Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 30.9s

Alternatives: 27

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -1.8581644789170158e-53
  2. Ec = 3.3454100146146156e-72
  3. Vef = 5.24666881568427e-236
  4. EDonor = 3.408885500396904e-231
  5. mu = -7.794978437387687e+169
  6. KbT = 8.0775833535382e-91
  7. NaChar = 4.838019603273554e-53
  8. Ev = -3.302290816654558e+216
  9. EAccept = 6.202093354177443e+158

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) - (NaChar / (-1.0 - exp(((Vef + (Ev + (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(((edonor - ((ec - vef) - mu)) / kbt)))) - (nachar / ((-1.0d0) - exp(((vef + (ev + (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(((EDonor - ((Ec - Vef) - mu)) / KbT)))) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
}

Python

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

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) - (NaChar / (-1.0 - exp(((Vef + (Ev + (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[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 76.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - t\_1\\ \mathbf{if}\;Vef \leq -1.02 \cdot 10^{+190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq -1.6 \cdot 10^{+109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq -6.8 \cdot 10^{-18}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq 2.6 \cdot 10^{-139}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq 1.45 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - t\_1\\ \mathbf{elif}\;Vef \leq 3.6 \cdot 10^{+112}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
        (t_1 (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_2 (- (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) t_1)))
   (if (<= Vef -1.02e+190)
     t_2
     (if (<= Vef -1.6e+109)
       t_0
       (if (<= Vef -6.8e-18)
         t_2
         (if (<= Vef 2.6e-139)
           t_0
           (if (<= Vef 1.45e+21)
             (- (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) t_1)
             (if (<= Vef 3.6e+112) t_0 t_2))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	double t_1 = NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = (NdChar / (1.0 + exp((Vef / KbT)))) - t_1;
	double tmp;
	if (Vef <= -1.02e+190) {
		tmp = t_2;
	} else if (Vef <= -1.6e+109) {
		tmp = t_0;
	} else if (Vef <= -6.8e-18) {
		tmp = t_2;
	} else if (Vef <= 2.6e-139) {
		tmp = t_0;
	} else if (Vef <= 1.45e+21) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) - t_1;
	} else if (Vef <= 3.6e+112) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    t_1 = nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_2 = (ndchar / (1.0d0 + exp((vef / kbt)))) - t_1
    if (vef <= (-1.02d+190)) then
        tmp = t_2
    else if (vef <= (-1.6d+109)) then
        tmp = t_0
    else if (vef <= (-6.8d-18)) then
        tmp = t_2
    else if (vef <= 2.6d-139) then
        tmp = t_0
    else if (vef <= 1.45d+21) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) - t_1
    else if (vef <= 3.6d+112) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	double t_1 = NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = (NdChar / (1.0 + Math.exp((Vef / KbT)))) - t_1;
	double tmp;
	if (Vef <= -1.02e+190) {
		tmp = t_2;
	} else if (Vef <= -1.6e+109) {
		tmp = t_0;
	} else if (Vef <= -6.8e-18) {
		tmp = t_2;
	} else if (Vef <= 2.6e-139) {
		tmp = t_0;
	} else if (Vef <= 1.45e+21) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) - t_1;
	} else if (Vef <= 3.6e+112) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	t_1 = NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_2 = (NdChar / (1.0 + math.exp((Vef / KbT)))) - t_1
	tmp = 0
	if Vef <= -1.02e+190:
		tmp = t_2
	elif Vef <= -1.6e+109:
		tmp = t_0
	elif Vef <= -6.8e-18:
		tmp = t_2
	elif Vef <= 2.6e-139:
		tmp = t_0
	elif Vef <= 1.45e+21:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) - t_1
	elif Vef <= 3.6e+112:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))))
	t_1 = Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - t_1)
	tmp = 0.0
	if (Vef <= -1.02e+190)
		tmp = t_2;
	elseif (Vef <= -1.6e+109)
		tmp = t_0;
	elseif (Vef <= -6.8e-18)
		tmp = t_2;
	elseif (Vef <= 2.6e-139)
		tmp = t_0;
	elseif (Vef <= 1.45e+21)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) - t_1);
	elseif (Vef <= 3.6e+112)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	t_1 = NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_2 = (NdChar / (1.0 + exp((Vef / KbT)))) - t_1;
	tmp = 0.0;
	if (Vef <= -1.02e+190)
		tmp = t_2;
	elseif (Vef <= -1.6e+109)
		tmp = t_0;
	elseif (Vef <= -6.8e-18)
		tmp = t_2;
	elseif (Vef <= 2.6e-139)
		tmp = t_0;
	elseif (Vef <= 1.45e+21)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) - t_1;
	elseif (Vef <= 3.6e+112)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision]}, If[LessEqual[Vef, -1.02e+190], t$95$2, If[LessEqual[Vef, -1.6e+109], t$95$0, If[LessEqual[Vef, -6.8e-18], t$95$2, If[LessEqual[Vef, 2.6e-139], t$95$0, If[LessEqual[Vef, 1.45e+21], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[Vef, 3.6e+112], t$95$0, t$95$2]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -1.0200000000000001e190 or -1.6000000000000001e109 < Vef < -6.80000000000000002e-18 or 3.6e112 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 88.3%

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

   if -1.0200000000000001e190 < Vef < -1.6000000000000001e109 or -6.80000000000000002e-18 < Vef < 2.5999999999999998e-139 or 1.45e21 < Vef < 3.6e112

   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 80.8%

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

   if 2.5999999999999998e-139 < Vef < 1.45e21

   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 EDonor around inf 78.0%

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

4. Final simplification 83.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1.02 \cdot 10^{+190}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.6 \cdot 10^{+109}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq -6.8 \cdot 10^{-18}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.6 \cdot 10^{-139}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.45 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.6 \cdot 10^{+112}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \mathbf{if}\;Vef \leq -3.8 \cdot 10^{+190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq -1.45 \cdot 10^{-302}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq 1.4 \cdot 10^{-183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;Vef \leq 7.1 \cdot 10^{+146}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
          (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))))
        (t_2
         (-
          (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NaChar (- -1.0 (exp (/ (+ Vef Ev) KbT)))))))
   (if (<= Vef -3.8e+190)
     t_2
     (if (<= Vef -1.45e-302)
       t_0
       (if (<= Vef 1.4e-183)
         t_1
         (if (<= Vef 7.5e-9) t_0 (if (<= Vef 7.1e+146) t_1 t_2)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((EDonor / KbT)))) - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	double t_2 = (NdChar / (1.0 + exp((Vef / KbT)))) - (NaChar / (-1.0 - exp(((Vef + Ev) / KbT))));
	double tmp;
	if (Vef <= -3.8e+190) {
		tmp = t_2;
	} else if (Vef <= -1.45e-302) {
		tmp = t_0;
	} else if (Vef <= 1.4e-183) {
		tmp = t_1;
	} else if (Vef <= 7.5e-9) {
		tmp = t_0;
	} else if (Vef <= 7.1e+146) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((edonor / kbt)))) - (nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt))))
    t_1 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    t_2 = (ndchar / (1.0d0 + exp((vef / kbt)))) - (nachar / ((-1.0d0) - exp(((vef + ev) / kbt))))
    if (vef <= (-3.8d+190)) then
        tmp = t_2
    else if (vef <= (-1.45d-302)) then
        tmp = t_0
    else if (vef <= 1.4d-183) then
        tmp = t_1
    else if (vef <= 7.5d-9) then
        tmp = t_0
    else if (vef <= 7.1d+146) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	double t_2 = (NdChar / (1.0 + Math.exp((Vef / KbT)))) - (NaChar / (-1.0 - Math.exp(((Vef + Ev) / KbT))));
	double tmp;
	if (Vef <= -3.8e+190) {
		tmp = t_2;
	} else if (Vef <= -1.45e-302) {
		tmp = t_0;
	} else if (Vef <= 1.4e-183) {
		tmp = t_1;
	} else if (Vef <= 7.5e-9) {
		tmp = t_0;
	} else if (Vef <= 7.1e+146) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) - (NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	t_1 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	t_2 = (NdChar / (1.0 + math.exp((Vef / KbT)))) - (NaChar / (-1.0 - math.exp(((Vef + Ev) / KbT))))
	tmp = 0
	if Vef <= -3.8e+190:
		tmp = t_2
	elif Vef <= -1.45e-302:
		tmp = t_0
	elif Vef <= 1.4e-183:
		tmp = t_1
	elif Vef <= 7.5e-9:
		tmp = t_0
	elif Vef <= 7.1e+146:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Ev) / KbT)))))
	tmp = 0.0
	if (Vef <= -3.8e+190)
		tmp = t_2;
	elseif (Vef <= -1.45e-302)
		tmp = t_0;
	elseif (Vef <= 1.4e-183)
		tmp = t_1;
	elseif (Vef <= 7.5e-9)
		tmp = t_0;
	elseif (Vef <= 7.1e+146)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((EDonor / KbT)))) - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	t_2 = (NdChar / (1.0 + exp((Vef / KbT)))) - (NaChar / (-1.0 - exp(((Vef + Ev) / KbT))));
	tmp = 0.0;
	if (Vef <= -3.8e+190)
		tmp = t_2;
	elseif (Vef <= -1.45e-302)
		tmp = t_0;
	elseif (Vef <= 1.4e-183)
		tmp = t_1;
	elseif (Vef <= 7.5e-9)
		tmp = t_0;
	elseif (Vef <= 7.1e+146)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + Ev), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -3.8e+190], t$95$2, If[LessEqual[Vef, -1.45e-302], t$95$0, If[LessEqual[Vef, 1.4e-183], t$95$1, If[LessEqual[Vef, 7.5e-9], t$95$0, If[LessEqual[Vef, 7.1e+146], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -3.79999999999999964e190 or 7.1e146 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 92.4%

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

   6. Taylor expanded in Ev around inf 83.5%

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

   if -3.79999999999999964e190 < Vef < -1.44999999999999997e-302 or 1.39999999999999992e-183 < Vef < 7.49999999999999933e-9

   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 EDonor around inf 77.2%

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

   if -1.44999999999999997e-302 < Vef < 1.39999999999999992e-183 or 7.49999999999999933e-9 < Vef < 7.1e146

