Bulmash initializePoisson

Percentage Accurate: 99.9% → 99.9%

Time: 29.1s

Alternatives: 21

Speedup: 1.0×

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: 99.9% 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: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef + \left(EDonor - Ec\right)\right)}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (exp (log1p (exp (/ (+ mu (+ Vef (- EDonor 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 / exp(log1p(exp(((mu + (Vef + (EDonor - Ec))) / KbT))))) + (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT))));
}

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / Math.exp(Math.log1p(Math.exp(((mu + (Vef + (EDonor - 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 / math.exp(math.log1p(math.exp(((mu + (Vef + (EDonor - 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 / exp(log1p(exp(Float64(Float64(mu + Float64(Vef + Float64(EDonor - Ec))) / KbT))))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))))
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[Exp[N[Log[1 + N[Exp[N[(N[(mu + N[(Vef + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $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 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. Add Preprocessing
5. Step-by-step derivation

   1. add-exp-log 100.0%

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

   2. log1p-udef 100.0%

      \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   3. +-commutative 100.0%

      \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   4. associate-+l- 100.0%

      \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

6. Applied egg-rr 100.0%

   \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

7. Final simplification 100.0%

   \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef + \left(EDonor - Ec\right)\right)}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
8. Add Preprocessing

Alternative 2: 75.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;mu \leq -4.2 \cdot 10^{+71}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;mu \leq 5.3 \cdot 10^{-107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;mu \leq 4.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.35 \cdot 10^{+138}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

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 (/ EDonor KbT))))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ mu KbT))))))
   (if (<= mu -4.2e+71)
     (+ t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
     (if (<= mu 5.3e-107)
       t_0
       (if (<= mu 4.8e-73)
         (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
         (if (<= mu 1.35e+138)
           t_0
           (+
            t_1
            (/ NaChar (+ 1.0 (exp (/ (- (+ 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) {
	double t_0 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_1 = NdChar / (1.0 + exp((mu / KbT)));
	double tmp;
	if (mu <= -4.2e+71) {
		tmp = t_1 + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	} else if (mu <= 5.3e-107) {
		tmp = t_0;
	} else if (mu <= 4.8e-73) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (mu <= 1.35e+138) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_1 = ndchar / (1.0d0 + exp((mu / kbt)))
    if (mu <= (-4.2d+71)) then
        tmp = t_1 + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    else if (mu <= 5.3d-107) then
        tmp = t_0
    else if (mu <= 4.8d-73) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else if (mu <= 1.35d+138) then
        tmp = t_0
    else
        tmp = t_1 + (nachar / (1.0d0 + exp((((vef + eaccept) - mu) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_1 = NdChar / (1.0 + Math.exp((mu / KbT)));
	double tmp;
	if (mu <= -4.2e+71) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	} else if (mu <= 5.3e-107) {
		tmp = t_0;
	} else if (mu <= 4.8e-73) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (mu <= 1.35e+138) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((((Vef + EAccept) - mu) / KbT))));
	}
	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((EDonor / KbT))))
	t_1 = NdChar / (1.0 + math.exp((mu / KbT)))
	tmp = 0
	if mu <= -4.2e+71:
		tmp = t_1 + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	elif mu <= 5.3e-107:
		tmp = t_0
	elif mu <= 4.8e-73:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	elif mu <= 1.35e+138:
		tmp = t_0
	else:
		tmp = t_1 + (NaChar / (1.0 + math.exp((((Vef + EAccept) - mu) / KbT))))
	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(EDonor / KbT)))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))))
	tmp = 0.0
	if (mu <= -4.2e+71)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	elseif (mu <= 5.3e-107)
		tmp = t_0;
	elseif (mu <= 4.8e-73)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	elseif (mu <= 1.35e+138)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + EAccept) - mu) / KbT)))));
	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((EDonor / KbT))));
	t_1 = NdChar / (1.0 + exp((mu / KbT)));
	tmp = 0.0;
	if (mu <= -4.2e+71)
		tmp = t_1 + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	elseif (mu <= 5.3e-107)
		tmp = t_0;
	elseif (mu <= 4.8e-73)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	elseif (mu <= 1.35e+138)
		tmp = t_0;
	else
		tmp = t_1 + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	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[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -4.2e+71], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 5.3e-107], t$95$0, If[LessEqual[mu, 4.8e-73], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 1.35e+138], t$95$0, N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if mu < -4.19999999999999978e71

   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. Add Preprocessing

   5. Taylor expanded in mu around inf 85.3%

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

   6. Taylor expanded in EAccept around 0 78.1%

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

   if -4.19999999999999978e71 < mu < 5.3e-107 or 4.80000000000000011e-73 < mu < 1.35000000000000004e138

   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. Add Preprocessing

   5. Taylor expanded in EDonor around inf 79.7%

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

   if 5.3e-107 < mu < 4.80000000000000011e-73

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 69.0%

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

      1. associate-+r+ 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in Ec around inf 36.8%

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

      1. mul-1-neg 36.8%

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

      2. associate-/l* 36.8%

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

   10. Simplified 36.8%

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

   11. Taylor expanded in KbT around 0 100.0%

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

   if 1.35000000000000004e138 < 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. Add Preprocessing

   5. Taylor expanded in mu around inf 89.9%

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

   6. Taylor expanded in Ev around 0 87.2%

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

      1. +-commutative 87.2%

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

   8. Simplified 87.2%

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

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -4.2 \cdot 10^{+71}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;mu \leq 5.3 \cdot 10^{-107}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;mu \leq 4.8 \cdot 10^{-73}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;mu \leq 1.35 \cdot 10^{+138}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 78.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+130}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -4.5 \cdot 10^{-194}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.5 \cdot 10^{+79}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

