Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 16.5s

Alternatives: 16

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: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) + -mu) / kbt))))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (ndchar / (exp(((edonor - ((ec - vef) - mu)) / kbt)) + 1.0d0)) + (nachar / (exp(((vef + (ev + (eaccept - mu))) / kbt)) + 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 65.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;Ev \leq -5.3 \cdot 10^{+256}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Ev \leq -4.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -4.1 \cdot 10^{-227}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (- (+ Vef (+ Ev EAccept)) mu) KbT)) 1.0))))
   (if (<= Ev -5.3e+256)
     t_0
     (if (<= Ev -4.9e+30)
       (/ NdChar (+ (exp (/ (- (+ EDonor (+ mu Vef)) Ec) KbT)) 1.0))
       (if (<= Ev -4.1e-227)
         t_0
         (+
          (/ NdChar (+ (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)) 1.0))
          (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0);
	double tmp;
	if (Ev <= -5.3e+256) {
		tmp = t_0;
	} else if (Ev <= -4.9e+30) {
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	} else if (Ev <= -4.1e-227) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / (exp((EAccept / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (exp((((vef + (ev + eaccept)) - mu) / kbt)) + 1.0d0)
    if (ev <= (-5.3d+256)) then
        tmp = t_0
    else if (ev <= (-4.9d+30)) then
        tmp = ndchar / (exp((((edonor + (mu + vef)) - ec) / kbt)) + 1.0d0)
    else if (ev <= (-4.1d-227)) then
        tmp = t_0
    else
        tmp = (ndchar / (exp(((edonor - ((ec - vef) - mu)) / kbt)) + 1.0d0)) + (nachar / (exp((eaccept / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0);
	double tmp;
	if (Ev <= -5.3e+256) {
		tmp = t_0;
	} else if (Ev <= -4.9e+30) {
		tmp = NdChar / (Math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	} else if (Ev <= -4.1e-227) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / (Math.exp((EAccept / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0)
	tmp = 0
	if Ev <= -5.3e+256:
		tmp = t_0
	elif Ev <= -4.9e+30:
		tmp = NdChar / (math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0)
	elif Ev <= -4.1e-227:
		tmp = t_0
	else:
		tmp = (NdChar / (math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / (math.exp((EAccept / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(Ev + EAccept)) - mu) / KbT)) + 1.0))
	tmp = 0.0
	if (Ev <= -5.3e+256)
		tmp = t_0;
	elseif (Ev <= -4.9e+30)
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT)) + 1.0));
	elseif (Ev <= -4.1e-227)
		tmp = t_0;
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0);
	tmp = 0.0;
	if (Ev <= -5.3e+256)
		tmp = t_0;
	elseif (Ev <= -4.9e+30)
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	elseif (Ev <= -4.1e-227)
		tmp = t_0;
	else
		tmp = (NdChar / (exp(((EDonor - ((Ec - Vef) - mu)) / KbT)) + 1.0)) + (NaChar / (exp((EAccept / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -5.3e+256], t$95$0, If[LessEqual[Ev, -4.9e+30], N[(NdChar / N[(N[Exp[N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -4.1e-227], t$95$0, N[(N[(NdChar / N[(N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -5.3e256 or -4.89999999999999984e30 < Ev < -4.10000000000000009e-227

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 70.9%

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

      1. associate--l+ 70.9%

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

      2. sub-neg 70.9%

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

      3. associate-+r+ 70.9%

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

      4. mul-1-neg 70.9%

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

      5. mul-1-neg 70.9%

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

      6. associate-+r+ 70.9%

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

      7. sub-neg 70.9%

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

      8. associate--l+ 70.9%

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

      9. associate-+r+ 70.9%

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

   7. Simplified 70.9%

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

   if -5.3e256 < Ev < -4.89999999999999984e30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 71.3%

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

   if -4.10000000000000009e-227 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.2%