   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 mu around inf 75.9%

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

   6. Taylor expanded in mu around inf 72.5%

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

      1. associate-*r/ 39.5%

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

      2. mul-1-neg 39.5%

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

   8. Simplified 72.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.8 \cdot 10^{+190}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.45 \cdot 10^{-302}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.4 \cdot 10^{-183}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;Vef \leq 7.5 \cdot 10^{-9}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 7.1 \cdot 10^{+146}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - t\_0\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - t\_0\\ \mathbf{if}\;Vef \leq -1.02 \cdot 10^{+190}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq -1.35 \cdot 10^{-302}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq 8.2 \cdot 10^{-184}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;Vef \leq 1.3 \cdot 10^{-37}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (- (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) t_0))
        (t_2 (- (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) t_0)))
   (if (<= Vef -1.02e+190)
     t_2
     (if (<= Vef -1.35e-302)
       t_1
       (if (<= Vef 8.2e-184)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))
         (if (<= Vef 1.3e-37) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + exp((EDonor / KbT)))) - t_0;
	double t_2 = (NdChar / (1.0 + exp((Vef / KbT)))) - t_0;
	double tmp;
	if (Vef <= -1.02e+190) {
		tmp = t_2;
	} else if (Vef <= -1.35e-302) {
		tmp = t_1;
	} else if (Vef <= 8.2e-184) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	} else if (Vef <= 1.3e-37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp((edonor / kbt)))) - t_0
    t_2 = (ndchar / (1.0d0 + exp((vef / kbt)))) - t_0
    if (vef <= (-1.02d+190)) then
        tmp = t_2
    else if (vef <= (-1.35d-302)) then
        tmp = t_1
    else if (vef <= 8.2d-184) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    else if (vef <= 1.3d-37) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) - t_0;
	double t_2 = (NdChar / (1.0 + Math.exp((Vef / KbT)))) - t_0;
	double tmp;
	if (Vef <= -1.02e+190) {
		tmp = t_2;
	} else if (Vef <= -1.35e-302) {
		tmp = t_1;
	} else if (Vef <= 8.2e-184) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	} else if (Vef <= 1.3e-37) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) - t_0
	t_2 = (NdChar / (1.0 + math.exp((Vef / KbT)))) - t_0
	tmp = 0
	if Vef <= -1.02e+190:
		tmp = t_2
	elif Vef <= -1.35e-302:
		tmp = t_1
	elif Vef <= 8.2e-184:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	elif Vef <= 1.3e-37:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) - t_0)
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - t_0)
	tmp = 0.0
	if (Vef <= -1.02e+190)
		tmp = t_2;
	elseif (Vef <= -1.35e-302)
		tmp = t_1;
	elseif (Vef <= 8.2e-184)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))));
	elseif (Vef <= 1.3e-37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = (NdChar / (1.0 + exp((EDonor / KbT)))) - t_0;
	t_2 = (NdChar / (1.0 + exp((Vef / KbT)))) - t_0;
	tmp = 0.0;
	if (Vef <= -1.02e+190)
		tmp = t_2;
	elseif (Vef <= -1.35e-302)
		tmp = t_1;
	elseif (Vef <= 8.2e-184)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	elseif (Vef <= 1.3e-37)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[Vef, -1.02e+190], t$95$2, If[LessEqual[Vef, -1.35e-302], t$95$1, If[LessEqual[Vef, 8.2e-184], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 1.3e-37], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -1.0200000000000001e190 or 1.2999999999999999e-37 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 83.3%

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

   if -1.0200000000000001e190 < Vef < -1.35000000000000003e-302 or 8.2e-184 < Vef < 1.2999999999999999e-37

   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 EDonor around inf 78.1%

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

   if -1.35000000000000003e-302 < Vef < 8.2e-184

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 78.1%

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

   6. Taylor expanded in mu around inf 72.5%

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

      1. associate-*r/ 35.9%

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

      2. mul-1-neg 35.9%

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

   8. Simplified 72.5%

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

4. Final simplification 79.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1.02 \cdot 10^{+190}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq -1.35 \cdot 10^{-302}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8.2 \cdot 10^{-184}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;Vef \leq 1.3 \cdot 10^{-37}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - t\_0\\ t_2 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - t\_0\\ \mathbf{if}\;Vef \leq -3.4 \cdot 10^{+189}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;Vef \leq -9.6 \cdot 10^{-300}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;Vef \leq 9 \cdot 10^{-179}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} - t\_0\\ \mathbf{elif}\;Vef \leq 3.3 \cdot 10^{-38}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_1 (- (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) t_0))
        (t_2 (- (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) t_0)))
   (if (<= Vef -3.4e+189)
     t_2
     (if (<= Vef -9.6e-300)
       t_1
       (if (<= Vef 9e-179)
         (- (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_0)
         (if (<= Vef 3.3e-38) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + exp((EDonor / KbT)))) - t_0;
	double t_2 = (NdChar / (1.0 + exp((Vef / KbT)))) - t_0;
	double tmp;
	if (Vef <= -3.4e+189) {
		tmp = t_2;
	} else if (Vef <= -9.6e-300) {
		tmp = t_1;
	} else if (Vef <= 9e-179) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) - t_0;
	} else if (Vef <= 3.3e-38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp((edonor / kbt)))) - t_0
    t_2 = (ndchar / (1.0d0 + exp((vef / kbt)))) - t_0
    if (vef <= (-3.4d+189)) then
        tmp = t_2
    else if (vef <= (-9.6d-300)) then
        tmp = t_1
    else if (vef <= 9d-179) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) - t_0
    else if (vef <= 3.3d-38) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) - t_0;
	double t_2 = (NdChar / (1.0 + Math.exp((Vef / KbT)))) - t_0;
	double tmp;
	if (Vef <= -3.4e+189) {
		tmp = t_2;
	} else if (Vef <= -9.6e-300) {
		tmp = t_1;
	} else if (Vef <= 9e-179) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) - t_0;
	} else if (Vef <= 3.3e-38) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp((EDonor / KbT)))) - t_0
	t_2 = (NdChar / (1.0 + math.exp((Vef / KbT)))) - t_0
	tmp = 0
	if Vef <= -3.4e+189:
		tmp = t_2
	elif Vef <= -9.6e-300:
		tmp = t_1
	elif Vef <= 9e-179:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) - t_0
	elif Vef <= 3.3e-38:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) - t_0)
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - t_0)
	tmp = 0.0
	if (Vef <= -3.4e+189)
		tmp = t_2;
	elseif (Vef <= -9.6e-300)
		tmp = t_1;
	elseif (Vef <= 9e-179)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) - t_0);
	elseif (Vef <= 3.3e-38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_1 = (NdChar / (1.0 + exp((EDonor / KbT)))) - t_0;
	t_2 = (NdChar / (1.0 + exp((Vef / KbT)))) - t_0;
	tmp = 0.0;
	if (Vef <= -3.4e+189)
		tmp = t_2;
	elseif (Vef <= -9.6e-300)
		tmp = t_1;
	elseif (Vef <= 9e-179)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) - t_0;
	elseif (Vef <= 3.3e-38)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]}, If[LessEqual[Vef, -3.4e+189], t$95$2, If[LessEqual[Vef, -9.6e-300], t$95$1, If[LessEqual[Vef, 9e-179], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[LessEqual[Vef, 3.3e-38], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -3.39999999999999983e189 or 3.3000000000000002e-38 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 83.3%

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

   if -3.39999999999999983e189 < Vef < -9.59999999999999998e-300 or 8.99999999999999984e-179 < Vef < 3.3000000000000002e-38

   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 EDonor around inf 78.6%

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

   if -9.59999999999999998e-300 < Vef < 8.99999999999999984e-179

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in mu around inf 76.9%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.4 \cdot 10^{+189}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq -9.6 \cdot 10^{-300}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 9 \cdot 10^{-179}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;Vef \leq 3.3 \cdot 10^{-38}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 72.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;EAccept \leq -3 \cdot 10^{-26}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq -7.5 \cdot 10^{-109}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;EAccept \leq 1.5 \cdot 10^{-49}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 6 \cdot 10^{+120}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT))))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
        (t_2 (+ t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))))
   (if (<= EAccept -3e-26)
     t_2
     (if (<= EAccept -7.5e-109)
       t_0
       (if (<= EAccept 1.5e-49)
         t_2
         (if (<= EAccept 6e+120)
           t_0
           (+ t_1 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((Vef / KbT)))) - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	double tmp;
	if (EAccept <= -3e-26) {
		tmp = t_2;
	} else if (EAccept <= -7.5e-109) {
		tmp = t_0;
	} else if (EAccept <= 1.5e-49) {
		tmp = t_2;
	} else if (EAccept <= 6e+120) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((vef / kbt)))) - (nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt))))
    t_1 = ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))
    t_2 = t_1 + (nachar / (1.0d0 + exp((ev / kbt))))
    if (eaccept <= (-3d-26)) then
        tmp = t_2
    else if (eaccept <= (-7.5d-109)) then
        tmp = t_0
    else if (eaccept <= 1.5d-49) then
        tmp = t_2
    else if (eaccept <= 6d+120) then
        tmp = t_0
    else
        tmp = t_1 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((Vef / KbT)))) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double tmp;
	if (EAccept <= -3e-26) {
		tmp = t_2;
	} else if (EAccept <= -7.5e-109) {
		tmp = t_0;
	} else if (EAccept <= 1.5e-49) {
		tmp = t_2;
	} else if (EAccept <= 6e+120) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((Vef / KbT)))) - (NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	t_1 = NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	t_2 = t_1 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	tmp = 0
	if EAccept <= -3e-26:
		tmp = t_2
	elif EAccept <= -7.5e-109:
		tmp = t_0
	elif EAccept <= 1.5e-49:
		tmp = t_2
	elif EAccept <= 6e+120:
		tmp = t_0
	else:
		tmp = t_1 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	tmp = 0.0
	if (EAccept <= -3e-26)
		tmp = t_2;
	elseif (EAccept <= -7.5e-109)
		tmp = t_0;
	elseif (EAccept <= 1.5e-49)
		tmp = t_2;
	elseif (EAccept <= 6e+120)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((Vef / KbT)))) - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	t_1 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	t_2 = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	tmp = 0.0;
	if (EAccept <= -3e-26)
		tmp = t_2;
	elseif (EAccept <= -7.5e-109)
		tmp = t_0;
	elseif (EAccept <= 1.5e-49)
		tmp = t_2;
	elseif (EAccept <= 6e+120)
		tmp = t_0;
	else
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -3e-26], t$95$2, If[LessEqual[EAccept, -7.5e-109], t$95$0, If[LessEqual[EAccept, 1.5e-49], t$95$2, If[LessEqual[EAccept, 6e+120], t$95$0, N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < -3.00000000000000012e-26 or -7.49999999999999982e-109 < EAccept < 1.5e-49

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 74.8%

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

   if -3.00000000000000012e-26 < EAccept < -7.49999999999999982e-109 or 1.5e-49 < EAccept < 6e120