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 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Vef -4.2e+130)
     t_1
     (if (<= Vef -4.5e-194)
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
       (if (<= Vef 8.5e+79)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
         t_1)))))

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 + (NdChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Vef <= -4.2e+130) {
		tmp = t_1;
	} else if (Vef <= -4.5e-194) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= 8.5e+79) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_1;
	}
	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 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    if (vef <= (-4.2d+130)) then
        tmp = t_1
    else if (vef <= (-4.5d-194)) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= 8.5d+79) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_1
    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 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Vef <= -4.2e+130) {
		tmp = t_1;
	} else if (Vef <= -4.5e-194) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= 8.5e+79) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_1;
	}
	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 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Vef <= -4.2e+130:
		tmp = t_1
	elif Vef <= -4.5e-194:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= 8.5e+79:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_1
	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(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Vef <= -4.2e+130)
		tmp = t_1;
	elseif (Vef <= -4.5e-194)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= 8.5e+79)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = t_1;
	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 + (NdChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Vef <= -4.2e+130)
		tmp = t_1;
	elseif (Vef <= -4.5e-194)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= 8.5e+79)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_1;
	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[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -4.2e+130], t$95$1, If[LessEqual[Vef, -4.5e-194], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 8.5e+79], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -4.19999999999999981e130 or 8.4999999999999998e79 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 84.5%

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

   if -4.19999999999999981e130 < Vef < -4.4999999999999999e-194

   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. Add Preprocessing

   5. Taylor expanded in mu around inf 81.8%

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

   if -4.4999999999999999e-194 < Vef < 8.4999999999999998e79

   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. Add Preprocessing

   5. Taylor expanded in EDonor around inf 85.1%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+130}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq -4.5 \cdot 10^{-194}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.5 \cdot 10^{+79}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 77.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;Vef \leq -2.1 \cdot 10^{+149} \lor \neg \left(Vef \leq 2.05 \cdot 10^{+85}\right):\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (or (<= Vef -2.1e+149) (not (<= Vef 2.05e+85)))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
     (+ t_0 (/ 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 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if ((Vef <= -2.1e+149) || !(Vef <= 2.05e+85)) {
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	} else {
		tmp = t_0 + (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 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    if ((vef <= (-2.1d+149)) .or. (.not. (vef <= 2.05d+85))) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    else
        tmp = t_0 + (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 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if ((Vef <= -2.1e+149) || !(Vef <= 2.05e+85)) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	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)))
	tmp = 0
	if (Vef <= -2.1e+149) or not (Vef <= 2.05e+85):
		tmp = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	else:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	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))))
	tmp = 0.0
	if ((Vef <= -2.1e+149) || !(Vef <= 2.05e+85))
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	else
		tmp = Float64(t_0 + 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 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if ((Vef <= -2.1e+149) || ~((Vef <= 2.05e+85)))
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	else
		tmp = t_0 + (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[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[Vef, -2.1e+149], N[Not[LessEqual[Vef, 2.05e+85]], $MachinePrecision]], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if Vef < -2.1000000000000002e149 or 2.04999999999999989e85 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 86.5%

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

   if -2.1000000000000002e149 < Vef < 2.04999999999999989e85

   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. Add Preprocessing

   5. Taylor expanded in EDonor around inf 79.9%

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

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -2.1 \cdot 10^{+149} \lor \neg \left(Vef \leq 2.05 \cdot 10^{+85}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

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. Add Preprocessing

5. Final simplification 100.0%

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

Alternative 6: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5.2 \cdot 10^{+138}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.2 \cdot 10^{-192} \lor \neg \left(NaChar \leq 2.3 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -5.2e+138)
   (+
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
    (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
   (if (or (<= NaChar -2.2e-192) (not (<= NaChar 2.3e-42)))
     (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
      (/
       NaChar
       (-
        (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev 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 <= -5.2e+138) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	} else if ((NaChar <= -2.2e-192) || !(NaChar <= 2.3e-42)) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / 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 <= (-5.2d+138)) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    else if ((nachar <= (-2.2d-192)) .or. (.not. (nachar <= 2.3d-42))) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / 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 <= -5.2e+138) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	} else if ((NaChar <= -2.2e-192) || !(NaChar <= 2.3e-42)) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -5.2e+138:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	elif (NaChar <= -2.2e-192) or not (NaChar <= 2.3e-42):
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -5.2e+138)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	elseif ((NaChar <= -2.2e-192) || !(NaChar <= 2.3e-42))
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / 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(Vef / KbT) + Float64(Ev / 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 <= -5.2e+138)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	elseif ((NaChar <= -2.2e-192) || ~((NaChar <= 2.3e-42)))
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -5.2e+138], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, -2.2e-192], N[Not[LessEqual[NaChar, 2.3e-42]], $MachinePrecision]], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $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[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -5.2000000000000002e138

   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. Add Preprocessing

   5. Taylor expanded in EDonor around inf 85.5%

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

   6. Taylor expanded in EAccept around 0 77.1%

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

   if -5.2000000000000002e138 < NaChar < -2.20000000000000006e-192 or 2.30000000000000004e-42 < 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. Add Preprocessing

