Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 35.2s

Alternatives: 23

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = 8.028554146210104e+172
  2. Ec = -3.5408943018728383e+307
  3. Vef = 4.6460327350376685e-236
  4. EDonor = 8.77777590403269e-188
  5. mu = 2.673247889354921e+151
  6. KbT = -1.2297512158352595e-139
  7. NaChar = 9.140232781073987e+172
  8. Ev = -1.5982840678389937e+156
  9. EAccept = 3.2677887001979786e+266

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 76.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;Vef \leq -1.35 \cdot 10^{+130}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Vef \leq -3.2 \cdot 10^{-93}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 5.4 \cdot 10^{+160}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1 (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_2
         (+
          (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))))
   (if (<= Vef -1.35e+130)
     t_2
     (if (<= Vef -3.2e-93)
       t_1
       (if (<= Vef -3.2e-275)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         (if (<= Vef 5.4e+160) t_1 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_2 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (Vef <= -1.35e+130) {
		tmp = t_2;
	} else if (Vef <= -3.2e-93) {
		tmp = t_1;
	} else if (Vef <= -3.2e-275) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= 5.4e+160) {
		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 + (eaccept + (ev - mu))) / kbt)))
    t_1 = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_2 = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    if (vef <= (-1.35d+130)) then
        tmp = t_2
    else if (vef <= (-3.2d-93)) then
        tmp = t_1
    else if (vef <= (-3.2d-275)) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= 5.4d+160) 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 + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_2 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (Vef <= -1.35e+130) {
		tmp = t_2;
	} else if (Vef <= -3.2e-93) {
		tmp = t_1;
	} else if (Vef <= -3.2e-275) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= 5.4e+160) {
		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 + (EAccept + (Ev - mu))) / KbT)))
	t_1 = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_2 = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	tmp = 0
	if Vef <= -1.35e+130:
		tmp = t_2
	elif Vef <= -3.2e-93:
		tmp = t_1
	elif Vef <= -3.2e-275:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= 5.4e+160:
		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(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))))
	tmp = 0.0
	if (Vef <= -1.35e+130)
		tmp = t_2;
	elseif (Vef <= -3.2e-93)
		tmp = t_1;
	elseif (Vef <= -3.2e-275)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= 5.4e+160)
		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 + (EAccept + (Ev - mu))) / KbT)));
	t_1 = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_2 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	tmp = 0.0;
	if (Vef <= -1.35e+130)
		tmp = t_2;
	elseif (Vef <= -3.2e-93)
		tmp = t_1;
	elseif (Vef <= -3.2e-275)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= 5.4e+160)
		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[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -1.35e+130], t$95$2, If[LessEqual[Vef, -3.2e-93], t$95$1, If[LessEqual[Vef, -3.2e-275], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 5.4e+160], t$95$1, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -1.3499999999999999e130 or 5.4e160 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 93.0%

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

   6. Taylor expanded in EDonor around 0 91.5%

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

      1. +-commutative 39.6%

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

   8. Simplified 91.5%

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

   if -1.3499999999999999e130 < Vef < -3.1999999999999999e-93 or -3.2e-275 < Vef < 5.4e160

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 82.4%

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

   if -3.1999999999999999e-93 < Vef < -3.2e-275

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 84.0%

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

4. Final simplification 84.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1.35 \cdot 10^{+130}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.2 \cdot 10^{-93}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3.2 \cdot 10^{-275}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 5.4 \cdot 10^{+160}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 76.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;Vef \leq -3.2 \cdot 10^{+112}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;Vef \leq -3 \cdot 10^{-170}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 9.2 \cdot 10^{-198}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8 \cdot 10^{+160}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))))
   (if (<= Vef -3.2e+112)
     t_1
     (if (<= Vef -3e-170)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
        (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
       (if (<= Vef 9.2e-198)
         (+ t_0 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         (if (<= Vef 8e+160)
           (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
           t_1))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (Vef <= -3.2e+112) {
		tmp = t_1;
	} else if (Vef <= -3e-170) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Vef <= 9.2e-198) {
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (Vef <= 8e+160) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    t_1 = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    if (vef <= (-3.2d+112)) then
        tmp = t_1
    else if (vef <= (-3d-170)) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (vef <= 9.2d-198) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (vef <= 8d+160) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (Vef <= -3.2e+112) {
		tmp = t_1;
	} else if (Vef <= -3e-170) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Vef <= 9.2e-198) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (Vef <= 8e+160) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	tmp = 0
	if Vef <= -3.2e+112:
		tmp = t_1
	elif Vef <= -3e-170:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Vef <= 9.2e-198:
		tmp = t_0 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif Vef <= 8e+160:
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))))
	tmp = 0.0
	if (Vef <= -3.2e+112)
		tmp = t_1;
	elseif (Vef <= -3e-170)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Vef <= 9.2e-198)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (Vef <= 8e+160)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	t_1 = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	tmp = 0.0;
	if (Vef <= -3.2e+112)
		tmp = t_1;
	elseif (Vef <= -3e-170)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Vef <= 9.2e-198)
		tmp = t_0 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (Vef <= 8e+160)
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -3.2e+112], t$95$1, If[LessEqual[Vef, -3e-170], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 9.2e-198], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 8e+160], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]