   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 Vef around inf 77.6%

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

   if 6e120 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 91.7%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -3 \cdot 10^{-26}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq -7.5 \cdot 10^{-109}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.5 \cdot 10^{-49}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 6 \cdot 10^{+120}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \mathbf{if}\;mu \leq -3 \cdot 10^{+96}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq -6.5 \cdot 10^{-171}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq 4.1 \cdot 10^{-266}:\\ \;\;\;\;\frac{NdChar}{1 + mu \cdot \left(\frac{\left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu} + \frac{1}{KbT}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 7 \cdot 10^{+147}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))))
        (t_1
         (-
          (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NaChar (- -1.0 (exp (/ (+ Vef Ev) KbT)))))))
   (if (<= mu -3e+96)
     t_0
     (if (<= mu -6.5e-171)
       t_1
       (if (<= mu 4.1e-266)
         (-
          (/
           NdChar
           (+
            1.0
            (*
             mu
             (+
              (/ (- (+ 1.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)) mu)
              (/ 1.0 KbT)))))
          (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
         (if (<= mu 7e+147) t_1 t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	double t_1 = (NdChar / (1.0 + exp((Vef / KbT)))) - (NaChar / (-1.0 - exp(((Vef + Ev) / KbT))));
	double tmp;
	if (mu <= -3e+96) {
		tmp = t_0;
	} else if (mu <= -6.5e-171) {
		tmp = t_1;
	} else if (mu <= 4.1e-266) {
		tmp = (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT))))) - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	} else if (mu <= 7e+147) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    t_1 = (ndchar / (1.0d0 + exp((vef / kbt)))) - (nachar / ((-1.0d0) - exp(((vef + ev) / kbt))))
    if (mu <= (-3d+96)) then
        tmp = t_0
    else if (mu <= (-6.5d-171)) then
        tmp = t_1
    else if (mu <= 4.1d-266) then
        tmp = (ndchar / (1.0d0 + (mu * ((((1.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu) + (1.0d0 / kbt))))) - (nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt))))
    else if (mu <= 7d+147) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	double t_1 = (NdChar / (1.0 + Math.exp((Vef / KbT)))) - (NaChar / (-1.0 - Math.exp(((Vef + Ev) / KbT))));
	double tmp;
	if (mu <= -3e+96) {
		tmp = t_0;
	} else if (mu <= -6.5e-171) {
		tmp = t_1;
	} else if (mu <= 4.1e-266) {
		tmp = (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT))))) - (NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	} else if (mu <= 7e+147) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	t_1 = (NdChar / (1.0 + math.exp((Vef / KbT)))) - (NaChar / (-1.0 - math.exp(((Vef + Ev) / KbT))))
	tmp = 0
	if mu <= -3e+96:
		tmp = t_0
	elif mu <= -6.5e-171:
		tmp = t_1
	elif mu <= 4.1e-266:
		tmp = (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT))))) - (NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	elif mu <= 7e+147:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Ev) / KbT)))))
	tmp = 0.0
	if (mu <= -3e+96)
		tmp = t_0;
	elseif (mu <= -6.5e-171)
		tmp = t_1;
	elseif (mu <= 4.1e-266)
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(mu * Float64(Float64(Float64(Float64(1.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu) + Float64(1.0 / KbT))))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))));
	elseif (mu <= 7e+147)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	t_1 = (NdChar / (1.0 + exp((Vef / KbT)))) - (NaChar / (-1.0 - exp(((Vef + Ev) / KbT))));
	tmp = 0.0;
	if (mu <= -3e+96)
		tmp = t_0;
	elseif (mu <= -6.5e-171)
		tmp = t_1;
	elseif (mu <= 4.1e-266)
		tmp = (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT))))) - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	elseif (mu <= 7e+147)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + Ev), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -3e+96], t$95$0, If[LessEqual[mu, -6.5e-171], t$95$1, If[LessEqual[mu, 4.1e-266], N[(N[(NdChar / N[(1.0 + N[(mu * N[(N[(N[(N[(1.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 7e+147], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -3e96 or 6.99999999999999949e147 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 91.6%

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

   6. Taylor expanded in mu around inf 87.0%

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

      1. associate-*r/ 39.2%

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

      2. mul-1-neg 39.2%

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

   8. Simplified 87.0%

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

   if -3e96 < mu < -6.5000000000000004e-171 or 4.1000000000000003e-266 < mu < 6.99999999999999949e147

   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 Vef around inf 74.6%

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

   6. Taylor expanded in Ev around inf 69.0%

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

   if -6.5000000000000004e-171 < mu < 4.1000000000000003e-266

   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 52.6%

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

   6. Taylor expanded in mu around -inf 72.3%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -3 \cdot 10^{+96}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -6.5 \cdot 10^{-171}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \mathbf{elif}\;mu \leq 4.1 \cdot 10^{-266}:\\ \;\;\;\;\frac{NdChar}{1 + mu \cdot \left(\frac{\left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu} + \frac{1}{KbT}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 7 \cdot 10^{+147}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 67.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ t_1 := \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ t_2 := NdChar - t\_1\\ \mathbf{if}\;mu \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq -7.2 \cdot 10^{-56}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;mu \leq 2.8 \cdot 10^{-196}:\\ \;\;\;\;\frac{NdChar}{1 + mu \cdot \left(\frac{\left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu} + \frac{1}{KbT}\right)} - t\_1\\ \mathbf{elif}\;mu \leq 4.4 \cdot 10^{+149}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))))
        (t_1 (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
        (t_2 (- NdChar t_1)))
   (if (<= mu -2.8e+130)
     t_0
     (if (<= mu -7.2e-56)
       t_2
       (if (<= mu 2.8e-196)
         (-
          (/
           NdChar
           (+
            1.0
            (*
             mu
             (+
              (/ (- (+ 1.0 (+ (/ Vef KbT) (/ EDonor KbT))) (/ Ec KbT)) mu)
              (/ 1.0 KbT)))))
          t_1)
         (if (<= mu 4.4e+149) t_2 t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	double t_1 = NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = NdChar - t_1;
	double tmp;
	if (mu <= -2.8e+130) {
		tmp = t_0;
	} else if (mu <= -7.2e-56) {
		tmp = t_2;
	} else if (mu <= 2.8e-196) {
		tmp = (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT))))) - t_1;
	} else if (mu <= 4.4e+149) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((mu / -kbt))))
    t_1 = nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt)))
    t_2 = ndchar - t_1
    if (mu <= (-2.8d+130)) then
        tmp = t_0
    else if (mu <= (-7.2d-56)) then
        tmp = t_2
    else if (mu <= 2.8d-196) then
        tmp = (ndchar / (1.0d0 + (mu * ((((1.0d0 + ((vef / kbt) + (edonor / kbt))) - (ec / kbt)) / mu) + (1.0d0 / kbt))))) - t_1
    else if (mu <= 4.4d+149) then
        tmp = t_2
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	double t_1 = NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	double t_2 = NdChar - t_1;
	double tmp;
	if (mu <= -2.8e+130) {
		tmp = t_0;
	} else if (mu <= -7.2e-56) {
		tmp = t_2;
	} else if (mu <= 2.8e-196) {
		tmp = (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT))))) - t_1;
	} else if (mu <= 4.4e+149) {
		tmp = t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((mu / -KbT))))
	t_1 = NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT)))
	t_2 = NdChar - t_1
	tmp = 0
	if mu <= -2.8e+130:
		tmp = t_0
	elif mu <= -7.2e-56:
		tmp = t_2
	elif mu <= 2.8e-196:
		tmp = (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT))))) - t_1
	elif mu <= 4.4e+149:
		tmp = t_2
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))))
	t_1 = Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))))
	t_2 = Float64(NdChar - t_1)
	tmp = 0.0
	if (mu <= -2.8e+130)
		tmp = t_0;
	elseif (mu <= -7.2e-56)
		tmp = t_2;
	elseif (mu <= 2.8e-196)
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(mu * Float64(Float64(Float64(Float64(1.0 + Float64(Float64(Vef / KbT) + Float64(EDonor / KbT))) - Float64(Ec / KbT)) / mu) + Float64(1.0 / KbT))))) - t_1);
	elseif (mu <= 4.4e+149)
		tmp = t_2;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((mu / -KbT))));
	t_1 = NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT)));
	t_2 = NdChar - t_1;
	tmp = 0.0;
	if (mu <= -2.8e+130)
		tmp = t_0;
	elseif (mu <= -7.2e-56)
		tmp = t_2;
	elseif (mu <= 2.8e-196)
		tmp = (NdChar / (1.0 + (mu * ((((1.0 + ((Vef / KbT) + (EDonor / KbT))) - (Ec / KbT)) / mu) + (1.0 / KbT))))) - t_1;
	elseif (mu <= 4.4e+149)
		tmp = t_2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar - t$95$1), $MachinePrecision]}, If[LessEqual[mu, -2.8e+130], t$95$0, If[LessEqual[mu, -7.2e-56], t$95$2, If[LessEqual[mu, 2.8e-196], N[(N[(NdChar / N[(1.0 + N[(mu * N[(N[(N[(N[(1.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / mu), $MachinePrecision] + N[(1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[mu, 4.4e+149], t$95$2, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -2.7999999999999999e130 or 4.4e149 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 95.6%

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

   6. Taylor expanded in mu around inf 91.3%

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

      1. associate-*r/ 38.2%

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

      2. mul-1-neg 38.2%

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

   8. Simplified 91.3%

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

   if -2.7999999999999999e130 < mu < -7.19999999999999956e-56 or 2.7999999999999998e-196 < mu < 4.4e149