   5. Taylor expanded in KbT around inf 51.0%

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

      1. associate-+r+ 51.0%

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

   7. Simplified 51.0%

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

   8. Taylor expanded in Ec around inf 33.0%

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

      1. mul-1-neg 33.0%

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

      2. associate-/l* 33.1%

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

   10. Simplified 33.1%

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

   11. Taylor expanded in KbT around 0 70.3%

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

   if -2.20000000000000006e-192 < NaChar < 2.30000000000000004e-42

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 76.3%

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

4. Final simplification 73.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.2 \cdot 10^{+138}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.2 \cdot 10^{-192} \lor \neg \left(NaChar \leq 2.3 \cdot 10^{-42}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -7.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.7 \cdot 10^{+240}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -7.8e+152)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar 2.0))
   (if (<= KbT 1.7e+240)
     (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
      (/
       NaChar
       (-
        (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev 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 (KbT <= -7.8e+152) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.7e+240) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / 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 (kbt <= (-7.8d+152)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 1.7d+240) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / 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 (KbT <= -7.8e+152) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.7e+240) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -7.8e+152:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0)
	elif KbT <= 1.7e+240:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -7.8e+152)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 1.7e+240)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / 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(Vef / KbT) + Float64(Ev / 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 (KbT <= -7.8e+152)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 1.7e+240)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -7.8e+152], 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[KbT, 1.7e+240], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $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[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -7.80000000000000022e152

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add-exp-log 100.0%

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

      2. log1p-udef 100.0%

         \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. +-commutative 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in KbT around inf 72.6%

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

   if -7.80000000000000022e152 < KbT < 1.70000000000000004e240

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 48.3%

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

      1. associate-+r+ 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in Ec around inf 33.5%

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

      1. mul-1-neg 33.5%

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

      2. associate-/l* 31.7%

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

   10. Simplified 31.7%

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

   11. Taylor expanded in KbT around 0 67.2%

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

   if 1.70000000000000004e240 < KbT

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 91.4%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -7.8 \cdot 10^{+152}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.7 \cdot 10^{+240}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.7 \cdot 10^{+240}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.8e+154)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar 2.0))
   (if (<= KbT 1.7e+240)
     (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
     (+
      (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- 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 (KbT <= -1.8e+154) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.7e+240) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (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 (kbt <= (-1.8d+154)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 1.7d+240) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (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 (KbT <= -1.8e+154) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.7e+240) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -1.8e+154:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0)
	elif KbT <= 1.7e+240:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -1.8e+154)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 1.7e+240)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(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 (KbT <= -1.8e+154)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 1.7e+240)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -1.8e+154], 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[KbT, 1.7e+240], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $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 / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.8e154

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add-exp-log 100.0%

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

      2. log1p-udef 100.0%

         \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. +-commutative 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in KbT around inf 72.6%

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

   if -1.8e154 < KbT < 1.70000000000000004e240

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 48.3%

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

      1. associate-+r+ 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in Ec around inf 33.5%

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

      1. mul-1-neg 33.5%

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

      2. associate-/l* 31.7%

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

   10. Simplified 31.7%

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

   11. Taylor expanded in KbT around 0 67.2%

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

   if 1.70000000000000004e240 < KbT

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 85.6%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.8 \cdot 10^{+154}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.7 \cdot 10^{+240}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 63.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -4.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.7 \cdot 10^{+241}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -4.8e+166)
   (+ (/ NdChar 2.0) (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
   (if (<= KbT 1.7e+241)
     (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
     (+ (/ NaChar 2.0) (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -4.8e+166) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (KbT <= 1.7e+241) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-4.8d+166)) then
        tmp = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (kbt <= 1.7d+241) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else
        tmp = (nachar / 2.0d0) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -4.8e+166) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (KbT <= 1.7e+241) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -4.8e+166:
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif KbT <= 1.7e+241:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	else:
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -4.8e+166)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (KbT <= 1.7e+241)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	else
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -4.8e+166)
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (KbT <= 1.7e+241)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	else
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -4.8e+166], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.7e+241], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -4.79999999999999984e166

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add-exp-log 100.0%

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

      2. log1p-udef 100.0%

         \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. +-commutative 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in KbT around inf 77.6%

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

   8. Taylor expanded in EAccept around inf 70.2%

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

   if -4.79999999999999984e166 < KbT < 1.69999999999999997e241

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 48.2%

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

      1. associate-+r+ 48.2%

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

   7. Simplified 48.2%

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

   8. Taylor expanded in Ec around inf 32.7%

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

      1. mul-1-neg 32.7%

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

      2. associate-/l* 31.0%

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

   10. Simplified 31.0%

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

   11. Taylor expanded in KbT around 0 66.6%

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

   if 1.69999999999999997e241 < KbT

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 85.6%

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

   6. Taylor expanded in Ec around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. mul-1-neg 80.1%

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

   8. Simplified 80.1%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.8 \cdot 10^{+166}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 1.7 \cdot 10^{+241}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 6.2 \cdot 10^{+243}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2.35e+154)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar 2.0))
   (if (<= KbT 6.2e+243)
     (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
     (+ (/ NaChar 2.0) (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -2.35e+154) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 6.2e+243) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-2.35d+154)) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 6.2d+243) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else
        tmp = (nachar / 2.0d0) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -2.35e+154) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 6.2e+243) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -2.35e+154:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0)
	elif KbT <= 6.2e+243:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	else:
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -2.35e+154)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 6.2e+243)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	else
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -2.35e+154)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 6.2e+243)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	else
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -2.35e+154], 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[KbT, 6.2e+243], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -2.34999999999999992e154

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add-exp-log 100.0%

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

      2. log1p-udef 100.0%

         \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. +-commutative 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in KbT around inf 72.6%

