)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / 2.0d0)
    else if (ev <= 7.5d-108) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (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 (Ev <= -2.55e+129) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (Ev <= -9.8e-139) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / 2.0);
	} else if (Ev <= 7.5e-108) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -2.55e+129:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	elif Ev <= -9.8e-139:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / 2.0)
	elif Ev <= 7.5e-108:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -2.55e+129)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	elseif (Ev <= -9.8e-139)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / 2.0));
	elseif (Ev <= 7.5e-108)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + 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 (Ev <= -2.55e+129)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	elseif (Ev <= -9.8e-139)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / 2.0);
	elseif (Ev <= 7.5e-108)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -2.55e+129], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -9.8e-139], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 7.5e-108], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -2.54999999999999998e129

   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%

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

   4. Taylor expanded in Ev around inf 92.7%

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

   5. Taylor expanded in KbT around inf 44.6%

      \[\leadsto \frac{NdChar}{\color{blue}{2}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -2.54999999999999998e129 < Ev < -9.80000000000000063e-139

   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%

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

   4. Taylor expanded in KbT around inf 48.3%

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

   5. Taylor expanded in mu around inf 37.4%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{mu}{KbT}}}} + \frac{NaChar}{2} \]

   if -9.80000000000000063e-139 < Ev < 7.4999999999999993e-108

   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%

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

   4. Taylor expanded in KbT around inf 47.6%

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

   5. Taylor expanded in EDonor around inf 36.0%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{2} \]

   if 7.4999999999999993e-108 < 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%

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

   4. Taylor expanded in EAccept around inf 66.2%

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

   5. Taylor expanded in KbT around inf 33.5%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -2.55 \cdot 10^{+129}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Ev \leq -9.8 \cdot 10^{-139}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;Ev \leq 7.5 \cdot 10^{-108}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]

Alternative 20: 39.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -5.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;mu \leq 1.7 \cdot 10^{+96}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= mu -5.2e+67)
   (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (/ NaChar (+ (/ EAccept KbT) 2.0)))
   (if (<= mu 1.7e+96)
     (+ (/ NaChar 2.0) (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
     (+ (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))) (/ NdChar 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 (mu <= -5.2e+67) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (mu <= 1.7e+96) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + (NdChar / 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 (mu <= (-5.2d+67)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else if (mu <= 1.7d+96) then
        tmp = (nachar / 2.0d0) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp((-mu / kbt)))) + (ndchar / 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 (mu <= -5.2e+67) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else if (mu <= 1.7e+96) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((-mu / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if mu <= -5.2e+67:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	elif mu <= 1.7e+96:
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp((-mu / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (mu <= -5.2e+67)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	elseif (mu <= 1.7e+96)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (mu <= -5.2e+67)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	elseif (mu <= 1.7e+96)
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	else
		tmp = (NaChar / (1.0 + exp((-mu / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[mu, -5.2e+67], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.7e+96], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if mu < -5.2000000000000001e67

   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%

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

   4. Taylor expanded in mu around inf 81.0%

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

   5. Taylor expanded in EAccept around inf 51.7%

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

   6. Taylor expanded in EAccept around 0 50.3%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{EAccept}{KbT}}} \]

   if -5.2000000000000001e67 < mu < 1.7e96

   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%

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

   4. Taylor expanded in KbT around inf 48.5%

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

   5. Taylor expanded in Ec around inf 41.1%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-1 \cdot \frac{Ec}{KbT}}}} + \frac{NaChar}{2} \]
   6. Step-by-step derivation

      1. mul-1-neg 41.1%

         \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-\frac{Ec}{KbT}}}} + \frac{NaChar}{2} \]

      2. distribute-neg-frac 41.1%

         \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2} \]

   7. Simplified 41.1%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2} \]

   if 1.7e96 < mu

   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%

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

   4. Taylor expanded in mu around inf 86.2%

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

      1. associate-*r/ 86.2%

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

      2. mul-1-neg 86.2%

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

   6. Simplified 86.2%

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

   7. Taylor expanded in KbT around inf 45.5%

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

4. Final simplification 43.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -5.2 \cdot 10^{+67}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{elif}\;mu \leq 1.7 \cdot 10^{+96}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{-mu}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 21: 38.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -4 \cdot 10^{+131}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Ev \leq 3.1 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -4e+131)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (if (<= Ev 3.1e-91)
     (+ (/ NaChar 2.0) (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* 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 (Ev <= -4e+131) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (Ev <= 3.1e-91) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (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 (ev <= (-4d+131)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else if (ev <= 3.1d-91) then
        tmp = (nachar / 2.0d0) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (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 (Ev <= -4e+131) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (Ev <= 3.1e-91) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -4e+131:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	elif Ev <= 3.1e-91:
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -4e+131)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	elseif (Ev <= 3.1e-91)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + 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 (Ev <= -4e+131)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	elseif (Ev <= 3.1e-91)
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -4e+131], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 3.1e-91], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -3.9999999999999996e131

   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%

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

   4. Taylor expanded in Ev around inf 92.7%

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

   5. Taylor expanded in KbT around inf 44.6%

      \[\leadsto \frac{NdChar}{\color{blue}{2}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -3.9999999999999996e131 < Ev < 3.09999999999999981e-91

   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%

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

   4. Taylor expanded in KbT around inf 49.1%

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

   5. Taylor expanded in Ec around inf 39.1%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-1 \cdot \frac{Ec}{KbT}}}} + \frac{NaChar}{2} \]
   6. Step-by-step derivation