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

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -5.3 \cdot 10^{+256}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -4.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -4.1 \cdot 10^{-227}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 36.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -6 \cdot 10^{+256}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.2 \cdot 10^{+111}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.7 \cdot 10^{-251}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq 1.12 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{-Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -6e+256)
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
   (if (<= Ev -1.2e+111)
     (/ NdChar (+ (exp (/ mu KbT)) 1.0))
     (if (<= Ev -1.7e-251)
       (/ NaChar (+ (exp (/ Vef KbT)) 1.0))
       (if (<= Ev 1.12e-166)
         (/ NdChar (+ (exp (/ (- Ec) KbT)) 1.0))
         (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -6e+256) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -1.2e+111) {
		tmp = NdChar / (exp((mu / KbT)) + 1.0);
	} else if (Ev <= -1.7e-251) {
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	} else if (Ev <= 1.12e-166) {
		tmp = NdChar / (exp((-Ec / KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-6d+256)) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else if (ev <= (-1.2d+111)) then
        tmp = ndchar / (exp((mu / kbt)) + 1.0d0)
    else if (ev <= (-1.7d-251)) then
        tmp = nachar / (exp((vef / kbt)) + 1.0d0)
    else if (ev <= 1.12d-166) then
        tmp = ndchar / (exp((-ec / kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -6e+256) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -1.2e+111) {
		tmp = NdChar / (Math.exp((mu / KbT)) + 1.0);
	} else if (Ev <= -1.7e-251) {
		tmp = NaChar / (Math.exp((Vef / KbT)) + 1.0);
	} else if (Ev <= 1.12e-166) {
		tmp = NdChar / (Math.exp((-Ec / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -6e+256:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	elif Ev <= -1.2e+111:
		tmp = NdChar / (math.exp((mu / KbT)) + 1.0)
	elif Ev <= -1.7e-251:
		tmp = NaChar / (math.exp((Vef / KbT)) + 1.0)
	elif Ev <= 1.12e-166:
		tmp = NdChar / (math.exp((-Ec / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -6e+256)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	elseif (Ev <= -1.2e+111)
		tmp = Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0));
	elseif (Ev <= -1.7e-251)
		tmp = Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0));
	elseif (Ev <= 1.12e-166)
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(-Ec) / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -6e+256)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	elseif (Ev <= -1.2e+111)
		tmp = NdChar / (exp((mu / KbT)) + 1.0);
	elseif (Ev <= -1.7e-251)
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	elseif (Ev <= 1.12e-166)
		tmp = NdChar / (exp((-Ec / KbT)) + 1.0);
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -6e+256], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.2e+111], N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.7e-251], N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 1.12e-166], N[(NdChar / N[(N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if Ev < -6.0000000000000002e256

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 83.7%

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

      1. associate--l+ 83.7%

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

      2. sub-neg 83.7%

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

      3. associate-+r+ 83.7%

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

      4. mul-1-neg 83.7%

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

      5. mul-1-neg 83.7%

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

      6. associate-+r+ 83.7%

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

      7. sub-neg 83.7%

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

      8. associate--l+ 83.7%

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

      9. associate-+r+ 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in Ev around inf 83.7%

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

   if -6.0000000000000002e256 < Ev < -1.20000000000000003e111

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 71.8%

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

   6. Taylor expanded in mu around inf 54.6%

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

   if -1.20000000000000003e111 < Ev < -1.70000000000000008e-251

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 68.4%

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

      1. associate--l+ 68.4%

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

      2. sub-neg 68.4%

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

      3. associate-+r+ 68.4%

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

      4. mul-1-neg 68.4%

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

      5. mul-1-neg 68.4%

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

      6. associate-+r+ 68.4%

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

      7. sub-neg 68.4%

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

      8. associate--l+ 68.4%

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

      9. associate-+r+ 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in Vef around inf 47.0%

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

   if -1.70000000000000008e-251 < Ev < 1.11999999999999994e-166

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 62.1%

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

   6. Taylor expanded in Ec around inf 44.7%

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

      1. associate-*r/ 44.7%

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

      2. mul-1-neg 44.7%

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

   8. Simplified 44.7%

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

   if 1.11999999999999994e-166 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 60.3%

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

      1. associate--l+ 60.3%

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

      2. sub-neg 60.3%

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

      3. associate-+r+ 60.3%

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

      4. mul-1-neg 60.3%

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

      5. mul-1-neg 60.3%

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

      6. associate-+r+ 60.3%

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

      7. sub-neg 60.3%

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

      8. associate--l+ 60.3%

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

      9. associate-+r+ 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in EAccept around inf 37.8%