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

   if -2.34999999999999992e154 < KbT < 6.2e243

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 48.3%

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

      1. associate-+r+ 48.3%

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

   7. Simplified 48.3%

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

   8. Taylor expanded in Ec around inf 33.5%

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

      1. mul-1-neg 33.5%

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

      2. associate-/l* 31.7%

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

   10. Simplified 31.7%

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

   11. Taylor expanded in KbT around 0 67.2%

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

   if 6.2e243 < KbT

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 85.6%

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

   6. Taylor expanded in Ec around inf 80.1%

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

      1. associate-*r/ 80.1%

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

      2. mul-1-neg 80.1%

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

   8. Simplified 80.1%

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

4. Final simplification 68.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 6.2 \cdot 10^{+243}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 39.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -8 \cdot 10^{-134}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1900000000000:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -8e-134)
   (+ (/ NdChar 2.0) (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
   (if (<= NaChar 1900000000000.0)
     (+ (/ NaChar 2.0) (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
     (+ (/ NdChar 2.0) (/ 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 tmp;
	if (NaChar <= -8e-134) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (NaChar <= 1900000000000.0) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	} else {
		tmp = (NdChar / 2.0) + (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) :: tmp
    if (nachar <= (-8d-134)) then
        tmp = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (nachar <= 1900000000000.0d0) then
        tmp = (nachar / 2.0d0) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    else
        tmp = (ndchar / 2.0d0) + (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 (NaChar <= -8e-134) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (NaChar <= 1900000000000.0) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -8e-134:
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif NaChar <= 1900000000000.0:
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	else:
		tmp = (NdChar / 2.0) + (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 (NaChar <= -8e-134)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (NaChar <= 1900000000000.0)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / 2.0) + 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)
	tmp = 0.0;
	if (NaChar <= -8e-134)
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (NaChar <= 1900000000000.0)
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((-Ec / KbT))));
	else
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -8e-134], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1900000000000.0], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $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 NaChar < -8.00000000000000032e-134

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add-exp-log 100.0%

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

      2. log1p-udef 100.0%

         \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. +-commutative 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in KbT around inf 49.2%

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

   8. Taylor expanded in Ev around inf 32.7%

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

   if -8.00000000000000032e-134 < NaChar < 1.9e12

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 55.8%

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

   6. Taylor expanded in Ec around inf 42.8%

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

      1. associate-*r/ 42.8%

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

      2. mul-1-neg 42.8%

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

   8. Simplified 42.8%

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

   if 1.9e12 < 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. Add Preprocessing
   5. Step-by-step derivation

      1. add-exp-log 100.0%

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

      2. log1p-udef 100.0%

         \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. +-commutative 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in KbT around inf 54.4%

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

   8. Taylor expanded in EAccept around inf 33.8%

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

4. Final simplification 36.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8 \cdot 10^{-134}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1900000000000:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 7.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 7.4e-93)
   (+
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT)))
    (/
     NdChar
     (- (+ (+ (/ EDonor KbT) 2.0) (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
   (+ (/ NdChar 2.0) (/ 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 tmp;
	if (EAccept <= 7.4e-93) {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = (NdChar / 2.0) + (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) :: tmp
    if (eaccept <= 7.4d-93) then
        tmp = (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt))) + (ndchar / ((((edonor / kbt) + 2.0d0) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))
    else
        tmp = (ndchar / 2.0d0) + (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 <= 7.4e-93) {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = (NdChar / 2.0) + (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 <= 7.4e-93:
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))
	else:
		tmp = (NdChar / 2.0) + (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 <= 7.4e-93)
		tmp = Float64(Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))) + Float64(NdChar / Float64(Float64(Float64(Float64(EDonor / KbT) + 2.0) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT))));
	else
		tmp = Float64(Float64(NdChar / 2.0) + 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)
	tmp = 0.0;
	if (EAccept <= 7.4e-93)
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	else
		tmp = (NdChar / 2.0) + (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, 7.4e-93], N[(N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 7.40000000000000005e-93

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 51.3%

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

      1. associate-+r+ 51.3%

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

   7. Simplified 51.3%

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

   8. Taylor expanded in KbT around inf 27.4%

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

   if 7.40000000000000005e-93 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

      1. add-exp-log 99.9%

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

      2. log1p-udef 99.9%

         \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. +-commutative 99.9%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      4. associate-+l- 99.9%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Applied egg-rr 99.9%

      \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in KbT around inf 52.2%

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

   8. Taylor expanded in EAccept around inf 43.9%

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

4. Final simplification 33.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 7.4 \cdot 10^{-93}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 37.1% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -7.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -7.8e+117)
   (+ (/ NdChar 2.0) (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
   (+ (/ NdChar 2.0) (/ 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 tmp;
	if (Ev <= -7.8e+117) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = (NdChar / 2.0) + (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) :: tmp
    if (ev <= (-7.8d+117)) then
        tmp = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = (ndchar / 2.0d0) + (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 (Ev <= -7.8e+117) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -7.8e+117:
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = (NdChar / 2.0) + (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 (Ev <= -7.8e+117)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(Float64(NdChar / 2.0) + 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)
	tmp = 0.0;
	if (Ev <= -7.8e+117)
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -7.8e+117], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] + 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 < -7.79999999999999981e117

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add-exp-log 100.0%

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

      2. log1p-udef 100.0%

         \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. +-commutative 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in KbT around inf 36.1%

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

   8. Taylor expanded in Ev around inf 33.3%

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

   if -7.79999999999999981e117 < 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. Add Preprocessing
   5. Step-by-step derivation

      1. add-exp-log 100.0%

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

      2. log1p-udef 100.0%

         \[\leadsto \frac{NdChar}{e^{\color{blue}{\mathsf{log1p}\left(e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      3. +-commutative 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(\left(Vef - Ec\right) + EDonor\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

      4. associate-+l- 100.0%

         \[\leadsto \frac{NdChar}{e^{\mathsf{log1p}\left(e^{\frac{mu + \color{blue}{\left(Vef - \left(Ec - EDonor\right)\right)}}{KbT}}\right)}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \frac{NdChar}{\color{blue}{e^{\mathsf{log1p}\left(e^{\frac{mu + \left(Vef - \left(Ec - EDonor\right)\right)}{KbT}}\right)}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]