Derivation

1. Split input into 4 regimes

2. if Vef < -3.19999999999999986e112 or 8.00000000000000005e160 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 93.4%

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

   6. Taylor expanded in EDonor around 0 92.0%

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

      1. +-commutative 39.1%

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

   8. Simplified 92.0%

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

   if -3.19999999999999986e112 < Vef < -3.00000000000000013e-170

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 86.7%

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

   if -3.00000000000000013e-170 < Vef < 9.20000000000000053e-198

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 81.7%

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

   if 9.20000000000000053e-198 < Vef < 8.00000000000000005e160

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 82.5%

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

4. Final simplification 85.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.2 \cdot 10^{+112}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;Vef \leq -3 \cdot 10^{-170}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Vef \leq 9.2 \cdot 10^{-198}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq 8 \cdot 10^{+160}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 76.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -1.5 \cdot 10^{+129} \lor \neg \left(Vef \leq 9.4 \cdot 10^{+160}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= Vef -1.5e+129) (not (<= Vef 9.4e+160)))
   (+
    (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
    (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
    (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -1.5e+129) || !(Vef <= 9.4e+160)) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((vef <= (-1.5d+129)) .or. (.not. (vef <= 9.4d+160))) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((Vef <= -1.5e+129) || !(Vef <= 9.4e+160)) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (Vef <= -1.5e+129) or not (Vef <= 9.4e+160):
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((Vef <= -1.5e+129) || !(Vef <= 9.4e+160))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((Vef <= -1.5e+129) || ~((Vef <= 9.4e+160)))
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[Vef, -1.5e+129], N[Not[LessEqual[Vef, 9.4e+160]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -1.50000000000000015e129 or 9.39999999999999941e160 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 93.0%

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

   6. Taylor expanded in EDonor around 0 91.5%

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

      1. +-commutative 39.6%

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

   8. Simplified 91.5%

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

   if -1.50000000000000015e129 < Vef < 9.39999999999999941e160

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 80.5%

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

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -1.5 \cdot 10^{+129} \lor \neg \left(Vef \leq 9.4 \cdot 10^{+160}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Vef \leq -3.6 \cdot 10^{+129}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + t_0\\ \mathbf{elif}\;Vef \leq 1.06 \cdot 10^{+161}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ Vef KbT))))))
   (if (<= Vef -3.6e+129)
     (+ (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))) t_0)
     (if (<= Vef 1.06e+161)
       (+
        (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
        (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
       (+ t_0 (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((Vef / KbT)));
	double tmp;
	if (Vef <= -3.6e+129) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + t_0;
	} else if (Vef <= 1.06e+161) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((vef / kbt)))
    if (vef <= (-3.6d+129)) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + t_0
    else if (vef <= 1.06d+161) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_0 + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((Vef / KbT)));
	double tmp;
	if (Vef <= -3.6e+129) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + t_0;
	} else if (Vef <= 1.06e+161) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((Vef / KbT)))
	tmp = 0
	if Vef <= -3.6e+129:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + t_0
	elif Vef <= 1.06e+161:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_0 + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	tmp = 0.0
	if (Vef <= -3.6e+129)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + t_0);
	elseif (Vef <= 1.06e+161)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((Vef / KbT)));
	tmp = 0.0;
	if (Vef <= -3.6e+129)
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + t_0;
	elseif (Vef <= 1.06e+161)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_0 + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -3.6e+129], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[Vef, 1.06e+161], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -3.6000000000000001e129

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 89.9%

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

   if -3.6000000000000001e129 < Vef < 1.06e161

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 80.5%

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

   if 1.06e161 < Vef

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 99.9%

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

   6. Taylor expanded in EDonor around 0 99.9%

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

      1. +-commutative 48.4%

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

   8. Simplified 99.9%

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

4. Final simplification 83.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -3.6 \cdot 10^{+129}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Vef \leq 1.06 \cdot 10^{+161}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 59.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;Ev \leq -5.6 \cdot 10^{+158}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq 9 \cdot 10^{-249}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
   (if (<= Ev -5.6e+158)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= Ev 9e-249)
       (+
        (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
       (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((EDonor / KbT)));
	double tmp;
	if (Ev <= -5.6e+158) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Ev <= 9e-249) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((edonor / kbt)))
    if (ev <= (-5.6d+158)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (ev <= 9d-249) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	double tmp;
	if (Ev <= -5.6e+158) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Ev <= 9e-249) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((EDonor / KbT)))
	tmp = 0
	if Ev <= -5.6e+158:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Ev <= 9e-249:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))))
	tmp = 0.0
	if (Ev <= -5.6e+158)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Ev <= 9e-249)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((EDonor / KbT)));
	tmp = 0.0;
	if (Ev <= -5.6e+158)
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Ev <= 9e-249)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -5.6e+158], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 9e-249], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -5.60000000000000003e158

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Ev around inf 79.1%

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

   6. Taylor expanded in EDonor around inf 50.8%

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

   if -5.60000000000000003e158 < Ev < 8.99999999999999962e-249

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 72.0%

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

   6. Taylor expanded in EDonor around 0 68.2%

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

      1. +-commutative 47.6%

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

   8. Simplified 68.2%

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

   if 8.99999999999999962e-249 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.1%