      \[\leadsto \frac{NaChar}{1 + e^{\color{blue}{\frac{EAccept}{KbT}}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -6 \cdot 10^{+256}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.2 \cdot 10^{+111}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.7 \cdot 10^{-251}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq 1.12 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{-Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 37.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{if}\;Ev \leq -4.8 \cdot 10^{+256}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.05 \cdot 10^{+111}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Ev \leq -2.2 \cdot 10^{-256}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -6.2 \cdot 10^{-306}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ mu KbT)) 1.0))))
   (if (<= Ev -4.8e+256)
     (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
     (if (<= Ev -1.05e+111)
       t_0
       (if (<= Ev -2.2e-256)
         (/ NaChar (+ (exp (/ Vef KbT)) 1.0))
         (if (<= Ev -6.2e-306)
           t_0
           (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp((mu / KbT)) + 1.0);
	double tmp;
	if (Ev <= -4.8e+256) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -1.05e+111) {
		tmp = t_0;
	} else if (Ev <= -2.2e-256) {
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	} else if (Ev <= -6.2e-306) {
		tmp = t_0;
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp((mu / kbt)) + 1.0d0)
    if (ev <= (-4.8d+256)) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else if (ev <= (-1.05d+111)) then
        tmp = t_0
    else if (ev <= (-2.2d-256)) then
        tmp = nachar / (exp((vef / kbt)) + 1.0d0)
    else if (ev <= (-6.2d-306)) then
        tmp = t_0
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp((mu / KbT)) + 1.0);
	double tmp;
	if (Ev <= -4.8e+256) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -1.05e+111) {
		tmp = t_0;
	} else if (Ev <= -2.2e-256) {
		tmp = NaChar / (Math.exp((Vef / KbT)) + 1.0);
	} else if (Ev <= -6.2e-306) {
		tmp = t_0;
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp((mu / KbT)) + 1.0)
	tmp = 0
	if Ev <= -4.8e+256:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	elif Ev <= -1.05e+111:
		tmp = t_0
	elif Ev <= -2.2e-256:
		tmp = NaChar / (math.exp((Vef / KbT)) + 1.0)
	elif Ev <= -6.2e-306:
		tmp = t_0
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0))
	tmp = 0.0
	if (Ev <= -4.8e+256)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	elseif (Ev <= -1.05e+111)
		tmp = t_0;
	elseif (Ev <= -2.2e-256)
		tmp = Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0));
	elseif (Ev <= -6.2e-306)
		tmp = t_0;
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp((mu / KbT)) + 1.0);
	tmp = 0.0;
	if (Ev <= -4.8e+256)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	elseif (Ev <= -1.05e+111)
		tmp = t_0;
	elseif (Ev <= -2.2e-256)
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	elseif (Ev <= -6.2e-306)
		tmp = t_0;
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -4.8e+256], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.05e+111], t$95$0, If[LessEqual[Ev, -2.2e-256], N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -6.2e-306], t$95$0, N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -4.80000000000000028e256

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 83.7%

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

      1. associate--l+ 83.7%

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

      2. sub-neg 83.7%

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

      3. associate-+r+ 83.7%

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

      4. mul-1-neg 83.7%

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

      5. mul-1-neg 83.7%

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

      6. associate-+r+ 83.7%

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

      7. sub-neg 83.7%

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

      8. associate--l+ 83.7%

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

      9. associate-+r+ 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in Ev around inf 83.7%

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

   if -4.80000000000000028e256 < Ev < -1.04999999999999997e111 or -2.2000000000000001e-256 < Ev < -6.19999999999999995e-306

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 73.3%

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

   6. Taylor expanded in mu around inf 55.9%

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

   if -1.04999999999999997e111 < Ev < -2.2000000000000001e-256

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 68.4%

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

      1. associate--l+ 68.4%

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

      2. sub-neg 68.4%

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

      3. associate-+r+ 68.4%

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

      4. mul-1-neg 68.4%

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

      5. mul-1-neg 68.4%

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

      6. associate-+r+ 68.4%

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

      7. sub-neg 68.4%

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

      8. associate--l+ 68.4%

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

      9. associate-+r+ 68.4%

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

   7. Simplified 68.4%

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

   8. Taylor expanded in Vef around inf 47.0%

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

   if -6.19999999999999995e-306 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 59.8%

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

      1. associate--l+ 59.8%

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

      2. sub-neg 59.8%

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

      3. associate-+r+ 59.8%

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

      4. mul-1-neg 59.8%

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

      5. mul-1-neg 59.8%

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

      6. associate-+r+ 59.8%

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

      7. sub-neg 59.8%

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

      8. associate--l+ 59.8%

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

      9. associate-+r+ 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in EAccept around inf 37.8%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -4.8 \cdot 10^{+256}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.05 \cdot 10^{+111}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -2.2 \cdot 10^{-256}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -6.2 \cdot 10^{-306}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 37.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;Ev \leq -1.55 \cdot 10^{+209}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.22 \cdot 10^{+110}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Ev \leq -2.45 \cdot 10^{-256}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq 3.3 \cdot 10^{-166}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))))
   (if (<= Ev -1.55e+209)
     (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
     (if (<= Ev -1.22e+110)
       t_0
       (if (<= Ev -2.45e-256)
         (/ NaChar (+ (exp (/ Vef KbT)) 1.0))
         (if (<= Ev 3.3e-166)
           t_0
           (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp((EDonor / KbT)) + 1.0);
	double tmp;
	if (Ev <= -1.55e+209) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -1.22e+110) {
		tmp = t_0;
	} else if (Ev <= -2.45e-256) {
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	} else if (Ev <= 3.3e-166) {
		tmp = t_0;
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp((edonor / kbt)) + 1.0d0)
    if (ev <= (-1.55d+209)) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else if (ev <= (-1.22d+110)) then
        tmp = t_0
    else if (ev <= (-2.45d-256)) then
        tmp = nachar / (exp((vef / kbt)) + 1.0d0)
    else if (ev <= 3.3d-166) then
        tmp = t_0
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp((EDonor / KbT)) + 1.0);
	double tmp;
	if (Ev <= -1.55e+209) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -1.22e+110) {
		tmp = t_0;
	} else if (Ev <= -2.45e-256) {
		tmp = NaChar / (Math.exp((Vef / KbT)) + 1.0);
	} else if (Ev <= 3.3e-166) {
		tmp = t_0;
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp((EDonor / KbT)) + 1.0)
	tmp = 0
	if Ev <= -1.55e+209:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	elif Ev <= -1.22e+110:
		tmp = t_0
	elif Ev <= -2.45e-256:
		tmp = NaChar / (math.exp((Vef / KbT)) + 1.0)
	elif Ev <= 3.3e-166:
		tmp = t_0
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0))
	tmp = 0.0
	if (Ev <= -1.55e+209)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	elseif (Ev <= -1.22e+110)
		tmp = t_0;
	elseif (Ev <= -2.45e-256)
		tmp = Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0));
	elseif (Ev <= 3.3e-166)
		tmp = t_0;
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp((EDonor / KbT)) + 1.0);
	tmp = 0.0;
	if (Ev <= -1.55e+209)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	elseif (Ev <= -1.22e+110)
		tmp = t_0;
	elseif (Ev <= -2.45e-256)
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	elseif (Ev <= 3.3e-166)
		tmp = t_0;
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -1.55e+209], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.22e+110], t$95$0, If[LessEqual[Ev, -2.45e-256], N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 3.3e-166], t$95$0, N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -1.55e209