   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 49.7%

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

   6. Taylor expanded in mu around inf 50.4%

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

   7. Taylor expanded in mu around 0 68.3%

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

   if -7.19999999999999956e-56 < mu < 2.7999999999999998e-196

   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 53.8%

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

   6. Taylor expanded in mu around -inf 68.2%

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

4. Final simplification 74.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -2.8 \cdot 10^{+130}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -7.2 \cdot 10^{-56}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 2.8 \cdot 10^{-196}:\\ \;\;\;\;\frac{NdChar}{1 + mu \cdot \left(\frac{\left(1 + \left(\frac{Vef}{KbT} + \frac{EDonor}{KbT}\right)\right) - \frac{Ec}{KbT}}{mu} + \frac{1}{KbT}\right)} - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;mu \leq 4.4 \cdot 10^{+149}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\\ t_2 := \frac{NaChar}{1 + t\_1} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ t_3 := NdChar - \frac{NaChar}{-1 - t\_1}\\ \mathbf{if}\;EAccept \leq -1.45 \cdot 10^{-119}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq -2.7 \cdot 10^{-266}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 3.3 \cdot 10^{-220}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq 1.8 \cdot 10^{-126}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EAccept \leq 1700000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq 5 \cdot 10^{+165}:\\ \;\;\;\;t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
        (t_1 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))
        (t_2
         (+
          (/ NaChar (+ 1.0 t_1))
          (/
           NdChar
           (+
            1.0
            (*
             Ec
             (+
              (/ (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT)))) Ec)
              (/ -1.0 KbT)))))))
        (t_3 (- NdChar (/ NaChar (- -1.0 t_1)))))
   (if (<= EAccept -1.45e-119)
     t_3
     (if (<= EAccept -2.7e-266)
       (+ t_0 (/ NaChar (+ (/ Ev KbT) 2.0)))
       (if (<= EAccept 3.3e-220)
         t_3
         (if (<= EAccept 1.8e-126)
           t_2
           (if (<= EAccept 1700000.0)
             t_3
             (if (<= EAccept 5e+165)
               t_2
               (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_2 = (NaChar / (1.0 + t_1)) + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	double t_3 = NdChar - (NaChar / (-1.0 - t_1));
	double tmp;
	if (EAccept <= -1.45e-119) {
		tmp = t_3;
	} else if (EAccept <= -2.7e-266) {
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (EAccept <= 3.3e-220) {
		tmp = t_3;
	} else if (EAccept <= 1.8e-126) {
		tmp = t_2;
	} else if (EAccept <= 1700000.0) {
		tmp = t_3;
	} else if (EAccept <= 5e+165) {
		tmp = t_2;
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))
    t_1 = exp(((vef + (ev + (eaccept - mu))) / kbt))
    t_2 = (nachar / (1.0d0 + t_1)) + (ndchar / (1.0d0 + (ec * (((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) / ec) + ((-1.0d0) / kbt)))))
    t_3 = ndchar - (nachar / ((-1.0d0) - t_1))
    if (eaccept <= (-1.45d-119)) then
        tmp = t_3
    else if (eaccept <= (-2.7d-266)) then
        tmp = t_0 + (nachar / ((ev / kbt) + 2.0d0))
    else if (eaccept <= 3.3d-220) then
        tmp = t_3
    else if (eaccept <= 1.8d-126) then
        tmp = t_2
    else if (eaccept <= 1700000.0d0) then
        tmp = t_3
    else if (eaccept <= 5d+165) then
        tmp = t_2
    else
        tmp = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_2 = (NaChar / (1.0 + t_1)) + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	double t_3 = NdChar - (NaChar / (-1.0 - t_1));
	double tmp;
	if (EAccept <= -1.45e-119) {
		tmp = t_3;
	} else if (EAccept <= -2.7e-266) {
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (EAccept <= 3.3e-220) {
		tmp = t_3;
	} else if (EAccept <= 1.8e-126) {
		tmp = t_2;
	} else if (EAccept <= 1700000.0) {
		tmp = t_3;
	} else if (EAccept <= 5e+165) {
		tmp = t_2;
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	t_1 = math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))
	t_2 = (NaChar / (1.0 + t_1)) + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))))
	t_3 = NdChar - (NaChar / (-1.0 - t_1))
	tmp = 0
	if EAccept <= -1.45e-119:
		tmp = t_3
	elif EAccept <= -2.7e-266:
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0))
	elif EAccept <= 3.3e-220:
		tmp = t_3
	elif EAccept <= 1.8e-126:
		tmp = t_2
	elif EAccept <= 1700000.0:
		tmp = t_3
	elif EAccept <= 5e+165:
		tmp = t_2
	else:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	t_1 = exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + t_1)) + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / KbT))))))
	t_3 = Float64(NdChar - Float64(NaChar / Float64(-1.0 - t_1)))
	tmp = 0.0
	if (EAccept <= -1.45e-119)
		tmp = t_3;
	elseif (EAccept <= -2.7e-266)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (EAccept <= 3.3e-220)
		tmp = t_3;
	elseif (EAccept <= 1.8e-126)
		tmp = t_2;
	elseif (EAccept <= 1700000.0)
		tmp = t_3;
	elseif (EAccept <= 5e+165)
		tmp = t_2;
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	t_1 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	t_2 = (NaChar / (1.0 + t_1)) + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	t_3 = NdChar - (NaChar / (-1.0 - t_1));
	tmp = 0.0;
	if (EAccept <= -1.45e-119)
		tmp = t_3;
	elseif (EAccept <= -2.7e-266)
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	elseif (EAccept <= 3.3e-220)
		tmp = t_3;
	elseif (EAccept <= 1.8e-126)
		tmp = t_2;
	elseif (EAccept <= 1700000.0)
		tmp = t_3;
	elseif (EAccept <= 5e+165)
		tmp = t_2;
	else
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar - N[(NaChar / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -1.45e-119], t$95$3, If[LessEqual[EAccept, -2.7e-266], N[(t$95$0 + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.3e-220], t$95$3, If[LessEqual[EAccept, 1.8e-126], t$95$2, If[LessEqual[EAccept, 1700000.0], t$95$3, If[LessEqual[EAccept, 5e+165], t$95$2, N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if EAccept < -1.45e-119 or -2.69999999999999996e-266 < EAccept < 3.29999999999999999e-220 or 1.8e-126 < EAccept < 1.7e6

   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 51.2%

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

   6. Taylor expanded in mu around inf 48.6%

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

   7. Taylor expanded in mu around 0 66.0%

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

   if -1.45e-119 < EAccept < -2.69999999999999996e-266

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Ev around inf 91.4%

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

   6. Taylor expanded in Ev around 0 69.6%

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

   if 3.29999999999999999e-220 < EAccept < 1.8e-126 or 1.7e6 < EAccept < 4.9999999999999997e165

   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 64.5%

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

   6. Taylor expanded in Ec around -inf 71.5%

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

      1. associate-*r* 71.5%

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

      2. mul-1-neg 71.5%

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

      3. +-commutative 71.5%

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

      4. mul-1-neg 71.5%

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

      5. unsub-neg 71.5%

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

   8. Simplified 71.5%

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

   if 4.9999999999999997e165 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 92.9%

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

   6. Taylor expanded in EAccept around 0 74.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -1.45 \cdot 10^{-119}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq -2.7 \cdot 10^{-266}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 3.3 \cdot 10^{-220}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.8 \cdot 10^{-126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 1700000:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 5 \cdot 10^{+165}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.3% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\\ t_2 := \frac{NaChar}{1 + t\_1}\\ t_3 := NdChar - \frac{NaChar}{-1 - t\_1}\\ \mathbf{if}\;EAccept \leq -1.25 \cdot 10^{-123}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq -1.42 \cdot 10^{-267}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 4.5 \cdot 10^{-220}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq 2.4 \cdot 10^{-169}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 - Ec \cdot \left(\frac{1}{KbT} - \frac{\frac{EDonor}{Ec} + \left(\frac{KbT}{Ec} + \left(\frac{Vef}{Ec} + \frac{mu}{Ec}\right)\right)}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 820000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq 5.5 \cdot 10^{+163}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
        (t_1 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))
        (t_2 (/ NaChar (+ 1.0 t_1)))
        (t_3 (- NdChar (/ NaChar (- -1.0 t_1)))))
   (if (<= EAccept -1.25e-123)
     t_3
     (if (<= EAccept -1.42e-267)
       (+ t_0 (/ NaChar (+ (/ Ev KbT) 2.0)))
       (if (<= EAccept 4.5e-220)
         t_3
         (if (<= EAccept 2.4e-169)
           (+
            t_2
            (/
             NdChar
             (-
              1.0
              (*
               Ec
               (-
                (/ 1.0 KbT)
                (/
                 (+ (/ EDonor Ec) (+ (/ KbT Ec) (+ (/ Vef Ec) (/ mu Ec))))
                 KbT))))))
           (if (<= EAccept 820000.0)
             t_3
             (if (<= EAccept 5.5e+163)
               (+
                t_2
                (/
                 NdChar
                 (+
                  1.0
                  (*
                   Ec
                   (+
                    (/
                     (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
                     Ec)
                    (/ -1.0 KbT))))))
               (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = NdChar - (NaChar / (-1.0 - t_1));
	double tmp;
	if (EAccept <= -1.25e-123) {
		tmp = t_3;
	} else if (EAccept <= -1.42e-267) {
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (EAccept <= 4.5e-220) {
		tmp = t_3;
	} else if (EAccept <= 2.4e-169) {
		tmp = t_2 + (NdChar / (1.0 - (Ec * ((1.0 / KbT) - (((EDonor / Ec) + ((KbT / Ec) + ((Vef / Ec) + (mu / Ec)))) / KbT)))));
	} else if (EAccept <= 820000.0) {
		tmp = t_3;
	} else if (EAccept <= 5.5e+163) {
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))
    t_1 = exp(((vef + (ev + (eaccept - mu))) / kbt))
    t_2 = nachar / (1.0d0 + t_1)
    t_3 = ndchar - (nachar / ((-1.0d0) - t_1))
    if (eaccept <= (-1.25d-123)) then
        tmp = t_3
    else if (eaccept <= (-1.42d-267)) then
        tmp = t_0 + (nachar / ((ev / kbt) + 2.0d0))
    else if (eaccept <= 4.5d-220) then
        tmp = t_3
    else if (eaccept <= 2.4d-169) then
        tmp = t_2 + (ndchar / (1.0d0 - (ec * ((1.0d0 / kbt) - (((edonor / ec) + ((kbt / ec) + ((vef / ec) + (mu / ec)))) / kbt)))))
    else if (eaccept <= 820000.0d0) then
        tmp = t_3
    else if (eaccept <= 5.5d+163) then
        tmp = t_2 + (ndchar / (1.0d0 + (ec * (((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) / ec) + ((-1.0d0) / kbt)))))
    else
        tmp = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = NdChar - (NaChar / (-1.0 - t_1));
	double tmp;
	if (EAccept <= -1.25e-123) {
		tmp = t_3;
	} else if (EAccept <= -1.42e-267) {
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (EAccept <= 4.5e-220) {
		tmp = t_3;
	} else if (EAccept <= 2.4e-169) {
		tmp = t_2 + (NdChar / (1.0 - (Ec * ((1.0 / KbT) - (((EDonor / Ec) + ((KbT / Ec) + ((Vef / Ec) + (mu / Ec)))) / KbT)))));
	} else if (EAccept <= 820000.0) {
		tmp = t_3;
	} else if (EAccept <= 5.5e+163) {
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	t_1 = math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))
	t_2 = NaChar / (1.0 + t_1)
	t_3 = NdChar - (NaChar / (-1.0 - t_1))
	tmp = 0
	if EAccept <= -1.25e-123:
		tmp = t_3
	elif EAccept <= -1.42e-267:
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0))
	elif EAccept <= 4.5e-220:
		tmp = t_3
	elif EAccept <= 2.4e-169:
		tmp = t_2 + (NdChar / (1.0 - (Ec * ((1.0 / KbT) - (((EDonor / Ec) + ((KbT / Ec) + ((Vef / Ec) + (mu / Ec)))) / KbT)))))
	elif EAccept <= 820000.0:
		tmp = t_3
	elif EAccept <= 5.5e+163:
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))))
	else:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	t_1 = exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + t_1))
	t_3 = Float64(NdChar - Float64(NaChar / Float64(-1.0 - t_1)))
	tmp = 0.0
	if (EAccept <= -1.25e-123)
		tmp = t_3;
	elseif (EAccept <= -1.42e-267)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (EAccept <= 4.5e-220)
		tmp = t_3;
	elseif (EAccept <= 2.4e-169)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 - Float64(Ec * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(EDonor / Ec) + Float64(Float64(KbT / Ec) + Float64(Float64(Vef / Ec) + Float64(mu / Ec)))) / KbT))))));
	elseif (EAccept <= 820000.0)
		tmp = t_3;
	elseif (EAccept <= 5.5e+163)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / KbT))))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	t_1 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	t_2 = NaChar / (1.0 + t_1);
	t_3 = NdChar - (NaChar / (-1.0 - t_1));
	tmp = 0.0;
	if (EAccept <= -1.25e-123)
		tmp = t_3;
	elseif (EAccept <= -1.42e-267)
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	elseif (EAccept <= 4.5e-220)
		tmp = t_3;
	elseif (EAccept <= 2.4e-169)
		tmp = t_2 + (NdChar / (1.0 - (Ec * ((1.0 / KbT) - (((EDonor / Ec) + ((KbT / Ec) + ((Vef / Ec) + (mu / Ec)))) / KbT)))));
	elseif (EAccept <= 820000.0)
		tmp = t_3;
	elseif (EAccept <= 5.5e+163)
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	else
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar - N[(NaChar / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -1.25e-123], t$95$3, If[LessEqual[EAccept, -1.42e-267], N[(t$95$0 + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 4.5e-220], t$95$3, If[LessEqual[EAccept, 2.4e-169], N[(t$95$2 + N[(NdChar / N[(1.0 - N[(Ec * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(EDonor / Ec), $MachinePrecision] + N[(N[(KbT / Ec), $MachinePrecision] + N[(N[(Vef / Ec), $MachinePrecision] + N[(mu / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 820000.0], t$95$3, If[LessEqual[EAccept, 5.5e+163], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if EAccept < -1.25000000000000007e-123 or -1.4199999999999999e-267 < EAccept < 4.49999999999999967e-220 or 2.40000000000000011e-169 < EAccept < 8.2e5