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

   6. Taylor expanded in EDonor around inf 62.1%

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

4. Final simplification 63.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -5.6 \cdot 10^{+158}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq 9 \cdot 10^{-249}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 60.4% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{if}\;NdChar \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-281}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-181}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 3.35 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (*
           NaChar
           (/ 1.0 (+ 1.0 (exp (/ (+ Vef (- (+ EAccept Ev) mu)) KbT)))))
          (* NdChar 0.5)))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_2
         (+ t_1 (/ 1.0 (/ (+ 2.0 (/ (+ EAccept (- Vef mu)) KbT)) NaChar)))))
   (if (<= NdChar -3.7e+37)
     t_2
     (if (<= NdChar 8.5e-281)
       t_0
       (if (<= NdChar 3.3e-181)
         (+
          t_1
          (/
           NaChar
           (+
            1.0
            (-
             (+ 1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
             (/ mu KbT)))))
         (if (<= NdChar 3.35e-25) 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 = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	double t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	double tmp;
	if (NdChar <= -3.7e+37) {
		tmp = t_2;
	} else if (NdChar <= 8.5e-281) {
		tmp = t_0;
	} else if (NdChar <= 3.3e-181) {
		tmp = t_1 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))));
	} else if (NdChar <= 3.35e-25) {
		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 = (nachar * (1.0d0 / (1.0d0 + exp(((vef + ((eaccept + ev) - mu)) / kbt))))) + (ndchar * 0.5d0)
    t_1 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_2 = t_1 + (1.0d0 / ((2.0d0 + ((eaccept + (vef - mu)) / kbt)) / nachar))
    if (ndchar <= (-3.7d+37)) then
        tmp = t_2
    else if (ndchar <= 8.5d-281) then
        tmp = t_0
    else if (ndchar <= 3.3d-181) then
        tmp = t_1 + (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt))))
    else if (ndchar <= 3.35d-25) 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 = (NaChar * (1.0 / (1.0 + Math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	double t_1 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	double tmp;
	if (NdChar <= -3.7e+37) {
		tmp = t_2;
	} else if (NdChar <= 8.5e-281) {
		tmp = t_0;
	} else if (NdChar <= 3.3e-181) {
		tmp = t_1 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))));
	} else if (NdChar <= 3.35e-25) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar * (1.0 / (1.0 + math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5)
	t_1 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar))
	tmp = 0
	if NdChar <= -3.7e+37:
		tmp = t_2
	elif NdChar <= 8.5e-281:
		tmp = t_0
	elif NdChar <= 3.3e-181:
		tmp = t_1 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))))
	elif NdChar <= 3.35e-25:
		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(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(EAccept + Ev) - mu)) / KbT))))) + Float64(NdChar * 0.5))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(t_1 + Float64(1.0 / Float64(Float64(2.0 + Float64(Float64(EAccept + Float64(Vef - mu)) / KbT)) / NaChar)))
	tmp = 0.0
	if (NdChar <= -3.7e+37)
		tmp = t_2;
	elseif (NdChar <= 8.5e-281)
		tmp = t_0;
	elseif (NdChar <= 3.3e-181)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT)))));
	elseif (NdChar <= 3.35e-25)
		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 = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	tmp = 0.0;
	if (NdChar <= -3.7e+37)
		tmp = t_2;
	elseif (NdChar <= 8.5e-281)
		tmp = t_0;
	elseif (NdChar <= 3.3e-181)
		tmp = t_1 + (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT))));
	elseif (NdChar <= 3.35e-25)
		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[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(Vef + N[(N[(EAccept + Ev), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(1.0 / N[(N[(2.0 + N[(N[(EAccept + N[(Vef - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.7e+37], t$95$2, If[LessEqual[NdChar, 8.5e-281], t$95$0, If[LessEqual[NdChar, 3.3e-181], N[(t$95$1 + N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.35e-25], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -3.6999999999999999e37 or 3.35000000000000016e-25 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.8%

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

      1. +-commutative 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in Ev around 0 65.8%

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

      1. clear-num 66.2%

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

      2. inv-pow 66.2%

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

      3. +-commutative 66.2%

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

      4. associate--l+ 66.2%

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

      5. +-commutative 66.2%

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

      6. div-inv 66.2%

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

      7. div-inv 66.2%

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

      8. distribute-rgt-out 66.9%

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

   10. Applied egg-rr 66.9%

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

       1. unpow-1 66.9%

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

       2. associate-+r- 66.9%

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

       3. +-commutative 66.9%

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

       4. associate-+r- 66.9%

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

       5. associate-*l/ 66.9%

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

       6. *-lft-identity 66.9%

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

       7. +-commutative 66.9%

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

       8. div-sub 72.1%

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

       9. associate--l+ 72.1%

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

   12. Simplified 72.1%

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

   if -3.6999999999999999e37 < NdChar < 8.4999999999999994e-281 or 3.30000000000000009e-181 < NdChar < 3.35000000000000016e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. associate-/r/ 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 63.5%