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 72.2%

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

      1. associate--l+ 72.2%

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

      2. sub-neg 72.2%

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

      3. associate-+r+ 72.2%

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

      4. mul-1-neg 72.2%

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

      5. mul-1-neg 72.2%

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

      6. associate-+r+ 72.2%

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

      7. sub-neg 72.2%

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

      8. associate--l+ 72.2%

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

      9. associate-+r+ 72.2%

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

   7. Simplified 72.2%

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

   8. Taylor expanded in Ev around inf 72.2%

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

   if -1.55e209 < Ev < -1.22000000000000002e110 or -2.44999999999999998e-256 < Ev < 3.30000000000000018e-166

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 68.7%

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

   6. Taylor expanded in EDonor around inf 44.2%

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

   if -1.22000000000000002e110 < Ev < -2.44999999999999998e-256

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 69.3%

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

      1. associate--l+ 69.3%

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

      2. sub-neg 69.3%

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

      3. associate-+r+ 69.3%

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

      4. mul-1-neg 69.3%

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

      5. mul-1-neg 69.3%

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

      6. associate-+r+ 69.3%

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

      7. sub-neg 69.3%

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

      8. associate--l+ 69.3%

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

      9. associate-+r+ 69.3%

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

   7. Simplified 69.3%

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

   8. Taylor expanded in Vef around inf 47.7%

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

   if 3.30000000000000018e-166 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 60.3%

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

      1. associate--l+ 60.3%

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

      2. sub-neg 60.3%

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

      3. associate-+r+ 60.3%

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

      4. mul-1-neg 60.3%

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

      5. mul-1-neg 60.3%

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

      6. associate-+r+ 60.3%

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

      7. sub-neg 60.3%

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

      8. associate--l+ 60.3%

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

      9. associate-+r+ 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in EAccept around inf 37.8%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.55 \cdot 10^{+209}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.22 \cdot 10^{+110}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -2.45 \cdot 10^{-256}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq 3.3 \cdot 10^{-166}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 69.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -1.7 \cdot 10^{+42} \lor \neg \left(NdChar \leq 6.2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -1.7e+42) (not (<= NdChar 6.2e-32)))
   (/ NdChar (+ (exp (/ (- (+ EDonor (+ mu Vef)) Ec) KbT)) 1.0))
   (/ NaChar (+ (exp (/ (- (+ Vef (+ Ev EAccept)) mu) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -1.7e+42) || !(NdChar <= 6.2e-32)) {
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-1.7d+42)) .or. (.not. (ndchar <= 6.2d-32))) then
        tmp = ndchar / (exp((((edonor + (mu + vef)) - ec) / kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((((vef + (ev + eaccept)) - mu) / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -1.7e+42) || !(NdChar <= 6.2e-32)) {
		tmp = NdChar / (Math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -1.7e+42) or not (NdChar <= 6.2e-32):
		tmp = NdChar / (math.exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -1.7e+42) || !(NdChar <= 6.2e-32))
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(EDonor + Float64(mu + Vef)) - Ec) / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(Ev + EAccept)) - mu) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -1.7e+42) || ~((NdChar <= 6.2e-32)))
		tmp = NdChar / (exp((((EDonor + (mu + Vef)) - Ec) / KbT)) + 1.0);
	else
		tmp = NaChar / (exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -1.7e+42], N[Not[LessEqual[NdChar, 6.2e-32]], $MachinePrecision]], N[(NdChar / N[(N[Exp[N[(N[(N[(EDonor + N[(mu + Vef), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -1.69999999999999988e42 or 6.20000000000000021e-32 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 77.3%