   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 52.1%

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

   6. Taylor expanded in mu around inf 49.1%

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

   7. Taylor expanded in mu around 0 65.8%

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

   if -1.25000000000000007e-123 < EAccept < -1.4199999999999999e-267

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Ev around inf 91.4%

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

   6. Taylor expanded in Ev around 0 69.6%

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

   if 4.49999999999999967e-220 < EAccept < 2.40000000000000011e-169

   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 66.2%

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

   6. Taylor expanded in Ec around -inf 74.5%

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

      1. associate-*r* 74.5%

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

      2. mul-1-neg 74.5%

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

      3. +-commutative 74.5%

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

      4. mul-1-neg 74.5%

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

      5. unsub-neg 74.5%

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

   8. Simplified 74.5%

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

   9. Taylor expanded in KbT around 0 74.3%

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

   if 8.2e5 < EAccept < 5.50000000000000014e163

   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 60.6%

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

   6. Taylor expanded in Ec around -inf 68.3%

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

      1. associate-*r* 68.3%

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

      2. mul-1-neg 68.3%

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

      3. +-commutative 68.3%

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

      4. mul-1-neg 68.3%

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

      5. unsub-neg 68.3%

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

   8. Simplified 68.3%

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

   if 5.50000000000000014e163 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 92.9%

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

   6. Taylor expanded in EAccept around 0 74.6%

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

4. Final simplification 68.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -1.25 \cdot 10^{-123}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq -1.42 \cdot 10^{-267}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 4.5 \cdot 10^{-220}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 2.4 \cdot 10^{-169}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 - Ec \cdot \left(\frac{1}{KbT} - \frac{\frac{EDonor}{Ec} + \left(\frac{KbT}{Ec} + \left(\frac{Vef}{Ec} + \frac{mu}{Ec}\right)\right)}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 820000:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 5.5 \cdot 10^{+163}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\\ t_2 := \frac{NaChar}{1 + t\_1}\\ t_3 := NdChar - \frac{NaChar}{-1 - t\_1}\\ \mathbf{if}\;EAccept \leq -1.45 \cdot 10^{-123}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq -6.6 \cdot 10^{-266}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 7.5 \cdot 10^{-221}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq 1.6 \cdot 10^{-125}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 + \left(\left(1 - Vef \cdot \left(\frac{-1}{KbT} + EDonor \cdot \frac{\frac{-1}{KbT} - \frac{mu}{EDonor \cdot KbT}}{Vef}\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 3200000:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;EAccept \leq 5 \cdot 10^{+164}:\\ \;\;\;\;t\_2 + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
        (t_1 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))
        (t_2 (/ NaChar (+ 1.0 t_1)))
        (t_3 (- NdChar (/ NaChar (- -1.0 t_1)))))
   (if (<= EAccept -1.45e-123)
     t_3
     (if (<= EAccept -6.6e-266)
       (+ t_0 (/ NaChar (+ (/ Ev KbT) 2.0)))
       (if (<= EAccept 7.5e-221)
         t_3
         (if (<= EAccept 1.6e-125)
           (+
            t_2
            (/
             NdChar
             (+
              1.0
              (-
               (-
                1.0
                (*
                 Vef
                 (+
                  (/ -1.0 KbT)
                  (* EDonor (/ (- (/ -1.0 KbT) (/ mu (* EDonor KbT))) Vef)))))
               (/ Ec KbT)))))
           (if (<= EAccept 3200000.0)
             t_3
             (if (<= EAccept 5e+164)
               (+
                t_2
                (/
                 NdChar
                 (+
                  1.0
                  (*
                   Ec
                   (+
                    (/
                     (+ 1.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
                     Ec)
                    (/ -1.0 KbT))))))
               (+ t_0 (/ NaChar (+ (/ EAccept KbT) 2.0)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = NdChar - (NaChar / (-1.0 - t_1));
	double tmp;
	if (EAccept <= -1.45e-123) {
		tmp = t_3;
	} else if (EAccept <= -6.6e-266) {
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (EAccept <= 7.5e-221) {
		tmp = t_3;
	} else if (EAccept <= 1.6e-125) {
		tmp = t_2 + (NdChar / (1.0 + ((1.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT))));
	} else if (EAccept <= 3200000.0) {
		tmp = t_3;
	} else if (EAccept <= 5e+164) {
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))
    t_1 = exp(((vef + (ev + (eaccept - mu))) / kbt))
    t_2 = nachar / (1.0d0 + t_1)
    t_3 = ndchar - (nachar / ((-1.0d0) - t_1))
    if (eaccept <= (-1.45d-123)) then
        tmp = t_3
    else if (eaccept <= (-6.6d-266)) then
        tmp = t_0 + (nachar / ((ev / kbt) + 2.0d0))
    else if (eaccept <= 7.5d-221) then
        tmp = t_3
    else if (eaccept <= 1.6d-125) then
        tmp = t_2 + (ndchar / (1.0d0 + ((1.0d0 - (vef * (((-1.0d0) / kbt) + (edonor * ((((-1.0d0) / kbt) - (mu / (edonor * kbt))) / vef))))) - (ec / kbt))))
    else if (eaccept <= 3200000.0d0) then
        tmp = t_3
    else if (eaccept <= 5d+164) then
        tmp = t_2 + (ndchar / (1.0d0 + (ec * (((1.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) / ec) + ((-1.0d0) / kbt)))))
    else
        tmp = t_0 + (nachar / ((eaccept / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_1 = Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = NdChar - (NaChar / (-1.0 - t_1));
	double tmp;
	if (EAccept <= -1.45e-123) {
		tmp = t_3;
	} else if (EAccept <= -6.6e-266) {
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (EAccept <= 7.5e-221) {
		tmp = t_3;
	} else if (EAccept <= 1.6e-125) {
		tmp = t_2 + (NdChar / (1.0 + ((1.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT))));
	} else if (EAccept <= 3200000.0) {
		tmp = t_3;
	} else if (EAccept <= 5e+164) {
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	} else {
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	t_1 = math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))
	t_2 = NaChar / (1.0 + t_1)
	t_3 = NdChar - (NaChar / (-1.0 - t_1))
	tmp = 0
	if EAccept <= -1.45e-123:
		tmp = t_3
	elif EAccept <= -6.6e-266:
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0))
	elif EAccept <= 7.5e-221:
		tmp = t_3
	elif EAccept <= 1.6e-125:
		tmp = t_2 + (NdChar / (1.0 + ((1.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT))))
	elif EAccept <= 3200000.0:
		tmp = t_3
	elif EAccept <= 5e+164:
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))))
	else:
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	t_1 = exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + t_1))
	t_3 = Float64(NdChar - Float64(NaChar / Float64(-1.0 - t_1)))
	tmp = 0.0
	if (EAccept <= -1.45e-123)
		tmp = t_3;
	elseif (EAccept <= -6.6e-266)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (EAccept <= 7.5e-221)
		tmp = t_3;
	elseif (EAccept <= 1.6e-125)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + Float64(Float64(1.0 - Float64(Vef * Float64(Float64(-1.0 / KbT) + Float64(EDonor * Float64(Float64(Float64(-1.0 / KbT) - Float64(mu / Float64(EDonor * KbT))) / Vef))))) - Float64(Ec / KbT)))));
	elseif (EAccept <= 3200000.0)
		tmp = t_3;
	elseif (EAccept <= 5e+164)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + Float64(Ec * Float64(Float64(Float64(1.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) / Ec) + Float64(-1.0 / KbT))))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	t_1 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	t_2 = NaChar / (1.0 + t_1);
	t_3 = NdChar - (NaChar / (-1.0 - t_1));
	tmp = 0.0;
	if (EAccept <= -1.45e-123)
		tmp = t_3;
	elseif (EAccept <= -6.6e-266)
		tmp = t_0 + (NaChar / ((Ev / KbT) + 2.0));
	elseif (EAccept <= 7.5e-221)
		tmp = t_3;
	elseif (EAccept <= 1.6e-125)
		tmp = t_2 + (NdChar / (1.0 + ((1.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT))));
	elseif (EAccept <= 3200000.0)
		tmp = t_3;
	elseif (EAccept <= 5e+164)
		tmp = t_2 + (NdChar / (1.0 + (Ec * (((1.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) / Ec) + (-1.0 / KbT)))));
	else
		tmp = t_0 + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NdChar - N[(NaChar / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -1.45e-123], t$95$3, If[LessEqual[EAccept, -6.6e-266], N[(t$95$0 + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 7.5e-221], t$95$3, If[LessEqual[EAccept, 1.6e-125], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(N[(1.0 - N[(Vef * N[(N[(-1.0 / KbT), $MachinePrecision] + N[(EDonor * N[(N[(N[(-1.0 / KbT), $MachinePrecision] - N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3200000.0], t$95$3, If[LessEqual[EAccept, 5e+164], N[(t$95$2 + N[(NdChar / N[(1.0 + N[(Ec * N[(N[(N[(1.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision] + N[(-1.0 / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if EAccept < -1.45000000000000002e-123 or -6.6000000000000006e-266 < EAccept < 7.50000000000000043e-221 or 1.5999999999999999e-125 < EAccept < 3.2e6