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

   if 8.4999999999999994e-281 < NdChar < 3.30000000000000009e-181

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.4%

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

      1. +-commutative 66.4%

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

   7. Simplified 66.4%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.7 \cdot 10^{+37}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{elif}\;NdChar \leq 8.5 \cdot 10^{-281}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-181}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 3.35 \cdot 10^{-25}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 59.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{if}\;NdChar \leq -3.2 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq 4.5 \cdot 10^{-279}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-181}:\\ \;\;\;\;t_1 + \frac{NaChar}{\left(2 + \frac{KbT + EAccept \cdot \frac{KbT}{Vef}}{KbT \cdot \frac{KbT}{Vef}}\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.18 \cdot 10^{-26}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (*
           NaChar
           (/ 1.0 (+ 1.0 (exp (/ (+ Vef (- (+ EAccept Ev) mu)) KbT)))))
          (* NdChar 0.5)))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_2
         (+ t_1 (/ 1.0 (/ (+ 2.0 (/ (+ EAccept (- Vef mu)) KbT)) NaChar)))))
   (if (<= NdChar -3.2e+37)
     t_2
     (if (<= NdChar 4.5e-279)
       t_0
       (if (<= NdChar 3.3e-181)
         (+
          t_1
          (/
           NaChar
           (-
            (+ 2.0 (/ (+ KbT (* EAccept (/ KbT Vef))) (* KbT (/ KbT Vef))))
            (/ mu KbT))))
         (if (<= NdChar 1.18e-26) 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 = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	double t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	double tmp;
	if (NdChar <= -3.2e+37) {
		tmp = t_2;
	} else if (NdChar <= 4.5e-279) {
		tmp = t_0;
	} else if (NdChar <= 3.3e-181) {
		tmp = t_1 + (NaChar / ((2.0 + ((KbT + (EAccept * (KbT / Vef))) / (KbT * (KbT / Vef)))) - (mu / KbT)));
	} else if (NdChar <= 1.18e-26) {
		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 = (nachar * (1.0d0 / (1.0d0 + exp(((vef + ((eaccept + ev) - mu)) / kbt))))) + (ndchar * 0.5d0)
    t_1 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_2 = t_1 + (1.0d0 / ((2.0d0 + ((eaccept + (vef - mu)) / kbt)) / nachar))
    if (ndchar <= (-3.2d+37)) then
        tmp = t_2
    else if (ndchar <= 4.5d-279) then
        tmp = t_0
    else if (ndchar <= 3.3d-181) then
        tmp = t_1 + (nachar / ((2.0d0 + ((kbt + (eaccept * (kbt / vef))) / (kbt * (kbt / vef)))) - (mu / kbt)))
    else if (ndchar <= 1.18d-26) 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 = (NaChar * (1.0 / (1.0 + Math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	double t_1 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	double tmp;
	if (NdChar <= -3.2e+37) {
		tmp = t_2;
	} else if (NdChar <= 4.5e-279) {
		tmp = t_0;
	} else if (NdChar <= 3.3e-181) {
		tmp = t_1 + (NaChar / ((2.0 + ((KbT + (EAccept * (KbT / Vef))) / (KbT * (KbT / Vef)))) - (mu / KbT)));
	} else if (NdChar <= 1.18e-26) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar * (1.0 / (1.0 + math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5)
	t_1 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar))
	tmp = 0
	if NdChar <= -3.2e+37:
		tmp = t_2
	elif NdChar <= 4.5e-279:
		tmp = t_0
	elif NdChar <= 3.3e-181:
		tmp = t_1 + (NaChar / ((2.0 + ((KbT + (EAccept * (KbT / Vef))) / (KbT * (KbT / Vef)))) - (mu / KbT)))
	elif NdChar <= 1.18e-26:
		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(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(EAccept + Ev) - mu)) / KbT))))) + Float64(NdChar * 0.5))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(t_1 + Float64(1.0 / Float64(Float64(2.0 + Float64(Float64(EAccept + Float64(Vef - mu)) / KbT)) / NaChar)))
	tmp = 0.0
	if (NdChar <= -3.2e+37)
		tmp = t_2;
	elseif (NdChar <= 4.5e-279)
		tmp = t_0;
	elseif (NdChar <= 3.3e-181)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(KbT + Float64(EAccept * Float64(KbT / Vef))) / Float64(KbT * Float64(KbT / Vef)))) - Float64(mu / KbT))));
	elseif (NdChar <= 1.18e-26)
		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 = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	tmp = 0.0;
	if (NdChar <= -3.2e+37)
		tmp = t_2;
	elseif (NdChar <= 4.5e-279)
		tmp = t_0;
	elseif (NdChar <= 3.3e-181)
		tmp = t_1 + (NaChar / ((2.0 + ((KbT + (EAccept * (KbT / Vef))) / (KbT * (KbT / Vef)))) - (mu / KbT)));
	elseif (NdChar <= 1.18e-26)
		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[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(Vef + N[(N[(EAccept + Ev), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(1.0 / N[(N[(2.0 + N[(N[(EAccept + N[(Vef - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.2e+37], t$95$2, If[LessEqual[NdChar, 4.5e-279], t$95$0, If[LessEqual[NdChar, 3.3e-181], N[(t$95$1 + N[(NaChar / N[(N[(2.0 + N[(N[(KbT + N[(EAccept * N[(KbT / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(KbT * N[(KbT / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.18e-26], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -3.20000000000000014e37 or 1.17999999999999996e-26 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.8%