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

   if -1.69999999999999988e42 < NdChar < 6.20000000000000021e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 72.6%

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

      1. associate--l+ 72.6%

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

      2. sub-neg 72.6%

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

      3. associate-+r+ 72.6%

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

      4. mul-1-neg 72.6%

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

      5. mul-1-neg 72.6%

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

      6. associate-+r+ 72.6%

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

      7. sub-neg 72.6%

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

      8. associate--l+ 72.6%

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

      9. associate-+r+ 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 74.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.7 \cdot 10^{+42} \lor \neg \left(NdChar \leq 6.2 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(EDonor + \left(mu + Vef\right)\right) - Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 65.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -2.65 \cdot 10^{+42} \lor \neg \left(NdChar \leq 10^{-31}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(mu + Vef\right) - Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -2.65e+42) (not (<= NdChar 1e-31)))
   (/ NdChar (+ (exp (/ (- (+ mu Vef) Ec) KbT)) 1.0))
   (/ NaChar (+ (exp (/ (- (+ Vef (+ Ev EAccept)) mu) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -2.65e+42) || !(NdChar <= 1e-31)) {
		tmp = NdChar / (exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-2.65d+42)) .or. (.not. (ndchar <= 1d-31))) then
        tmp = ndchar / (exp((((mu + vef) - ec) / kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((((vef + (ev + eaccept)) - mu) / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -2.65e+42) || !(NdChar <= 1e-31)) {
		tmp = NdChar / (Math.exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -2.65e+42) or not (NdChar <= 1e-31):
		tmp = NdChar / (math.exp((((mu + Vef) - Ec) / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -2.65e+42) || !(NdChar <= 1e-31))
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(Ev + EAccept)) - mu) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -2.65e+42) || ~((NdChar <= 1e-31)))
		tmp = NdChar / (exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	else
		tmp = NaChar / (exp((((Vef + (Ev + EAccept)) - mu) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -2.65e+42], N[Not[LessEqual[NdChar, 1e-31]], $MachinePrecision]], N[(NdChar / N[(N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -2.65000000000000014e42 or 1e-31 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 77.3%

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

   6. Taylor expanded in EDonor around 0 71.5%

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

   if -2.65000000000000014e42 < NdChar < 1e-31

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 72.6%

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

      1. associate--l+ 72.6%

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

      2. sub-neg 72.6%

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

      3. associate-+r+ 72.6%

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

      4. mul-1-neg 72.6%

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

      5. mul-1-neg 72.6%

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

      6. associate-+r+ 72.6%

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

      7. sub-neg 72.6%

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

      8. associate--l+ 72.6%

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

      9. associate-+r+ 72.6%

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

   7. Simplified 72.6%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.65 \cdot 10^{+42} \lor \neg \left(NdChar \leq 10^{-31}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(mu + Vef\right) - Ec}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Vef + \left(Ev + EAccept\right)\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -2.35 \cdot 10^{+52}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.62 \cdot 10^{-248}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq 6.5 \cdot 10^{-291}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -2.35e+52)
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
   (if (<= Ev -1.62e-248)
     (/ NaChar (+ (exp (/ Vef KbT)) 1.0))
     (if (<= Ev 6.5e-291)
       (* 0.5 (+ NdChar NaChar))
       (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -2.35e+52) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -1.62e-248) {
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	} else if (Ev <= 6.5e-291) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-2.35d+52)) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else if (ev <= (-1.62d-248)) then
        tmp = nachar / (exp((vef / kbt)) + 1.0d0)
    else if (ev <= 6.5d-291) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -2.35e+52) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else if (Ev <= -1.62e-248) {
		tmp = NaChar / (Math.exp((Vef / KbT)) + 1.0);
	} else if (Ev <= 6.5e-291) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -2.35e+52:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	elif Ev <= -1.62e-248:
		tmp = NaChar / (math.exp((Vef / KbT)) + 1.0)
	elif Ev <= 6.5e-291:
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -2.35e+52)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	elseif (Ev <= -1.62e-248)
		tmp = Float64(NaChar / Float64(exp(Float64(Vef / KbT)) + 1.0));
	elseif (Ev <= 6.5e-291)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -2.35e+52)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	elseif (Ev <= -1.62e-248)
		tmp = NaChar / (exp((Vef / KbT)) + 1.0);
	elseif (Ev <= 6.5e-291)
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -2.35e+52], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.62e-248], N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 6.5e-291], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -2.35e52