   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 51.2%

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

   6. Taylor expanded in mu around inf 48.6%

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

   7. Taylor expanded in mu around 0 66.0%

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

   if -1.45000000000000002e-123 < EAccept < -6.6000000000000006e-266

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Ev around inf 91.4%

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

   6. Taylor expanded in Ev around 0 69.6%

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

   if 7.50000000000000043e-221 < EAccept < 1.5999999999999999e-125

   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 70.3%

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

   6. Taylor expanded in EDonor around inf 70.3%

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

      1. *-commutative 70.3%

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

      2. *-commutative 70.3%

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

   8. Simplified 70.3%

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

   9. Taylor expanded in Vef around inf 75.9%

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

       1. associate-/l* 76.1%

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

       2. *-commutative 76.1%

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

   11. Simplified 76.1%

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

   if 3.2e6 < EAccept < 4.9999999999999995e164

   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 60.6%

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

   6. Taylor expanded in Ec around -inf 68.3%

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

      1. associate-*r* 68.3%

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

      2. mul-1-neg 68.3%

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

      3. +-commutative 68.3%

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

      4. mul-1-neg 68.3%

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

      5. unsub-neg 68.3%

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

   8. Simplified 68.3%

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

   if 4.9999999999999995e164 < EAccept

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in EAccept around inf 92.9%

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

   6. Taylor expanded in EAccept around 0 74.6%

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

4. Final simplification 68.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -1.45 \cdot 10^{-123}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq -6.6 \cdot 10^{-266}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 7.5 \cdot 10^{-221}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.6 \cdot 10^{-125}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \left(\left(1 - Vef \cdot \left(\frac{-1}{KbT} + EDonor \cdot \frac{\frac{-1}{KbT} - \frac{mu}{EDonor \cdot KbT}}{Vef}\right)\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{elif}\;EAccept \leq 3200000:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 5 \cdot 10^{+164}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + Ec \cdot \left(\frac{1 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)}{Ec} + \frac{-1}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 64.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_2 := \frac{NaChar}{1 + t\_0} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 3.9 \cdot 10^{+30}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{+87}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq 7.2 \cdot 10^{+126}:\\ \;\;\;\;t\_1 + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
        (t_2 (+ (/ NaChar (+ 1.0 t_0)) (/ NdChar (+ 1.0 (/ Vef KbT))))))
   (if (<= NaChar -6.8e+65)
     t_2
     (if (<= NaChar 3.9e+30)
       (+ t_1 (/ NaChar (+ (/ Ev KbT) 2.0)))
       (if (<= NaChar 4.8e+87)
         t_2
         (if (<= NaChar 7.2e+126)
           (+ t_1 (/ NaChar (+ (/ EAccept KbT) 2.0)))
           (- NdChar (/ NaChar (- -1.0 t_0)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_1 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_2 = (NaChar / (1.0 + t_0)) + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -6.8e+65) {
		tmp = t_2;
	} else if (NaChar <= 3.9e+30) {
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NaChar <= 4.8e+87) {
		tmp = t_2;
	} else if (NaChar <= 7.2e+126) {
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - t_0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = exp(((vef + (ev + (eaccept - mu))) / kbt))
    t_1 = ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))
    t_2 = (nachar / (1.0d0 + t_0)) + (ndchar / (1.0d0 + (vef / kbt)))
    if (nachar <= (-6.8d+65)) then
        tmp = t_2
    else if (nachar <= 3.9d+30) then
        tmp = t_1 + (nachar / ((ev / kbt) + 2.0d0))
    else if (nachar <= 4.8d+87) then
        tmp = t_2
    else if (nachar <= 7.2d+126) then
        tmp = t_1 + (nachar / ((eaccept / kbt) + 2.0d0))
    else
        tmp = ndchar - (nachar / ((-1.0d0) - t_0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	double t_1 = NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double t_2 = (NaChar / (1.0 + t_0)) + (NdChar / (1.0 + (Vef / KbT)));
	double tmp;
	if (NaChar <= -6.8e+65) {
		tmp = t_2;
	} else if (NaChar <= 3.9e+30) {
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NaChar <= 4.8e+87) {
		tmp = t_2;
	} else if (NaChar <= 7.2e+126) {
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))
	t_1 = NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	t_2 = (NaChar / (1.0 + t_0)) + (NdChar / (1.0 + (Vef / KbT)))
	tmp = 0
	if NaChar <= -6.8e+65:
		tmp = t_2
	elif NaChar <= 3.9e+30:
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0))
	elif NaChar <= 4.8e+87:
		tmp = t_2
	elif NaChar <= 7.2e+126:
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0))
	else:
		tmp = NdChar - (NaChar / (-1.0 - t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + t_0)) + Float64(NdChar / Float64(1.0 + Float64(Vef / KbT))))
	tmp = 0.0
	if (NaChar <= -6.8e+65)
		tmp = t_2;
	elseif (NaChar <= 3.9e+30)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (NaChar <= 4.8e+87)
		tmp = t_2;
	elseif (NaChar <= 7.2e+126)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	else
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((Vef + (Ev + (EAccept - mu))) / KbT));
	t_1 = NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	t_2 = (NaChar / (1.0 + t_0)) + (NdChar / (1.0 + (Vef / KbT)));
	tmp = 0.0;
	if (NaChar <= -6.8e+65)
		tmp = t_2;
	elseif (NaChar <= 3.9e+30)
		tmp = t_1 + (NaChar / ((Ev / KbT) + 2.0));
	elseif (NaChar <= 4.8e+87)
		tmp = t_2;
	elseif (NaChar <= 7.2e+126)
		tmp = t_1 + (NaChar / ((EAccept / KbT) + 2.0));
	else
		tmp = NdChar - (NaChar / (-1.0 - t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.8e+65], t$95$2, If[LessEqual[NaChar, 3.9e+30], N[(t$95$1 + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.8e+87], t$95$2, If[LessEqual[NaChar, 7.2e+126], N[(t$95$1 + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -6.7999999999999999e65 or 3.90000000000000011e30 < NaChar < 4.79999999999999963e87

   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 66.6%

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

   6. Taylor expanded in Vef around inf 76.9%

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

   if -6.7999999999999999e65 < NaChar < 3.90000000000000011e30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 76.6%

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

   6. Taylor expanded in Ev around 0 64.3%

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

   if 4.79999999999999963e87 < NaChar < 7.2000000000000001e126

   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 83.8%

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

   6. Taylor expanded in EAccept around 0 84.1%

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

   if 7.2000000000000001e126 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.0%

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

   6. Taylor expanded in mu around inf 52.7%

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

   7. Taylor expanded in mu around 0 79.3%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 3.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 4.8 \cdot 10^{+87}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 7.2 \cdot 10^{+126}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 67.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -3.3 \cdot 10^{+16} \lor \neg \left(NaChar \leq 7.4 \cdot 10^{-164}\right):\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -3.3e+16) (not (<= NaChar 7.4e-164)))
   (- NdChar (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
    (/ NaChar (+ (/ EAccept 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 ((NaChar <= -3.3e+16) || !(NaChar <= 7.4e-164)) {
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((EAccept / 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 ((nachar <= (-3.3d+16)) .or. (.not. (nachar <= 7.4d-164))) then
        tmp = ndchar - (nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt))))
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / ((eaccept / 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 ((NaChar <= -3.3e+16) || !(NaChar <= 7.4e-164)) {
		tmp = NdChar - (NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -3.3e+16) or not (NaChar <= 7.4e-164):
		tmp = NdChar - (NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -3.3e+16) || !(NaChar <= 7.4e-164))
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / 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 ((NaChar <= -3.3e+16) || ~((NaChar <= 7.4e-164)))
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	else
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -3.3e+16], N[Not[LessEqual[NaChar, 7.4e-164]], $MachinePrecision]], N[(NdChar - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -3.3e16 or 7.3999999999999998e-164 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.4%

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

   6. Taylor expanded in mu around inf 54.6%

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

   7. Taylor expanded in mu around 0 68.9%

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

   if -3.3e16 < NaChar < 7.3999999999999998e-164

   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 81.6%

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

   6. Taylor expanded in EAccept around 0 71.1%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.3 \cdot 10^{+16} \lor \neg \left(NaChar \leq 7.4 \cdot 10^{-164}\right):\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 66.6% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+65} \lor \neg \left(NaChar \leq 16500\right):\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -6.8e+65) (not (<= NaChar 16500.0)))
   (- NdChar (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
    (/ NaChar (+ (/ Ev KbT) 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -6.8e+65) || !(NaChar <= 16500.0)) {
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-6.8d+65)) .or. (.not. (nachar <= 16500.0d0))) then
        tmp = ndchar - (nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt))))
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / ((ev / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -6.8e+65) || !(NaChar <= 16500.0)) {
		tmp = NdChar - (NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -6.8e+65) or not (NaChar <= 16500.0):
		tmp = NdChar - (NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -6.8e+65) || !(NaChar <= 16500.0))
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -6.8e+65) || ~((NaChar <= 16500.0)))
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	else
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -6.8e+65], N[Not[LessEqual[NaChar, 16500.0]], $MachinePrecision]], N[(NdChar - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -6.7999999999999999e65 or 16500 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 59.2%

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

   6. Taylor expanded in mu around inf 55.9%

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

   7. Taylor expanded in mu around 0 72.4%

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

   if -6.7999999999999999e65 < NaChar < 16500

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 76.3%

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

   6. Taylor expanded in Ev around 0 63.8%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.8 \cdot 10^{+65} \lor \neg \left(NaChar \leq 16500\right):\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 64.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -3.3 \cdot 10^{+16} \lor \neg \left(NaChar \leq 3.6 \cdot 10^{-215}\right):\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -3.3e+16) (not (<= NaChar 3.6e-215)))
   (- NdChar (/ NaChar (- -1.0 (exp (/ (+ Vef (+ Ev (- EAccept mu))) KbT)))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
    (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -3.3e+16) || !(NaChar <= 3.6e-215)) {
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-3.3d+16)) .or. (.not. (nachar <= 3.6d-215))) then
        tmp = ndchar - (nachar / ((-1.0d0) - exp(((vef + (ev + (eaccept - mu))) / kbt))))
    else
        tmp = (ndchar / (1.0d0 + exp(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -3.3e+16) || !(NaChar <= 3.6e-215)) {
		tmp = NdChar - (NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -3.3e+16) or not (NaChar <= 3.6e-215):
		tmp = NdChar - (NaChar / (-1.0 - math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))))
	else:
		tmp = (NdChar / (1.0 + math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -3.3e+16) || !(NaChar <= 3.6e-215))
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Float64(Ev + Float64(EAccept - mu))) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -3.3e+16) || ~((NaChar <= 3.6e-215)))
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
	else
		tmp = (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -3.3e+16], N[Not[LessEqual[NaChar, 3.6e-215]], $MachinePrecision]], N[(NdChar - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + N[(Ev + N[(EAccept - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -3.3e16 or 3.5999999999999999e-215 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.8%