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

      1. +-commutative 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in Ev around 0 65.8%

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

      1. clear-num 66.2%

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

      2. inv-pow 66.2%

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

      3. +-commutative 66.2%

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

      4. associate--l+ 66.2%

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

      5. +-commutative 66.2%

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

      6. div-inv 66.2%

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

      7. div-inv 66.2%

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

      8. distribute-rgt-out 66.9%

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

   10. Applied egg-rr 66.9%

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

       1. unpow-1 66.9%

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

       2. associate-+r- 66.9%

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

       3. +-commutative 66.9%

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

       4. associate-+r- 66.9%

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

       5. associate-*l/ 66.9%

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

       6. *-lft-identity 66.9%

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

       7. +-commutative 66.9%

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

       8. div-sub 72.1%

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

       9. associate--l+ 72.1%

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

   12. Simplified 72.1%

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

   if -3.20000000000000014e37 < NdChar < 4.49999999999999995e-279 or 3.30000000000000009e-181 < NdChar < 1.17999999999999996e-26

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 63.0%

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

   if 4.49999999999999995e-279 < NdChar < 3.30000000000000009e-181

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.0%

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

      1. +-commutative 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in Ev around 0 69.0%

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

      1. +-commutative 69.0%

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

      2. clear-num 69.0%

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

      3. frac-add 72.9%

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

      4. *-un-lft-identity 72.9%

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

   10. Applied egg-rr 72.9%

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

4. Final simplification 68.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.2 \cdot 10^{+37}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{elif}\;NdChar \leq 4.5 \cdot 10^{-279}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-181}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \frac{KbT + EAccept \cdot \frac{KbT}{Vef}}{KbT \cdot \frac{KbT}{Vef}}\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.18 \cdot 10^{-26}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -4.4 \cdot 10^{+37} \lor \neg \left(NdChar \leq 1.75 \cdot 10^{-279} \lor \neg \left(NdChar \leq 3.3 \cdot 10^{-181}\right) \land NdChar \leq 3.6 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -4.4e+37)
         (not
          (or (<= NdChar 1.75e-279)
              (and (not (<= NdChar 3.3e-181)) (<= NdChar 3.6e-25)))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ 1.0 (/ (+ 2.0 (/ (+ EAccept (- Vef mu)) KbT)) NaChar)))
   (+
    (* NaChar (/ 1.0 (+ 1.0 (exp (/ (+ Vef (- (+ EAccept Ev) mu)) KbT)))))
    (* NdChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -4.4e+37) || !((NdChar <= 1.75e-279) || (!(NdChar <= 3.3e-181) && (NdChar <= 3.6e-25)))) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	} else {
		tmp = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-4.4d+37)) .or. (.not. (ndchar <= 1.75d-279) .or. (.not. (ndchar <= 3.3d-181)) .and. (ndchar <= 3.6d-25))) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (1.0d0 / ((2.0d0 + ((eaccept + (vef - mu)) / kbt)) / nachar))
    else
        tmp = (nachar * (1.0d0 / (1.0d0 + exp(((vef + ((eaccept + ev) - mu)) / kbt))))) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -4.4e+37) || !((NdChar <= 1.75e-279) || (!(NdChar <= 3.3e-181) && (NdChar <= 3.6e-25)))) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	} else {
		tmp = (NaChar * (1.0 / (1.0 + Math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -4.4e+37) or not ((NdChar <= 1.75e-279) or (not (NdChar <= 3.3e-181) and (NdChar <= 3.6e-25))):
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar))
	else:
		tmp = (NaChar * (1.0 / (1.0 + math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -4.4e+37) || !((NdChar <= 1.75e-279) || (!(NdChar <= 3.3e-181) && (NdChar <= 3.6e-25))))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(1.0 / Float64(Float64(2.0 + Float64(Float64(EAccept + Float64(Vef - mu)) / KbT)) / NaChar)));
	else
		tmp = Float64(Float64(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(EAccept + Ev) - mu)) / KbT))))) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -4.4e+37) || ~(((NdChar <= 1.75e-279) || (~((NdChar <= 3.3e-181)) && (NdChar <= 3.6e-25)))))
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	else
		tmp = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -4.4e+37], N[Not[Or[LessEqual[NdChar, 1.75e-279], And[N[Not[LessEqual[NdChar, 3.3e-181]], $MachinePrecision], LessEqual[NdChar, 3.6e-25]]]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(2.0 + N[(N[(EAccept + N[(Vef - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(Vef + N[(N[(EAccept + Ev), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -4.4000000000000001e37 or 1.75000000000000005e-279 < NdChar < 3.30000000000000009e-181 or 3.5999999999999999e-25 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.9%