      1. mul-1-neg 39.1%

         \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-\frac{Ec}{KbT}}}} + \frac{NaChar}{2} \]

      2. distribute-neg-frac 39.1%

         \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2} \]

   7. Simplified 39.1%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2} \]

   if 3.09999999999999981e-91 < 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%

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

   4. Taylor expanded in EAccept around inf 65.6%

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

   5. Taylor expanded in KbT around inf 33.5%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -4 \cdot 10^{+131}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;Ev \leq 3.1 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]

Alternative 22: 37.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -1.65 \cdot 10^{+130}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -1.65e+130)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* 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 (Ev <= -1.65e+130) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (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 (ev <= (-1.65d+130)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (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 (Ev <= -1.65e+130) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -1.65e+130:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -1.65e+130)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + 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 (Ev <= -1.65e+130)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -1.65e+130], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -1.65e130

   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%

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

   4. Taylor expanded in Ev around inf 92.7%

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

   5. Taylor expanded in KbT around inf 44.6%

      \[\leadsto \frac{NdChar}{\color{blue}{2}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -1.65e130 < Ev

   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%

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

   4. Taylor expanded in EAccept around inf 69.7%

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

   5. Taylor expanded in KbT around inf 32.7%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.65 \cdot 10^{+130}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]

Alternative 23: 38.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -2.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -2.7e-101)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 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 (Ev <= -2.7e-101) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 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 (ev <= (-2.7d-101)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 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 (Ev <= -2.7e-101) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -2.7e-101:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -2.7e-101)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -2.7e-101)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -2.7e-101], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -2.7000000000000002e-101

   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%

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

   4. Taylor expanded in Ev around inf 85.4%

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

   5. Taylor expanded in KbT around inf 39.0%

      \[\leadsto \frac{NdChar}{\color{blue}{2}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]

   if -2.7000000000000002e-101 < 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%

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

   4. Taylor expanded in KbT around inf 49.0%

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

   5. Taylor expanded in EDonor around inf 37.4%

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

4. Final simplification 38.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -2.7 \cdot 10^{-101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]

Alternative 24: 35.8% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5 \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* 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 (NaChar / (1.0 + exp((EAccept / KbT)))) + (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 = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (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 (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar * 0.5))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]

Derivation

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%

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

4. Taylor expanded in EAccept around inf 66.8%

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

5. Taylor expanded in KbT around inf 30.7%

   \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

6. Final simplification 30.7%

   \[\leadsto \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5 \]

Alternative 25: 28.4% 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 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%

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

4. Taylor expanded in KbT around inf 47.0%

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

5. Taylor expanded in Ec around inf 36.3%

   \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-1 \cdot \frac{Ec}{KbT}}}} + \frac{NaChar}{2} \]
6. Step-by-step derivation

   1. mul-1-neg 36.3%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-\frac{Ec}{KbT}}}} + \frac{NaChar}{2} \]

   2. distribute-neg-frac 36.3%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2} \]

7. Simplified 36.3%

   \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2} \]

8. Taylor expanded in Ec around 0 24.7%

   \[\leadsto \frac{NdChar}{\color{blue}{2 + -1 \cdot \frac{Ec}{KbT}}} + \frac{NaChar}{2} \]
9. Step-by-step derivation

   1. mul-1-neg 24.7%

      \[\leadsto \frac{NdChar}{2 + \color{blue}{\left(-\frac{Ec}{KbT}\right)}} + \frac{NaChar}{2} \]

   2. unsub-neg 24.7%

      \[\leadsto \frac{NdChar}{\color{blue}{2 - \frac{Ec}{KbT}}} + \frac{NaChar}{2} \]

10. Simplified 24.7%

    \[\leadsto \frac{NdChar}{\color{blue}{2 - \frac{Ec}{KbT}}} + \frac{NaChar}{2} \]

11. Taylor expanded in Ec around 0 26.1%

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

    1. distribute-lft-out 26.1%

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

13. Simplified 26.1%

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

14. Final simplification 26.1%

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

Alternative 26: 18.3% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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%

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

4. Taylor expanded in KbT around inf 47.0%

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

5. Taylor expanded in Ec around inf 36.3%

   \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-1 \cdot \frac{Ec}{KbT}}}} + \frac{NaChar}{2} \]
6. Step-by-step derivation

   1. mul-1-neg 36.3%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{-\frac{Ec}{KbT}}}} + \frac{NaChar}{2} \]

   2. distribute-neg-frac 36.3%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2} \]

7. Simplified 36.3%

   \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{-Ec}{KbT}}}} + \frac{NaChar}{2} \]

8. Taylor expanded in Ec around 0 24.7%

   \[\leadsto \frac{NdChar}{\color{blue}{2 + -1 \cdot \frac{Ec}{KbT}}} + \frac{NaChar}{2} \]
9. Step-by-step derivation

   1. mul-1-neg 24.7%

      \[\leadsto \frac{NdChar}{2 + \color{blue}{\left(-\frac{Ec}{KbT}\right)}} + \frac{NaChar}{2} \]

   2. unsub-neg 24.7%

      \[\leadsto \frac{NdChar}{\color{blue}{2 - \frac{Ec}{KbT}}} + \frac{NaChar}{2} \]

10. Simplified 24.7%

    \[\leadsto \frac{NdChar}{\color{blue}{2 - \frac{Ec}{KbT}}} + \frac{NaChar}{2} \]

11. Taylor expanded in NdChar around 0 16.9%

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

12. Final simplification 16.9%

    \[\leadsto NaChar \cdot 0.5 \]

Reproduce

herbie shell --seed 2023322 
(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))))))