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

   6. Taylor expanded in mu around inf 52.4%

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

   7. Taylor expanded in mu around 0 67.0%

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

   if -3.3e16 < NaChar < 3.5999999999999999e-215

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 79.7%

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

   6. Taylor expanded in Ev around 0 65.9%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.3 \cdot 10^{+16} \lor \neg \left(NaChar \leq 3.6 \cdot 10^{-215}\right):\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 55.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NdChar + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{if}\;mu \leq -1.35 \cdot 10^{+93}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq -5.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;mu \leq 5 \cdot 10^{+149}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ NdChar (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))))
   (if (<= mu -1.35e+93)
     t_0
     (if (<= mu -5.8e+50)
       (+ (/ NaChar 2.0) (/ NdChar (+ 1.0 (exp (/ Ec (- KbT))))))
       (if (<= mu 5e+149)
         (- NdChar (/ NaChar (- -1.0 (exp (/ (+ Vef Ev) KbT)))))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar + (NaChar / (1.0 + exp((mu / -KbT))));
	double tmp;
	if (mu <= -1.35e+93) {
		tmp = t_0;
	} else if (mu <= -5.8e+50) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((Ec / -KbT))));
	} else if (mu <= 5e+149) {
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + Ev) / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar + (nachar / (1.0d0 + exp((mu / -kbt))))
    if (mu <= (-1.35d+93)) then
        tmp = t_0
    else if (mu <= (-5.8d+50)) then
        tmp = (nachar / 2.0d0) + (ndchar / (1.0d0 + exp((ec / -kbt))))
    else if (mu <= 5d+149) then
        tmp = ndchar - (nachar / ((-1.0d0) - exp(((vef + ev) / kbt))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	double tmp;
	if (mu <= -1.35e+93) {
		tmp = t_0;
	} else if (mu <= -5.8e+50) {
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + Math.exp((Ec / -KbT))));
	} else if (mu <= 5e+149) {
		tmp = NdChar - (NaChar / (-1.0 - Math.exp(((Vef + Ev) / KbT))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar + (NaChar / (1.0 + math.exp((mu / -KbT))))
	tmp = 0
	if mu <= -1.35e+93:
		tmp = t_0
	elif mu <= -5.8e+50:
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + math.exp((Ec / -KbT))))
	elif mu <= 5e+149:
		tmp = NdChar - (NaChar / (-1.0 - math.exp(((Vef + Ev) / KbT))))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))))
	tmp = 0.0
	if (mu <= -1.35e+93)
		tmp = t_0;
	elseif (mu <= -5.8e+50)
		tmp = Float64(Float64(NaChar / 2.0) + Float64(NdChar / Float64(1.0 + exp(Float64(Ec / Float64(-KbT))))));
	elseif (mu <= 5e+149)
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Ev) / KbT)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar + (NaChar / (1.0 + exp((mu / -KbT))));
	tmp = 0.0;
	if (mu <= -1.35e+93)
		tmp = t_0;
	elseif (mu <= -5.8e+50)
		tmp = (NaChar / 2.0) + (NdChar / (1.0 + exp((Ec / -KbT))));
	elseif (mu <= 5e+149)
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + Ev) / KbT))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -1.35e+93], t$95$0, If[LessEqual[mu, -5.8e+50], N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 5e+149], N[(NdChar - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + Ev), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -1.35e93 or 4.9999999999999999e149 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 48.5%

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

   6. Taylor expanded in mu around inf 47.9%

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

   7. Taylor expanded in mu around 0 72.8%

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

   8. Taylor expanded in mu around inf 70.4%

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

      1. associate-*r/ 39.2%

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

      2. mul-1-neg 39.2%

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

   10. Simplified 70.4%

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

   if -1.35e93 < mu < -5.8e50

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 74.8%

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

   6. Taylor expanded in Ev around 0 68.6%

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

   7. Taylor expanded in Ec around inf 68.6%

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

      1. associate-*r/ 68.6%

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

      2. mul-1-neg 68.6%

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

   9. Simplified 68.6%

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

   if -5.8e50 < mu < 4.9999999999999999e149

   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 51.3%

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

   6. Taylor expanded in mu around inf 46.5%

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

   7. Taylor expanded in mu around 0 58.0%

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

   8. Taylor expanded in Ev around inf 53.2%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -1.35 \cdot 10^{+93}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -5.8 \cdot 10^{+50}:\\ \;\;\;\;\frac{NaChar}{2} + \frac{NdChar}{1 + e^{\frac{Ec}{-KbT}}}\\ \mathbf{elif}\;mu \leq 5 \cdot 10^{+149}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 55.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -1.45 \cdot 10^{+96} \lor \neg \left(mu \leq 5 \cdot 10^{+148}\right):\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= mu -1.45e+96) (not (<= mu 5e+148)))
   (+ NdChar (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))
   (- NdChar (/ NaChar (- -1.0 (exp (/ (+ Vef Ev) 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 ((mu <= -1.45e+96) || !(mu <= 5e+148)) {
		tmp = NdChar + (NaChar / (1.0 + exp((mu / -KbT))));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + Ev) / 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 ((mu <= (-1.45d+96)) .or. (.not. (mu <= 5d+148))) then
        tmp = ndchar + (nachar / (1.0d0 + exp((mu / -kbt))))
    else
        tmp = ndchar - (nachar / ((-1.0d0) - exp(((vef + ev) / 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 ((mu <= -1.45e+96) || !(mu <= 5e+148)) {
		tmp = NdChar + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - Math.exp(((Vef + Ev) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (mu <= -1.45e+96) or not (mu <= 5e+148):
		tmp = NdChar + (NaChar / (1.0 + math.exp((mu / -KbT))))
	else:
		tmp = NdChar - (NaChar / (-1.0 - math.exp(((Vef + Ev) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((mu <= -1.45e+96) || !(mu <= 5e+148))
		tmp = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))));
	else
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef + Ev) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((mu <= -1.45e+96) || ~((mu <= 5e+148)))
		tmp = NdChar + (NaChar / (1.0 + exp((mu / -KbT))));
	else
		tmp = NdChar - (NaChar / (-1.0 - exp(((Vef + Ev) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[mu, -1.45e+96], N[Not[LessEqual[mu, 5e+148]], $MachinePrecision]], N[(NdChar + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef + Ev), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if mu < -1.44999999999999989e96 or 5.00000000000000024e148 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 48.5%

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

   6. Taylor expanded in mu around inf 47.9%

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

   7. Taylor expanded in mu around 0 72.8%

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

   8. Taylor expanded in mu around inf 70.4%

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

      1. associate-*r/ 39.2%

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

      2. mul-1-neg 39.2%

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

   10. Simplified 70.4%

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

   if -1.44999999999999989e96 < mu < 5.00000000000000024e148

   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 51.6%

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

   6. Taylor expanded in mu around inf 45.4%

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

   7. Taylor expanded in mu around 0 56.5%

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

   8. Taylor expanded in Ev around inf 51.9%

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

4. Final simplification 57.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -1.45 \cdot 10^{+96} \lor \neg \left(mu \leq 5 \cdot 10^{+148}\right):\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Vef + Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 52.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -2.3 \cdot 10^{+47} \lor \neg \left(mu \leq 4 \cdot 10^{+93}\right):\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= mu -2.3e+47) (not (<= mu 4e+93)))
   (+ NdChar (/ NaChar (+ 1.0 (exp (/ mu (- KbT))))))
   (- NdChar (/ NaChar (- -1.0 (exp (/ Ev 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 ((mu <= -2.3e+47) || !(mu <= 4e+93)) {
		tmp = NdChar + (NaChar / (1.0 + exp((mu / -KbT))));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - exp((Ev / 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 ((mu <= (-2.3d+47)) .or. (.not. (mu <= 4d+93))) then
        tmp = ndchar + (nachar / (1.0d0 + exp((mu / -kbt))))
    else
        tmp = ndchar - (nachar / ((-1.0d0) - exp((ev / 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 ((mu <= -2.3e+47) || !(mu <= 4e+93)) {
		tmp = NdChar + (NaChar / (1.0 + Math.exp((mu / -KbT))));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (mu <= -2.3e+47) or not (mu <= 4e+93):
		tmp = NdChar + (NaChar / (1.0 + math.exp((mu / -KbT))))
	else:
		tmp = NdChar - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((mu <= -2.3e+47) || !(mu <= 4e+93))
		tmp = Float64(NdChar + Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))));
	else
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((mu <= -2.3e+47) || ~((mu <= 4e+93)))
		tmp = NdChar + (NaChar / (1.0 + exp((mu / -KbT))));
	else
		tmp = NdChar - (NaChar / (-1.0 - exp((Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[mu, -2.3e+47], N[Not[LessEqual[mu, 4e+93]], $MachinePrecision]], N[(NdChar + N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if mu < -2.2999999999999999e47 or 4.00000000000000017e93 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 49.1%

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

   6. Taylor expanded in mu around inf 44.4%

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

   7. Taylor expanded in mu around 0 67.8%

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

   8. Taylor expanded in mu around inf 65.4%

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

      1. associate-*r/ 40.4%

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

      2. mul-1-neg 40.4%

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

   10. Simplified 65.4%

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

   if -2.2999999999999999e47 < mu < 4.00000000000000017e93

   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 51.6%

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

   6. Taylor expanded in mu around inf 47.4%

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

   7. Taylor expanded in mu around 0 57.3%

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

   8. Taylor expanded in Ev around inf 47.2%

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

4. Final simplification 54.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -2.3 \cdot 10^{+47} \lor \neg \left(mu \leq 4 \cdot 10^{+93}\right):\\ \;\;\;\;NdChar + \frac{NaChar}{1 + e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 62.2% accurate, 2.0× speedup

Math

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

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return NdChar - (NaChar / (-1.0 - exp(((Vef + (Ev + (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 - (nachar / ((-1.0d0) - exp(((vef + (ev + (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 - (NaChar / (-1.0 - Math.exp(((Vef + (Ev + (EAccept - mu))) / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 50.6%

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

6. Taylor expanded in mu around inf 46.2%

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

7. Taylor expanded in mu around 0 61.5%

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

8. Final simplification 61.5%

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

Alternative 20: 48.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -2 \cdot 10^{+178}:\\ \;\;\;\;NdChar \cdot 0.5 + \left(\left(NaChar \cdot \frac{Vef}{KbT}\right) \cdot -0.25 + NaChar \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -2e+178)
   (+ (* NdChar 0.5) (+ (* (* NaChar (/ Vef KbT)) -0.25) (* NaChar 0.5)))
   (- NdChar (/ NaChar (- -1.0 (exp (/ EAccept KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -2e+178) {
		tmp = (NdChar * 0.5) + (((NaChar * (Vef / KbT)) * -0.25) + (NaChar * 0.5));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-2d+178)) then
        tmp = (ndchar * 0.5d0) + (((nachar * (vef / kbt)) * (-0.25d0)) + (nachar * 0.5d0))
    else
        tmp = ndchar - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -2e+178) {
		tmp = (NdChar * 0.5) + (((NaChar * (Vef / KbT)) * -0.25) + (NaChar * 0.5));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -2e+178:
		tmp = (NdChar * 0.5) + (((NaChar * (Vef / KbT)) * -0.25) + (NaChar * 0.5))
	else:
		tmp = NdChar - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -2e+178)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(Float64(Float64(NaChar * Float64(Vef / KbT)) * -0.25) + Float64(NaChar * 0.5)));
	else
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -2e+178)
		tmp = (NdChar * 0.5) + (((NaChar * (Vef / KbT)) * -0.25) + (NaChar * 0.5));
	else
		tmp = NdChar - (NaChar / (-1.0 - exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -2e+178], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(N[(N[(NaChar * N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -2.0000000000000001e178

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 87.4%

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

   6. Taylor expanded in KbT around inf 63.0%

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

   7. Taylor expanded in Vef around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-/l* 74.8%

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

   9. Simplified 74.8%

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

   if -2.0000000000000001e178 < 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 46.1%