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

      1. +-commutative 64.9%

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

   7. Simplified 64.9%

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

   8. Taylor expanded in Ev around 0 66.3%

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

      1. clear-num 66.6%

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

      2. inv-pow 66.6%

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

      3. +-commutative 66.6%

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

      4. associate--l+ 66.6%

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

      5. +-commutative 66.6%

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

      6. div-inv 66.6%

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

      7. div-inv 66.6%

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

      8. distribute-rgt-out 67.2%

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

   10. Applied egg-rr 67.2%

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

       1. unpow-1 67.2%

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

       2. associate-+r- 67.2%

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

       3. +-commutative 67.2%

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

       4. associate-+r- 67.2%

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

       5. associate-*l/ 67.2%

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

       6. *-lft-identity 67.2%

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

       7. +-commutative 67.2%

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

       8. div-sub 71.6%

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

       9. associate--l+ 71.6%

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

   12. Simplified 71.6%

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

   if -4.4000000000000001e37 < NdChar < 1.75000000000000005e-279 or 3.30000000000000009e-181 < NdChar < 3.5999999999999999e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 63.0%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} \cdot NaChar \]
3. Recombined 2 regimes into one program.

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.4 \cdot 10^{+37} \lor \neg \left(NdChar \leq 1.75 \cdot 10^{-279} \lor \neg \left(NdChar \leq 3.3 \cdot 10^{-181}\right) \land NdChar \leq 3.6 \cdot 10^{-25}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 60.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_2 := t_1 + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{if}\;NdChar \leq -3.9 \cdot 10^{+37}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NdChar \leq 5.2 \cdot 10^{-279}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-181}:\\ \;\;\;\;t_1 + \frac{NaChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{EAccept}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.72 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (*
           NaChar
           (/ 1.0 (+ 1.0 (exp (/ (+ Vef (- (+ EAccept Ev) mu)) KbT)))))
          (* NdChar 0.5)))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_2
         (+ t_1 (/ 1.0 (/ (+ 2.0 (/ (+ EAccept (- Vef mu)) KbT)) NaChar)))))
   (if (<= NdChar -3.9e+37)
     t_2
     (if (<= NdChar 5.2e-279)
       t_0
       (if (<= NdChar 3.3e-181)
         (+
          t_1
          (/ NaChar (- (+ 2.0 (+ (/ Vef KbT) (/ EAccept KbT))) (/ mu KbT))))
         (if (<= NdChar 1.72e-25) 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 = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	double t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	double tmp;
	if (NdChar <= -3.9e+37) {
		tmp = t_2;
	} else if (NdChar <= 5.2e-279) {
		tmp = t_0;
	} else if (NdChar <= 3.3e-181) {
		tmp = t_1 + (NaChar / ((2.0 + ((Vef / KbT) + (EAccept / KbT))) - (mu / KbT)));
	} else if (NdChar <= 1.72e-25) {
		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 = (nachar * (1.0d0 / (1.0d0 + exp(((vef + ((eaccept + ev) - mu)) / kbt))))) + (ndchar * 0.5d0)
    t_1 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_2 = t_1 + (1.0d0 / ((2.0d0 + ((eaccept + (vef - mu)) / kbt)) / nachar))
    if (ndchar <= (-3.9d+37)) then
        tmp = t_2
    else if (ndchar <= 5.2d-279) then
        tmp = t_0
    else if (ndchar <= 3.3d-181) then
        tmp = t_1 + (nachar / ((2.0d0 + ((vef / kbt) + (eaccept / kbt))) - (mu / kbt)))
    else if (ndchar <= 1.72d-25) 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 = (NaChar * (1.0 / (1.0 + Math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	double t_1 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	double tmp;
	if (NdChar <= -3.9e+37) {
		tmp = t_2;
	} else if (NdChar <= 5.2e-279) {
		tmp = t_0;
	} else if (NdChar <= 3.3e-181) {
		tmp = t_1 + (NaChar / ((2.0 + ((Vef / KbT) + (EAccept / KbT))) - (mu / KbT)));
	} else if (NdChar <= 1.72e-25) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar * (1.0 / (1.0 + math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5)
	t_1 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar))
	tmp = 0
	if NdChar <= -3.9e+37:
		tmp = t_2
	elif NdChar <= 5.2e-279:
		tmp = t_0
	elif NdChar <= 3.3e-181:
		tmp = t_1 + (NaChar / ((2.0 + ((Vef / KbT) + (EAccept / KbT))) - (mu / KbT)))
	elif NdChar <= 1.72e-25:
		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(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(EAccept + Ev) - mu)) / KbT))))) + Float64(NdChar * 0.5))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_2 = Float64(t_1 + Float64(1.0 / Float64(Float64(2.0 + Float64(Float64(EAccept + Float64(Vef - mu)) / KbT)) / NaChar)))
	tmp = 0.0
	if (NdChar <= -3.9e+37)
		tmp = t_2;
	elseif (NdChar <= 5.2e-279)
		tmp = t_0;
	elseif (NdChar <= 3.3e-181)
		tmp = Float64(t_1 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(EAccept / KbT))) - Float64(mu / KbT))));
	elseif (NdChar <= 1.72e-25)
		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 = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	t_1 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_2 = t_1 + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	tmp = 0.0;
	if (NdChar <= -3.9e+37)
		tmp = t_2;
	elseif (NdChar <= 5.2e-279)
		tmp = t_0;
	elseif (NdChar <= 3.3e-181)
		tmp = t_1 + (NaChar / ((2.0 + ((Vef / KbT) + (EAccept / KbT))) - (mu / KbT)));
	elseif (NdChar <= 1.72e-25)
		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[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(Vef + N[(N[(EAccept + Ev), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(1.0 / N[(N[(2.0 + N[(N[(EAccept + N[(Vef - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -3.9e+37], t$95$2, If[LessEqual[NdChar, 5.2e-279], t$95$0, If[LessEqual[NdChar, 3.3e-181], N[(t$95$1 + N[(NaChar / N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.72e-25], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -3.8999999999999999e37 or 1.71999999999999995e-25 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.8%