   7. Taylor expanded in KbT around inf 46.8%

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

   8. Taylor expanded in EAccept around inf 36.5%

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

4. Final simplification 36.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -7.8 \cdot 10^{+117}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 27.2% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 1.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 1.8e-99)
   (+
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT)))
    (/
     NdChar
     (- (+ (+ (/ EDonor KbT) 2.0) (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
   (+ (/ NaChar 2.0) (* NdChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 1.8e-99) {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = (NaChar / 2.0) + (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 (eaccept <= 1.8d-99) then
        tmp = (nachar / ((2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt))) + (ndchar / ((((edonor / kbt) + 2.0d0) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))
    else
        tmp = (nachar / 2.0d0) + (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 (EAccept <= 1.8e-99) {
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	} else {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 1.8e-99:
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))
	else:
		tmp = (NaChar / 2.0) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 1.8e-99)
		tmp = Float64(Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))) + Float64(NdChar / Float64(Float64(Float64(Float64(EDonor / KbT) + 2.0) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT))));
	else
		tmp = Float64(Float64(NaChar / 2.0) + 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 (EAccept <= 1.8e-99)
		tmp = (NaChar / ((2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))) + (NdChar / ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)));
	else
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 1.8e-99], N[(N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 1.8e-99

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 51.3%

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

      1. associate-+r+ 51.3%

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

   7. Simplified 51.3%

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

   8. Taylor expanded in KbT around inf 27.4%

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

   if 1.8e-99 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 42.4%

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

   6. Taylor expanded in KbT around inf 28.0%

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

4. Final simplification 27.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 1.8 \cdot 10^{-99}:\\ \;\;\;\;\frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}} + \frac{NdChar}{\left(\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 8.4% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}\\ \mathbf{elif}\;KbT \leq 5.5 \cdot 10^{-163}:\\ \;\;\;\;\frac{NdChar \cdot \left(-KbT\right)}{Ec}\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{Ev}{\frac{KbT}{NaChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -5.5e-203)
   (* -0.25 (/ EAccept (/ KbT NaChar)))
   (if (<= KbT 5.5e-163)
     (/ (* NdChar (- KbT)) Ec)
     (* -0.25 (/ Ev (/ KbT NaChar))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -5.5e-203) {
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	} else if (KbT <= 5.5e-163) {
		tmp = (NdChar * -KbT) / Ec;
	} else {
		tmp = -0.25 * (Ev / (KbT / NaChar));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-5.5d-203)) then
        tmp = (-0.25d0) * (eaccept / (kbt / nachar))
    else if (kbt <= 5.5d-163) then
        tmp = (ndchar * -kbt) / ec
    else
        tmp = (-0.25d0) * (ev / (kbt / nachar))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -5.5e-203) {
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	} else if (KbT <= 5.5e-163) {
		tmp = (NdChar * -KbT) / Ec;
	} else {
		tmp = -0.25 * (Ev / (KbT / NaChar));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -5.5e-203:
		tmp = -0.25 * (EAccept / (KbT / NaChar))
	elif KbT <= 5.5e-163:
		tmp = (NdChar * -KbT) / Ec
	else:
		tmp = -0.25 * (Ev / (KbT / NaChar))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -5.5e-203)
		tmp = Float64(-0.25 * Float64(EAccept / Float64(KbT / NaChar)));
	elseif (KbT <= 5.5e-163)
		tmp = Float64(Float64(NdChar * Float64(-KbT)) / Ec);
	else
		tmp = Float64(-0.25 * Float64(Ev / Float64(KbT / NaChar)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -5.5e-203)
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	elseif (KbT <= 5.5e-163)
		tmp = (NdChar * -KbT) / Ec;
	else
		tmp = -0.25 * (Ev / (KbT / NaChar));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -5.5e-203], N[(-0.25 * N[(EAccept / N[(KbT / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 5.5e-163], N[(N[(NdChar * (-KbT)), $MachinePrecision] / Ec), $MachinePrecision], N[(-0.25 * N[(Ev / N[(KbT / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -5.5000000000000002e-203

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 55.6%

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

      1. associate-+r+ 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in Ec around inf 29.2%

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

      1. mul-1-neg 29.2%

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

      2. associate-/l* 29.5%

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

   10. Simplified 29.5%

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

   11. Taylor expanded in KbT around inf 6.2%

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

   12. Taylor expanded in EAccept around inf 6.2%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{EAccept \cdot NaChar}{KbT}} \]
   13. Step-by-step derivation

       1. associate-/l* 6.2%

          \[\leadsto -0.25 \cdot \color{blue}{\frac{EAccept}{\frac{KbT}{NaChar}}} \]

   14. Simplified 6.2%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}} \]

   if -5.5000000000000002e-203 < KbT < 5.4999999999999998e-163

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 50.2%

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

      1. associate-+r+ 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in Ec around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. associate-/l* 45.1%

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

   10. Simplified 45.1%

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

   11. Taylor expanded in KbT around inf 23.1%

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

       1. mul-1-neg 23.1%

          \[\leadsto \color{blue}{-\frac{KbT \cdot NdChar}{Ec}} \]

       2. associate-*l/ 17.0%

          \[\leadsto -\color{blue}{\frac{KbT}{Ec} \cdot NdChar} \]

       3. distribute-rgt-neg-in 17.0%

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

   13. Simplified 17.0%

       \[\leadsto \color{blue}{\frac{KbT}{Ec} \cdot \left(-NdChar\right)} \]
   14. Step-by-step derivation