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

   6. Taylor expanded in mu around inf 45.8%

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

   7. Taylor expanded in mu around 0 62.1%

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

   8. Taylor expanded in EAccept around inf 46.9%

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

4. Final simplification 49.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2 \cdot 10^{+178}:\\ \;\;\;\;NdChar \cdot 0.5 + \left(\left(NaChar \cdot \frac{Vef}{KbT}\right) \cdot -0.25 + NaChar \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 48.7% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -5.5 \cdot 10^{+22}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -5.5e+22)
   (- NdChar (/ NaChar (- -1.0 (exp (/ Ev KbT)))))
   (- NdChar (/ NaChar (- -1.0 (exp (/ EAccept KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -5.5e+22) {
		tmp = NdChar - (NaChar / (-1.0 - exp((Ev / KbT))));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-5.5d+22)) then
        tmp = ndchar - (nachar / ((-1.0d0) - exp((ev / kbt))))
    else
        tmp = ndchar - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -5.5e+22) {
		tmp = NdChar - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	} else {
		tmp = NdChar - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -5.5e+22:
		tmp = NdChar - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	else:
		tmp = NdChar - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -5.5e+22)
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(NdChar - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -5.5e+22)
		tmp = NdChar - (NaChar / (-1.0 - exp((Ev / KbT))));
	else
		tmp = NdChar - (NaChar / (-1.0 - exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -5.5e+22], N[(NdChar - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -5.50000000000000021e22

   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 47.4%

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

   6. Taylor expanded in mu around inf 45.5%

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

   7. Taylor expanded in mu around 0 60.1%

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

   8. Taylor expanded in Ev around inf 53.4%

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

   if -5.50000000000000021e22 < 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 KbT around inf 51.7%

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

   6. Taylor expanded in mu around inf 46.4%

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

   7. Taylor expanded in mu around 0 62.0%

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

   8. Taylor expanded in EAccept around inf 48.1%

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

4. Final simplification 49.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -5.5 \cdot 10^{+22}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 36.0% accurate, 8.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -3.6 \cdot 10^{-127}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar -3.6e-127)
   (+ NdChar (* NaChar 0.5))
   (-
    NdChar
    (/
     NaChar
     (- (/ mu KbT) (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -3.6e-127) {
		tmp = NdChar + (NaChar * 0.5);
	} else {
		tmp = NdChar - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ndchar <= (-3.6d-127)) then
        tmp = ndchar + (nachar * 0.5d0)
    else
        tmp = ndchar - (nachar / ((mu / kbt) - (2.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt))))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -3.6e-127) {
		tmp = NdChar + (NaChar * 0.5);
	} else {
		tmp = NdChar - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= -3.6e-127:
		tmp = NdChar + (NaChar * 0.5)
	else:
		tmp = NdChar - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= -3.6e-127)
		tmp = Float64(NdChar + Float64(NaChar * 0.5));
	else
		tmp = Float64(NdChar - Float64(NaChar / Float64(Float64(mu / KbT) - Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= -3.6e-127)
		tmp = NdChar + (NaChar * 0.5);
	else
		tmp = NdChar - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, -3.6e-127], N[(NdChar + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(NdChar - N[(NaChar / N[(N[(mu / KbT), $MachinePrecision] - N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -3.5999999999999999e-127

   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 40.9%

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

   6. Taylor expanded in mu around inf 45.3%

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

   7. Taylor expanded in mu around 0 60.2%

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

   8. Taylor expanded in KbT around inf 45.2%

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

   if -3.5999999999999999e-127 < 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 55.4%

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

   6. Taylor expanded in mu around inf 46.7%

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

   7. Taylor expanded in mu around 0 62.2%

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

   8. Taylor expanded in KbT around inf 39.3%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.6 \cdot 10^{-127}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NdChar - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 38.0% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -7.4 \cdot 10^{+167}:\\ \;\;\;\;NdChar \cdot 0.5 + \left(NaChar \cdot 0.5 + -0.25 \cdot \left(Ev \cdot \frac{NaChar}{KbT}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -7.4e+167)
   (+ (* NdChar 0.5) (+ (* NaChar 0.5) (* -0.25 (* Ev (/ NaChar KbT)))))
   (+ NdChar (* 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 (KbT <= -7.4e+167) {
		tmp = (NdChar * 0.5) + ((NaChar * 0.5) + (-0.25 * (Ev * (NaChar / KbT))));
	} else {
		tmp = NdChar + (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 (kbt <= (-7.4d+167)) then
        tmp = (ndchar * 0.5d0) + ((nachar * 0.5d0) + ((-0.25d0) * (ev * (nachar / kbt))))
    else
        tmp = ndchar + (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 (KbT <= -7.4e+167) {
		tmp = (NdChar * 0.5) + ((NaChar * 0.5) + (-0.25 * (Ev * (NaChar / KbT))));
	} else {
		tmp = NdChar + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -7.4e+167:
		tmp = (NdChar * 0.5) + ((NaChar * 0.5) + (-0.25 * (Ev * (NaChar / KbT))))
	else:
		tmp = NdChar + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -7.4e+167)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(Float64(NaChar * 0.5) + Float64(-0.25 * Float64(Ev * Float64(NaChar / KbT)))));
	else
		tmp = Float64(NdChar + 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 (KbT <= -7.4e+167)
		tmp = (NdChar * 0.5) + ((NaChar * 0.5) + (-0.25 * (Ev * (NaChar / KbT))));
	else
		tmp = NdChar + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -7.4e+167], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(N[(NaChar * 0.5), $MachinePrecision] + N[(-0.25 * N[(Ev * N[(NaChar / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -7.4000000000000002e167

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 87.4%

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

   6. Taylor expanded in KbT around inf 63.0%

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

   7. Taylor expanded in Ev around inf 68.9%

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

      1. *-commutative 68.9%

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

      2. associate-/l* 73.8%

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

   9. Simplified 73.8%

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

   if -7.4000000000000002e167 < 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 46.1%

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

   6. Taylor expanded in mu around inf 45.8%

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

   7. Taylor expanded in mu around 0 62.1%

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

   8. Taylor expanded in KbT around inf 35.6%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -7.4 \cdot 10^{+167}:\\ \;\;\;\;NdChar \cdot 0.5 + \left(NaChar \cdot 0.5 + -0.25 \cdot \left(Ev \cdot \frac{NaChar}{KbT}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 38.0% accurate, 11.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -5.2 \cdot 10^{+186}:\\ \;\;\;\;NdChar \cdot 0.5 + \left(\left(NaChar \cdot \frac{Vef}{KbT}\right) \cdot -0.25 + NaChar \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -5.2e+186)
   (+ (* NdChar 0.5) (+ (* (* NaChar (/ Vef KbT)) -0.25) (* NaChar 0.5)))
   (+ NdChar (* 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 (KbT <= -5.2e+186) {
		tmp = (NdChar * 0.5) + (((NaChar * (Vef / KbT)) * -0.25) + (NaChar * 0.5));
	} else {
		tmp = NdChar + (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 (kbt <= (-5.2d+186)) then
        tmp = (ndchar * 0.5d0) + (((nachar * (vef / kbt)) * (-0.25d0)) + (nachar * 0.5d0))
    else
        tmp = ndchar + (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 (KbT <= -5.2e+186) {
		tmp = (NdChar * 0.5) + (((NaChar * (Vef / KbT)) * -0.25) + (NaChar * 0.5));
	} else {
		tmp = NdChar + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -5.2e+186:
		tmp = (NdChar * 0.5) + (((NaChar * (Vef / KbT)) * -0.25) + (NaChar * 0.5))
	else:
		tmp = NdChar + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -5.2e+186)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(Float64(Float64(NaChar * Float64(Vef / KbT)) * -0.25) + Float64(NaChar * 0.5)));
	else
		tmp = Float64(NdChar + 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 (KbT <= -5.2e+186)
		tmp = (NdChar * 0.5) + (((NaChar * (Vef / KbT)) * -0.25) + (NaChar * 0.5));
	else
		tmp = NdChar + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -5.2e+186], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(N[(N[(NaChar * N[(Vef / KbT), $MachinePrecision]), $MachinePrecision] * -0.25), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NdChar + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -5.2000000000000001e186

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 87.4%

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

   6. Taylor expanded in KbT around inf 63.0%

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

   7. Taylor expanded in Vef around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-/l* 74.8%

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

   9. Simplified 74.8%

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

   if -5.2000000000000001e186 < 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 46.1%

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

   6. Taylor expanded in mu around inf 45.8%

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

   7. Taylor expanded in mu around 0 62.1%

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

   8. Taylor expanded in KbT around inf 35.6%

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

4. Final simplification 39.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -5.2 \cdot 10^{+186}:\\ \;\;\;\;NdChar \cdot 0.5 + \left(\left(NaChar \cdot \frac{Vef}{KbT}\right) \cdot -0.25 + NaChar \cdot 0.5\right)\\ \mathbf{else}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 38.1% accurate, 22.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.6 \cdot 10^{+169}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.6e+169) (* 0.5 (+ NdChar NaChar)) (+ NdChar (* 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 (KbT <= -1.6e+169) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NdChar + (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 (kbt <= (-1.6d+169)) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = ndchar + (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 (KbT <= -1.6e+169) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NdChar + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -1.6e+169:
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NdChar + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -1.6e+169)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NdChar + 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 (KbT <= -1.6e+169)
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NdChar + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -1.6e+169], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NdChar + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -1.5999999999999999e169

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 87.4%

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

   6. Taylor expanded in mu around inf 79.6%

      \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\color{blue}{-1 \cdot \frac{mu}{KbT}}}} \]
   7. Step-by-step derivation

      1. associate-*r/ 79.6%

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

      2. mul-1-neg 79.6%

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

   8. Simplified 79.6%

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

   9. Taylor expanded in mu around 0 73.8%

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

       1. distribute-lft-out 73.8%

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

   11. Simplified 73.8%

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

   if -1.5999999999999999e169 < 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 46.1%

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

   6. Taylor expanded in mu around inf 45.8%

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

   7. Taylor expanded in mu around 0 62.1%

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

   8. Taylor expanded in KbT around inf 35.6%

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

4. Final simplification 39.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.6 \cdot 10^{+169}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;NdChar + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 27.7% 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 41.0%

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

6. Taylor expanded in mu around inf 33.9%

   \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\color{blue}{-1 \cdot \frac{mu}{KbT}}}} \]
7. Step-by-step derivation

   1. associate-*r/ 33.9%

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

   2. mul-1-neg 33.9%

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

8. Simplified 33.9%

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

9. Taylor expanded in mu around 0 24.7%

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

    1. distribute-lft-out 24.7%

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

11. Simplified 24.7%

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

12. Final simplification 24.7%

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

Alternative 27: 17.9% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 41.0%

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

6. Taylor expanded in mu around inf 33.9%

   \[\leadsto 0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\color{blue}{-1 \cdot \frac{mu}{KbT}}}} \]
7. Step-by-step derivation

   1. associate-*r/ 33.9%

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

   2. mul-1-neg 33.9%

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

8. Simplified 33.9%

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

9. Taylor expanded in NdChar around inf 18.8%

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

10. Final simplification 18.8%

    \[\leadsto NdChar \cdot 0.5 \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024072 
(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))))))