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

      1. +-commutative 64.8%

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

   7. Simplified 64.8%

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

   8. Taylor expanded in Ev around 0 65.8%

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

      1. clear-num 66.2%

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

      2. inv-pow 66.2%

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

      3. +-commutative 66.2%

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

      4. associate--l+ 66.2%

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

      5. +-commutative 66.2%

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

      6. div-inv 66.2%

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

      7. div-inv 66.2%

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

      8. distribute-rgt-out 66.9%

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

   10. Applied egg-rr 66.9%

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

       1. unpow-1 66.9%

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

       2. associate-+r- 66.9%

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

       3. +-commutative 66.9%

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

       4. associate-+r- 66.9%

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

       5. associate-*l/ 66.9%

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

       6. *-lft-identity 66.9%

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

       7. +-commutative 66.9%

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

       8. div-sub 72.1%

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

       9. associate--l+ 72.1%

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

   12. Simplified 72.1%

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

   if -3.8999999999999999e37 < NdChar < 5.2000000000000004e-279 or 3.30000000000000009e-181 < NdChar < 1.71999999999999995e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 63.0%

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

   if 5.2000000000000004e-279 < NdChar < 3.30000000000000009e-181

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.0%

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

      1. +-commutative 65.0%

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

   7. Simplified 65.0%

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

   8. Taylor expanded in Ev around 0 69.0%

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

4. Final simplification 68.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.9 \cdot 10^{+37}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{elif}\;NdChar \leq 5.2 \cdot 10^{-279}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 3.3 \cdot 10^{-181}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{EAccept}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NdChar \leq 1.72 \cdot 10^{-25}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 65.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -1.14 \cdot 10^{+46} \lor \neg \left(NdChar \leq 2.8 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -1.14e+46) (not (<= NdChar 2.8e-47)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ 1.0 (/ (+ 2.0 (/ (+ EAccept (- Vef mu)) KbT)) NaChar)))
   (+
    (/
     NdChar
     (+
      1.0
      (- (+ (+ 1.0 (/ EDonor KbT)) (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
    (* NaChar (/ 1.0 (+ 1.0 (exp (/ (+ Vef (- (+ EAccept Ev) mu)) KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -1.14e+46) || !(NdChar <= 2.8e-47)) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	} else {
		tmp = (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT)))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-1.14d+46)) .or. (.not. (ndchar <= 2.8d-47))) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (1.0d0 / ((2.0d0 + ((eaccept + (vef - mu)) / kbt)) / nachar))
    else
        tmp = (ndchar / (1.0d0 + (((1.0d0 + (edonor / kbt)) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))) + (nachar * (1.0d0 / (1.0d0 + exp(((vef + ((eaccept + ev) - mu)) / kbt)))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -1.14e+46) || !(NdChar <= 2.8e-47)) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	} else {
		tmp = (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * (1.0 / (1.0 + Math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT)))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -1.14e+46) or not (NdChar <= 2.8e-47):
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar))
	else:
		tmp = (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * (1.0 / (1.0 + math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT)))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -1.14e+46) || !(NdChar <= 2.8e-47))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(1.0 / Float64(Float64(2.0 + Float64(Float64(EAccept + Float64(Vef - mu)) / KbT)) / NaChar)));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(Float64(Float64(1.0 + Float64(EDonor / KbT)) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)))) + Float64(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(EAccept + Ev) - mu)) / KbT))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -1.14e+46) || ~((NdChar <= 2.8e-47)))
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (1.0 / ((2.0 + ((EAccept + (Vef - mu)) / KbT)) / NaChar));
	else
		tmp = (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT)))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -1.14e+46], N[Not[LessEqual[NdChar, 2.8e-47]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(2.0 + N[(N[(EAccept + N[(Vef - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[(N[(N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(Vef + N[(N[(EAccept + Ev), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -1.14000000000000005e46 or 2.79999999999999993e-47 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.6%