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 55.8%

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

      1. associate--l+ 55.8%

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

      2. sub-neg 55.8%

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

      3. associate-+r+ 55.8%

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

      4. mul-1-neg 55.8%

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

      5. mul-1-neg 55.8%

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

      6. associate-+r+ 55.8%

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

      7. sub-neg 55.8%

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

      8. associate--l+ 55.8%

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

      9. associate-+r+ 55.8%

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

   7. Simplified 55.8%

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

   8. Taylor expanded in Ev around inf 49.4%

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

   if -2.35e52 < Ev < -1.6200000000000001e-248

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 66.2%

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

      1. associate--l+ 66.2%

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

      2. sub-neg 66.2%

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

      3. associate-+r+ 66.2%

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

      4. mul-1-neg 66.2%

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

      5. mul-1-neg 66.2%

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

      6. associate-+r+ 66.2%

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

      7. sub-neg 66.2%

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

      8. associate--l+ 66.2%

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

      9. associate-+r+ 66.2%

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

   7. Simplified 66.2%

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

   8. Taylor expanded in Vef around inf 43.6%

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

   if -1.6200000000000001e-248 < Ev < 6.50000000000000002e-291

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 52.7%

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

      1. distribute-lft-out 52.7%

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

   7. Simplified 52.7%

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

   if 6.50000000000000002e-291 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 58.6%

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

      1. associate--l+ 58.6%

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

      2. sub-neg 58.6%

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

      3. associate-+r+ 58.6%

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

      4. mul-1-neg 58.6%

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

      5. mul-1-neg 58.6%

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

      6. associate-+r+ 58.6%

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

      7. sub-neg 58.6%

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

      8. associate--l+ 58.6%

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

      9. associate-+r+ 58.6%

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

   7. Simplified 58.6%

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

   8. Taylor expanded in EAccept around inf 37.2%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -2.35 \cdot 10^{+52}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq -1.62 \cdot 10^{-248}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} + 1}\\ \mathbf{elif}\;Ev \leq 6.5 \cdot 10^{-291}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 40.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.05 \cdot 10^{+131} \lor \neg \left(KbT \leq 4.2 \cdot 10^{+193}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) - -0.25 \cdot \left(mu \cdot \frac{NaChar - NdChar}{KbT}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -1.05e+131) (not (<= KbT 4.2e+193)))
   (- (* 0.5 (+ NdChar NaChar)) (* -0.25 (* mu (/ (- NaChar NdChar) KbT))))
   (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -1.05e+131) || !(KbT <= 4.2e+193)) {
		tmp = (0.5 * (NdChar + NaChar)) - (-0.25 * (mu * ((NaChar - NdChar) / KbT)));
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((kbt <= (-1.05d+131)) .or. (.not. (kbt <= 4.2d+193))) then
        tmp = (0.5d0 * (ndchar + nachar)) - ((-0.25d0) * (mu * ((nachar - ndchar) / kbt)))
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((KbT <= -1.05e+131) || !(KbT <= 4.2e+193)) {
		tmp = (0.5 * (NdChar + NaChar)) - (-0.25 * (mu * ((NaChar - NdChar) / KbT)));
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -1.05e+131) or not (KbT <= 4.2e+193):
		tmp = (0.5 * (NdChar + NaChar)) - (-0.25 * (mu * ((NaChar - NdChar) / KbT)))
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -1.05e+131) || !(KbT <= 4.2e+193))
		tmp = Float64(Float64(0.5 * Float64(NdChar + NaChar)) - Float64(-0.25 * Float64(mu * Float64(Float64(NaChar - NdChar) / KbT))));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((KbT <= -1.05e+131) || ~((KbT <= 4.2e+193)))
		tmp = (0.5 * (NdChar + NaChar)) - (-0.25 * (mu * ((NaChar - NdChar) / KbT)));
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -1.05e+131], N[Not[LessEqual[KbT, 4.2e+193]], $MachinePrecision]], N[(N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision] - N[(-0.25 * N[(mu * N[(N[(NaChar - NdChar), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -1.04999999999999993e131 or 4.2e193 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 35.8%

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

   7. Simplified 35.8%

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

   8. Taylor expanded in mu around -inf 51.1%

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

      1. associate-/l* 60.2%

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

      2. mul-1-neg 60.2%

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

      3. sub-neg 60.2%

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

   10. Simplified 60.2%

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

   if -1.04999999999999993e131 < KbT < 4.2e193

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 64.1%

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

      1. associate--l+ 64.1%

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

      2. sub-neg 64.1%

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

      3. associate-+r+ 64.1%

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

      4. mul-1-neg 64.1%

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

      5. mul-1-neg 64.1%

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

      6. associate-+r+ 64.1%

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

      7. sub-neg 64.1%

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

      8. associate--l+ 64.1%

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

      9. associate-+r+ 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in EAccept around inf 39.2%