       1. associate-*l/ 23.1%

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

   15. Applied egg-rr 23.1%

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

   if 5.4999999999999998e-163 < KbT

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 51.2%

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

      1. associate-+r+ 51.2%

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

   7. Simplified 51.2%

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

   8. Taylor expanded in Ec around inf 19.7%

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

      1. mul-1-neg 19.7%

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

      2. associate-/l* 21.6%

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

   10. Simplified 21.6%

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

   11. Taylor expanded in KbT around inf 7.7%

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

   12. Taylor expanded in Ev around inf 12.1%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{Ev \cdot NaChar}{KbT}} \]
   13. Step-by-step derivation

       1. associate-/l* 12.1%

          \[\leadsto -0.25 \cdot \color{blue}{\frac{Ev}{\frac{KbT}{NaChar}}} \]

   14. Simplified 12.1%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{Ev}{\frac{KbT}{NaChar}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 11.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -5.5 \cdot 10^{-203}:\\ \;\;\;\;-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}\\ \mathbf{elif}\;KbT \leq 5.5 \cdot 10^{-163}:\\ \;\;\;\;\frac{NdChar \cdot \left(-KbT\right)}{Ec}\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{Ev}{\frac{KbT}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 8.3% accurate, 13.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.4 \cdot 10^{-203}:\\ \;\;\;\;-0.25 \cdot \frac{NaChar \cdot EAccept}{KbT}\\ \mathbf{elif}\;KbT \leq 10^{-162}:\\ \;\;\;\;\frac{NdChar \cdot \left(-KbT\right)}{Ec}\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{Ev}{\frac{KbT}{NaChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.4e-203)
   (* -0.25 (/ (* NaChar EAccept) KbT))
   (if (<= KbT 1e-162)
     (/ (* NdChar (- KbT)) Ec)
     (* -0.25 (/ Ev (/ KbT NaChar))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.4e-203) {
		tmp = -0.25 * ((NaChar * EAccept) / KbT);
	} else if (KbT <= 1e-162) {
		tmp = (NdChar * -KbT) / Ec;
	} else {
		tmp = -0.25 * (Ev / (KbT / NaChar));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-1.4d-203)) then
        tmp = (-0.25d0) * ((nachar * eaccept) / kbt)
    else if (kbt <= 1d-162) then
        tmp = (ndchar * -kbt) / ec
    else
        tmp = (-0.25d0) * (ev / (kbt / nachar))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.4e-203) {
		tmp = -0.25 * ((NaChar * EAccept) / KbT);
	} else if (KbT <= 1e-162) {
		tmp = (NdChar * -KbT) / Ec;
	} else {
		tmp = -0.25 * (Ev / (KbT / NaChar));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -1.4e-203:
		tmp = -0.25 * ((NaChar * EAccept) / KbT)
	elif KbT <= 1e-162:
		tmp = (NdChar * -KbT) / Ec
	else:
		tmp = -0.25 * (Ev / (KbT / NaChar))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -1.4e-203)
		tmp = Float64(-0.25 * Float64(Float64(NaChar * EAccept) / KbT));
	elseif (KbT <= 1e-162)
		tmp = Float64(Float64(NdChar * Float64(-KbT)) / Ec);
	else
		tmp = Float64(-0.25 * Float64(Ev / Float64(KbT / NaChar)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -1.4e-203)
		tmp = -0.25 * ((NaChar * EAccept) / KbT);
	elseif (KbT <= 1e-162)
		tmp = (NdChar * -KbT) / Ec;
	else
		tmp = -0.25 * (Ev / (KbT / NaChar));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -1.4e-203], N[(-0.25 * N[(N[(NaChar * EAccept), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1e-162], N[(N[(NdChar * (-KbT)), $MachinePrecision] / Ec), $MachinePrecision], N[(-0.25 * N[(Ev / N[(KbT / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.40000000000000011e-203

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 55.6%

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

      1. associate-+r+ 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in Ec around inf 29.2%

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

      1. mul-1-neg 29.2%

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

      2. associate-/l* 29.5%

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

   10. Simplified 29.5%

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

   11. Taylor expanded in KbT around inf 6.2%

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

   12. Taylor expanded in EAccept around inf 6.2%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{EAccept \cdot NaChar}{KbT}} \]

   if -1.40000000000000011e-203 < KbT < 9.99999999999999954e-163

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 50.2%

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

      1. associate-+r+ 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in Ec around inf 53.4%

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

      1. mul-1-neg 53.4%

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

      2. associate-/l* 45.1%

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

   10. Simplified 45.1%

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

   11. Taylor expanded in KbT around inf 23.1%

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

       1. mul-1-neg 23.1%

          \[\leadsto \color{blue}{-\frac{KbT \cdot NdChar}{Ec}} \]

       2. associate-*l/ 17.0%

          \[\leadsto -\color{blue}{\frac{KbT}{Ec} \cdot NdChar} \]

       3. distribute-rgt-neg-in 17.0%

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

   13. Simplified 17.0%

       \[\leadsto \color{blue}{\frac{KbT}{Ec} \cdot \left(-NdChar\right)} \]
   14. Step-by-step derivation

       1. associate-*l/ 23.1%

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

   15. Applied egg-rr 23.1%

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

   if 9.99999999999999954e-163 < KbT

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 51.2%

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

      1. associate-+r+ 51.2%

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

   7. Simplified 51.2%

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

   8. Taylor expanded in Ec around inf 19.7%

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

      1. mul-1-neg 19.7%

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

      2. associate-/l* 21.6%

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

   10. Simplified 21.6%

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

   11. Taylor expanded in KbT around inf 7.7%

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

   12. Taylor expanded in Ev around inf 12.1%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{Ev \cdot NaChar}{KbT}} \]
   13. Step-by-step derivation

       1. associate-/l* 12.1%

          \[\leadsto -0.25 \cdot \color{blue}{\frac{Ev}{\frac{KbT}{NaChar}}} \]