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

4. Final simplification 44.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.05 \cdot 10^{+131} \lor \neg \left(KbT \leq 4.2 \cdot 10^{+193}\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right) - -0.25 \cdot \left(mu \cdot \frac{NaChar - NdChar}{KbT}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.5% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -7.2 \cdot 10^{+255}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(mu + Vef\right) - Ec}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -7.2e+255)
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
   (/ NdChar (+ (exp (/ (- (+ mu Vef) Ec) KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -7.2e+255) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else {
		tmp = NdChar / (exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-7.2d+255)) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else
        tmp = ndchar / (exp((((mu + vef) - ec) / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -7.2e+255) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else {
		tmp = NdChar / (Math.exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -7.2e+255:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	else:
		tmp = NdChar / (math.exp((((mu + Vef) - Ec) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -7.2e+255)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	else
		tmp = Float64(NdChar / Float64(exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -7.2e+255)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	else
		tmp = NdChar / (exp((((mu + Vef) - Ec) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -7.2e+255], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -7.1999999999999998e255

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 83.7%

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

      1. associate--l+ 83.7%

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

      2. sub-neg 83.7%

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

      3. associate-+r+ 83.7%

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

      4. mul-1-neg 83.7%

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

      5. mul-1-neg 83.7%

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

      6. associate-+r+ 83.7%

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

      7. sub-neg 83.7%

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

      8. associate--l+ 83.7%

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

      9. associate-+r+ 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in Ev around inf 83.7%

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

   if -7.1999999999999998e255 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 62.1%

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

   6. Taylor expanded in EDonor around 0 57.0%

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

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -7.2 \cdot 10^{+255}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(mu + Vef\right) - Ec}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 37.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -2.9 \cdot 10^{-65}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -2.9e-65)
   (/ NaChar (+ (exp (/ Ev KbT)) 1.0))
   (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -2.9e-65) {
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-2.9d-65)) then
        tmp = nachar / (exp((ev / kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((eaccept / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -2.9e-65) {
		tmp = NaChar / (Math.exp((Ev / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -2.9e-65:
		tmp = NaChar / (math.exp((Ev / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -2.9e-65)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -2.9e-65)
		tmp = NaChar / (exp((Ev / KbT)) + 1.0);
	else
		tmp = NaChar / (exp((EAccept / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -2.9e-65], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -2.8999999999999998e-65

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 57.0%

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

      1. associate--l+ 57.0%

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

      2. sub-neg 57.0%

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

      3. associate-+r+ 57.0%

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

      4. mul-1-neg 57.0%

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

      5. mul-1-neg 57.0%

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

      6. associate-+r+ 57.0%

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

      7. sub-neg 57.0%

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

      8. associate--l+ 57.0%

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

      9. associate-+r+ 57.0%

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

   7. Simplified 57.0%

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

   8. Taylor expanded in Ev around inf 46.8%

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

   if -2.8999999999999998e-65 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 60.5%

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

      1. associate--l+ 60.5%

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

      2. sub-neg 60.5%

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

      3. associate-+r+ 60.5%

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

      4. mul-1-neg 60.5%

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

      5. mul-1-neg 60.5%

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

      6. associate-+r+ 60.5%

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

      7. sub-neg 60.5%

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

      8. associate--l+ 60.5%

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

      9. associate-+r+ 60.5%

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

   7. Simplified 60.5%

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

   8. Taylor expanded in EAccept around inf 38.1%

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

4. Final simplification 40.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -2.9 \cdot 10^{-65}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 30.6% accurate, 9.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2.4 \cdot 10^{+24} \lor \neg \left(KbT \leq 0.98\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{mu - Ec}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= KbT -2.4e+24) (not (<= KbT 0.98)))
   (* 0.5 (+ NdChar NaChar))
   (/ NdChar (+ 2.0 (+ (/ Vef KbT) (/ (- mu 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 <= -2.4e+24) || !(KbT <= 0.98)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NdChar / (2.0 + ((Vef / KbT) + ((mu - 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 <= (-2.4d+24)) .or. (.not. (kbt <= 0.98d0))) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = ndchar / (2.0d0 + ((vef / kbt) + ((mu - 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 <= -2.4e+24) || !(KbT <= 0.98)) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NdChar / (2.0 + ((Vef / KbT) + ((mu - Ec) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (KbT <= -2.4e+24) or not (KbT <= 0.98):
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NdChar / (2.0 + ((Vef / KbT) + ((mu - Ec) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((KbT <= -2.4e+24) || !(KbT <= 0.98))
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NdChar / Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Float64(mu - 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 <= -2.4e+24) || ~((KbT <= 0.98)))
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NdChar / (2.0 + ((Vef / KbT) + ((mu - Ec) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[KbT, -2.4e+24], N[Not[LessEqual[KbT, 0.98]], $MachinePrecision]], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(mu - Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -2.4000000000000001e24 or 0.97999999999999998 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 42.7%

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

      1. distribute-lft-out 42.7%

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

   7. Simplified 42.7%

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

   if -2.4000000000000001e24 < KbT < 0.97999999999999998

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around inf 63.4%

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

   6. Taylor expanded in EDonor around 0 57.2%

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

   7. Taylor expanded in KbT around inf 22.0%

      \[\leadsto \frac{NdChar}{\color{blue}{\left(2 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}}} \]
   8. Step-by-step derivation

      1. associate--l+ 22.0%

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

      2. associate--l+ 22.0%

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

      3. div-sub 22.1%

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

   9. Simplified 22.1%

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

4. Final simplification 31.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2.4 \cdot 10^{+24} \lor \neg \left(KbT \leq 0.98\right):\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 + \left(\frac{Vef}{KbT} + \frac{mu - Ec}{KbT}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 22.9% accurate, 17.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -3.4 \cdot 10^{-45} \lor \neg \left(NdChar \leq 7 \cdot 10^{-45}\right):\\ \;\;\;\;NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -3.4e-45) (not (<= NdChar 7e-45)))
   (* NdChar 0.5)
   (* NaChar 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 ((NdChar <= -3.4e-45) || !(NdChar <= 7e-45)) {
		tmp = NdChar * 0.5;
	} else {
		tmp = NaChar * 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 ((ndchar <= (-3.4d-45)) .or. (.not. (ndchar <= 7d-45))) then
        tmp = ndchar * 0.5d0
    else
        tmp = nachar * 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 ((NdChar <= -3.4e-45) || !(NdChar <= 7e-45)) {
		tmp = NdChar * 0.5;
	} else {
		tmp = NaChar * 0.5;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -3.4e-45) or not (NdChar <= 7e-45):
		tmp = NdChar * 0.5
	else:
		tmp = NaChar * 0.5
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -3.4e-45) || !(NdChar <= 7e-45))
		tmp = Float64(NdChar * 0.5);
	else
		tmp = Float64(NaChar * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -3.4e-45) || ~((NdChar <= 7e-45)))
		tmp = NdChar * 0.5;
	else
		tmp = NaChar * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -3.4e-45], N[Not[LessEqual[NdChar, 7e-45]], $MachinePrecision]], N[(NdChar * 0.5), $MachinePrecision], N[(NaChar * 0.5), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -3.40000000000000004e-45 or 7e-45 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 27.4%

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

      1. distribute-lft-out 27.4%

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

   7. Simplified 27.4%

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

   8. Taylor expanded in NaChar around 0 26.0%

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

      1. *-commutative 26.0%

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

   10. Simplified 26.0%

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

   if -3.40000000000000004e-45 < NdChar < 7e-45

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 26.7%

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

      1. distribute-lft-out 26.7%

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

   7. Simplified 26.7%

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

   8. Taylor expanded in NaChar around inf 26.0%

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

      1. *-commutative 26.0%

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

   10. Simplified 26.0%

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

4. Final simplification 26.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.4 \cdot 10^{-45} \lor \neg \left(NdChar \leq 7 \cdot 10^{-45}\right):\\ \;\;\;\;NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 25.9% accurate, 19.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ec \leq 680:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ec 680.0) (* 0.5 (+ NdChar NaChar)) (/ NaChar (+ (/ Ev KbT) 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= 680.0) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / ((Ev / KbT) + 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ec <= 680.0d0) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = nachar / ((ev / kbt) + 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ec <= 680.0) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / ((Ev / KbT) + 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ec <= 680.0:
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NaChar / ((Ev / KbT) + 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ec <= 680.0)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ec <= 680.0)
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NaChar / ((Ev / KbT) + 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ec, 680.0], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ec < 680

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 28.7%

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

      1. distribute-lft-out 28.7%

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

   7. Simplified 28.7%

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

   if 680 < Ec

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in NdChar around 0 69.0%

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

      1. associate--l+ 69.0%

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

      2. sub-neg 69.0%

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

      3. associate-+r+ 69.0%

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

      4. mul-1-neg 69.0%

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

      5. mul-1-neg 69.0%

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

      6. associate-+r+ 69.0%

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

      7. sub-neg 69.0%

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

      8. associate--l+ 69.0%

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

      9. associate-+r+ 69.0%

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

   7. Simplified 69.0%

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

   8. Taylor expanded in Ev around inf 39.8%

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

   9. Taylor expanded in Ev around 0 22.0%

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

4. Final simplification 27.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ec \leq 680:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 27.3% accurate, 45.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = 0.5d0 * (ndchar + nachar)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 27.1%

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

   1. distribute-lft-out 27.1%

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

7. Simplified 27.1%

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

8. Final simplification 27.1%

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

Alternative 16: 18.0% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = nachar * 0.5d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 27.1%

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

   1. distribute-lft-out 27.1%

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

7. Simplified 27.1%

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

8. Taylor expanded in NaChar around inf 18.1%

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

   1. *-commutative 18.1%

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

10. Simplified 18.1%

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

Reproduce

herbie shell --seed 2024181 
(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))))))