   14. Simplified 12.1%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{Ev}{\frac{KbT}{NaChar}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 11.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.4 \cdot 10^{-203}:\\ \;\;\;\;-0.25 \cdot \frac{NaChar \cdot EAccept}{KbT}\\ \mathbf{elif}\;KbT \leq 10^{-162}:\\ \;\;\;\;\frac{NdChar \cdot \left(-KbT\right)}{Ec}\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{Ev}{\frac{KbT}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 26.1% accurate, 14.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq 4.7 \cdot 10^{+192}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Vef 4.7e+192)
   (+ (/ NaChar 2.0) (/ NdChar (- 2.0 (/ Ec KbT))))
   (* -0.25 (/ EAccept (/ KbT NaChar)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Vef <= 4.7e+192) {
		tmp = (NaChar / 2.0) + (NdChar / (2.0 - (Ec / KbT)));
	} else {
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	}
	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 (vef <= 4.7d+192) then
        tmp = (nachar / 2.0d0) + (ndchar / (2.0d0 - (ec / kbt)))
    else
        tmp = (-0.25d0) * (eaccept / (kbt / nachar))
    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 (Vef <= 4.7e+192) {
		tmp = (NaChar / 2.0) + (NdChar / (2.0 - (Ec / KbT)));
	} else {
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Vef <= 4.7e+192:
		tmp = (NaChar / 2.0) + (NdChar / (2.0 - (Ec / KbT)))
	else:
		tmp = -0.25 * (EAccept / (KbT / NaChar))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Vef <= 4.7e+192)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(2.0 - Float64(Ec / KbT))));
	else
		tmp = Float64(-0.25 * Float64(EAccept / Float64(KbT / NaChar)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Vef <= 4.7e+192)
		tmp = (NaChar / 2.0) + (NdChar / (2.0 - (Ec / KbT)));
	else
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Vef, 4.7e+192], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(2.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-0.25 * N[(EAccept / N[(KbT / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < 4.6999999999999997e192

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 42.1%

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

   6. Taylor expanded in Ec around inf 33.6%

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

      1. associate-*r/ 33.6%

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

      2. mul-1-neg 33.6%

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

   8. Simplified 33.6%

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

   9. Taylor expanded in Ec around 0 26.5%

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

       1. mul-1-neg 26.5%

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

       2. unsub-neg 26.5%

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

   11. Simplified 26.5%

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

   if 4.6999999999999997e192 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 47.4%

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

      1. associate-+r+ 47.4%

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

   7. Simplified 47.4%

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

   8. Taylor expanded in Ec around inf 27.0%

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

      1. mul-1-neg 27.0%

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

      2. associate-/l* 27.0%

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

   10. Simplified 27.0%

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

   11. Taylor expanded in KbT around inf 2.3%

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

   12. Taylor expanded in EAccept around inf 13.5%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{EAccept \cdot NaChar}{KbT}} \]
   13. Step-by-step derivation

       1. associate-/l* 23.7%

          \[\leadsto -0.25 \cdot \color{blue}{\frac{EAccept}{\frac{KbT}{NaChar}}} \]

   14. Simplified 23.7%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq 4.7 \cdot 10^{+192}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{2 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 8.8% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq 8.2 \cdot 10^{-23}:\\ \;\;\;\;\frac{NdChar \cdot \left(-KbT\right)}{Ec}\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar 8.2e-23)
   (/ (* NdChar (- KbT)) Ec)
   (* -0.25 (/ EAccept (/ KbT NaChar)))))

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 <= 8.2e-23) {
		tmp = (NdChar * -KbT) / Ec;
	} else {
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	}
	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 <= 8.2d-23) then
        tmp = (ndchar * -kbt) / ec
    else
        tmp = (-0.25d0) * (eaccept / (kbt / nachar))
    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 <= 8.2e-23) {
		tmp = (NdChar * -KbT) / Ec;
	} else {
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= 8.2e-23:
		tmp = (NdChar * -KbT) / Ec
	else:
		tmp = -0.25 * (EAccept / (KbT / NaChar))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= 8.2e-23)
		tmp = Float64(Float64(NdChar * Float64(-KbT)) / Ec);
	else
		tmp = Float64(-0.25 * Float64(EAccept / Float64(KbT / NaChar)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= 8.2e-23)
		tmp = (NdChar * -KbT) / Ec;
	else
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, 8.2e-23], N[(N[(NdChar * (-KbT)), $MachinePrecision] / Ec), $MachinePrecision], N[(-0.25 * N[(EAccept / N[(KbT / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < 8.20000000000000059e-23

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 56.1%

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

      1. associate-+r+ 56.1%

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

   7. Simplified 56.1%

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

   8. Taylor expanded in Ec around inf 34.6%

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

      1. mul-1-neg 34.6%

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

      2. associate-/l* 33.4%

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

   10. Simplified 33.4%

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

   11. Taylor expanded in KbT around inf 7.9%

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

       1. mul-1-neg 7.9%

          \[\leadsto \color{blue}{-\frac{KbT \cdot NdChar}{Ec}} \]

       2. associate-*l/ 6.5%

          \[\leadsto -\color{blue}{\frac{KbT}{Ec} \cdot NdChar} \]

       3. distribute-rgt-neg-in 6.5%

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

   13. Simplified 6.5%

       \[\leadsto \color{blue}{\frac{KbT}{Ec} \cdot \left(-NdChar\right)} \]
   14. Step-by-step derivation

       1. associate-*l/ 7.9%

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

   15. Applied egg-rr 7.9%

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

   if 8.20000000000000059e-23 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 44.2%

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

      1. associate-+r+ 44.2%

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

   7. Simplified 44.2%

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

   8. Taylor expanded in Ec around inf 16.2%

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

      1. mul-1-neg 16.2%

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

      2. associate-/l* 17.6%

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

   10. Simplified 17.6%

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

   11. Taylor expanded in KbT around inf 4.1%

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

   12. Taylor expanded in EAccept around inf 10.9%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{EAccept \cdot NaChar}{KbT}} \]
   13. Step-by-step derivation

       1. associate-/l* 13.9%

          \[\leadsto -0.25 \cdot \color{blue}{\frac{EAccept}{\frac{KbT}{NaChar}}} \]

   14. Simplified 13.9%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 9.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq 8.2 \cdot 10^{-23}:\\ \;\;\;\;\frac{NdChar \cdot \left(-KbT\right)}{Ec}\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.1% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq 3.45 \cdot 10^{+192}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Vef 3.45e+192)
   (+ (/ NaChar 2.0) (* NdChar 0.5))
   (* -0.25 (/ EAccept (/ KbT NaChar)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Vef <= 3.45e+192) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else {
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	}
	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 (vef <= 3.45d+192) then
        tmp = (nachar / 2.0d0) + (ndchar * 0.5d0)
    else
        tmp = (-0.25d0) * (eaccept / (kbt / nachar))
    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 (Vef <= 3.45e+192) {
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	} else {
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Vef <= 3.45e+192:
		tmp = (NaChar / 2.0) + (NdChar * 0.5)
	else:
		tmp = -0.25 * (EAccept / (KbT / NaChar))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Vef <= 3.45e+192)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar * 0.5));
	else
		tmp = Float64(-0.25 * Float64(EAccept / Float64(KbT / NaChar)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Vef <= 3.45e+192)
		tmp = (NaChar / 2.0) + (NdChar * 0.5);
	else
		tmp = -0.25 * (EAccept / (KbT / NaChar));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Vef, 3.45e+192], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(-0.25 * N[(EAccept / N[(KbT / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < 3.44999999999999989e192

   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. Add Preprocessing

   5. Taylor expanded in KbT around inf 42.1%

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

   6. Taylor expanded in KbT around inf 26.5%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{2} \]

   if 3.44999999999999989e192 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 47.4%

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

      1. associate-+r+ 47.4%

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

   7. Simplified 47.4%

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

   8. Taylor expanded in Ec around inf 27.0%

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

      1. mul-1-neg 27.0%

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

      2. associate-/l* 27.0%

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

   10. Simplified 27.0%

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

   11. Taylor expanded in KbT around inf 2.3%

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

   12. Taylor expanded in EAccept around inf 13.5%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{EAccept \cdot NaChar}{KbT}} \]
   13. Step-by-step derivation

       1. associate-/l* 23.7%

          \[\leadsto -0.25 \cdot \color{blue}{\frac{EAccept}{\frac{KbT}{NaChar}}} \]

   14. Simplified 23.7%

       \[\leadsto \color{blue}{-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 26.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq 3.45 \cdot 10^{+192}:\\ \;\;\;\;\frac{NaChar}{2} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;-0.25 \cdot \frac{EAccept}{\frac{KbT}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 8.2% accurate, 38.2× speedup

Math

\[\begin{array}{l} \\ NdChar \cdot \frac{-KbT}{Ec} \end{array} \]

FPCore

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

C

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

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 * (-kbt / ec)
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 * (-KbT / Ec);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 53.0%

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

   1. associate-+r+ 53.0%

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

7. Simplified 53.0%

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

8. Taylor expanded in Ec around inf 30.0%

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

   1. mul-1-neg 30.0%

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

   2. associate-/l* 29.4%

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

10. Simplified 29.4%

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

11. Taylor expanded in KbT around inf 6.6%

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

    1. mul-1-neg 6.6%

       \[\leadsto \color{blue}{-\frac{KbT \cdot NdChar}{Ec}} \]

    2. associate-*l/ 6.0%

       \[\leadsto -\color{blue}{\frac{KbT}{Ec} \cdot NdChar} \]

    3. distribute-rgt-neg-in 6.0%

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

13. Simplified 6.0%

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

14. Final simplification 6.0%

    \[\leadsto NdChar \cdot \frac{-KbT}{Ec} \]
15. Add Preprocessing

Alternative 21: 8.4% accurate, 38.2× speedup

Math

\[\begin{array}{l} \\ \frac{NdChar \cdot \left(-KbT\right)}{Ec} \end{array} \]

FPCore

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

C

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

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 * -kbt) / ec
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 * -KbT) / Ec;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 53.0%

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

   1. associate-+r+ 53.0%

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

7. Simplified 53.0%

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

8. Taylor expanded in Ec around inf 30.0%

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

   1. mul-1-neg 30.0%

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

   2. associate-/l* 29.4%

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

10. Simplified 29.4%

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

11. Taylor expanded in KbT around inf 6.6%

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

    1. mul-1-neg 6.6%

       \[\leadsto \color{blue}{-\frac{KbT \cdot NdChar}{Ec}} \]

    2. associate-*l/ 6.0%

       \[\leadsto -\color{blue}{\frac{KbT}{Ec} \cdot NdChar} \]

    3. distribute-rgt-neg-in 6.0%

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

13. Simplified 6.0%

    \[\leadsto \color{blue}{\frac{KbT}{Ec} \cdot \left(-NdChar\right)} \]
14. Step-by-step derivation

    1. associate-*l/ 6.6%

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

15. Applied egg-rr 6.6%

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

16. Final simplification 6.6%

    \[\leadsto \frac{NdChar \cdot \left(-KbT\right)}{Ec} \]
17. Add Preprocessing

Reproduce

herbie shell --seed 2024016 
(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))))))