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

      1. +-commutative 64.6%

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

   7. Simplified 64.6%

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

   8. Taylor expanded in Ev around 0 65.6%

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

      1. clear-num 66.0%

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

      2. inv-pow 66.0%

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

      3. +-commutative 66.0%

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

      4. associate--l+ 66.0%

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

      5. +-commutative 66.0%

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

      6. div-inv 66.0%

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

      7. div-inv 66.0%

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

      8. distribute-rgt-out 66.8%

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

   10. Applied egg-rr 66.8%

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

       1. unpow-1 66.8%

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

       2. associate-+r- 66.8%

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

       3. +-commutative 66.8%

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

       4. associate-+r- 66.8%

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

       5. associate-*l/ 66.8%

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

       6. *-lft-identity 66.8%

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

       7. +-commutative 66.8%

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

       8. div-sub 71.2%

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

       9. associate--l+ 71.2%

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

   12. Simplified 71.2%

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

   if -1.14000000000000005e46 < NdChar < 2.79999999999999993e-47

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 72.0%

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

      1. associate-+r+ 32.6%

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

   9. Simplified 72.0%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.14 \cdot 10^{+46} \lor \neg \left(NdChar \leq 2.8 \cdot 10^{-47}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{1}{\frac{2 + \frac{EAccept + \left(Vef - mu\right)}{KbT}}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.6 \cdot 10^{+154} \lor \neg \left(NaChar \leq -1.95 \cdot 10^{+46} \lor \neg \left(NaChar \leq -4500\right) \land NaChar \leq 5.2 \cdot 10^{-32}\right):\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.6e+154)
         (not
          (or (<= NaChar -1.95e+46)
              (and (not (<= NaChar -4500.0)) (<= NaChar 5.2e-32)))))
   (+
    (* NaChar (/ 1.0 (+ 1.0 (exp (/ (+ Vef (- (+ EAccept Ev) mu)) KbT)))))
    (* NdChar 0.5))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ Ev KbT) 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.6e+154) || !((NaChar <= -1.95e+46) || (!(NaChar <= -4500.0) && (NaChar <= 5.2e-32)))) {
		tmp = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-2.6d+154)) .or. (.not. (nachar <= (-1.95d+46)) .or. (.not. (nachar <= (-4500.0d0))) .and. (nachar <= 5.2d-32))) then
        tmp = (nachar * (1.0d0 / (1.0d0 + exp(((vef + ((eaccept + ev) - mu)) / kbt))))) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((ev / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.6e+154) || !((NaChar <= -1.95e+46) || (!(NaChar <= -4500.0) && (NaChar <= 5.2e-32)))) {
		tmp = (NaChar * (1.0 / (1.0 + Math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2.6e+154) or not ((NaChar <= -1.95e+46) or (not (NaChar <= -4500.0) and (NaChar <= 5.2e-32))):
		tmp = (NaChar * (1.0 / (1.0 + math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / 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 <= -2.6e+154) || !((NaChar <= -1.95e+46) || (!(NaChar <= -4500.0) && (NaChar <= 5.2e-32))))
		tmp = Float64(Float64(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(EAccept + Ev) - mu)) / KbT))))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -2.6e+154) || ~(((NaChar <= -1.95e+46) || (~((NaChar <= -4500.0)) && (NaChar <= 5.2e-32)))))
		tmp = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / 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, -2.6e+154], N[Not[Or[LessEqual[NaChar, -1.95e+46], And[N[Not[LessEqual[NaChar, -4500.0]], $MachinePrecision], LessEqual[NaChar, 5.2e-32]]]], $MachinePrecision]], N[(N[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(Vef + N[(N[(EAccept + Ev), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.59999999999999989e154 or -1.94999999999999997e46 < NaChar < -4500 or 5.1999999999999995e-32 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 61.8%

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

   if -2.59999999999999989e154 < NaChar < -1.94999999999999997e46 or -4500 < NaChar < 5.1999999999999995e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 73.7%

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

   6. Taylor expanded in Ev around 0 65.9%

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

      1. +-commutative 65.9%

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

   8. Simplified 65.9%

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

4. Final simplification 64.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.6 \cdot 10^{+154} \lor \neg \left(NaChar \leq -1.95 \cdot 10^{+46} \lor \neg \left(NaChar \leq -4500\right) \land NaChar \leq 5.2 \cdot 10^{-32}\right):\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.5% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -6.2 \cdot 10^{+37} \lor \neg \left(NdChar \leq 3.45 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -6.2e+37) (not (<= NdChar 3.45e-26)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ EAccept KbT) 2.0)))
   (+
    (* NaChar (/ 1.0 (+ 1.0 (exp (/ (+ Vef (- (+ EAccept Ev) mu)) KbT)))))
    (* NdChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -6.2e+37) || !(NdChar <= 3.45e-26)) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-6.2d+37)) .or. (.not. (ndchar <= 3.45d-26))) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((eaccept / kbt) + 2.0d0))
    else
        tmp = (nachar * (1.0d0 / (1.0d0 + exp(((vef + ((eaccept + ev) - mu)) / kbt))))) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -6.2e+37) || !(NdChar <= 3.45e-26)) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	} else {
		tmp = (NaChar * (1.0 / (1.0 + Math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -6.2e+37) or not (NdChar <= 3.45e-26):
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0))
	else:
		tmp = (NaChar * (1.0 / (1.0 + math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -6.2e+37) || !(NdChar <= 3.45e-26))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(EAccept + Ev) - mu)) / KbT))))) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -6.2e+37) || ~((NdChar <= 3.45e-26)))
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((EAccept / KbT) + 2.0));
	else
		tmp = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -6.2e+37], N[Not[LessEqual[NdChar, 3.45e-26]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(Vef + N[(N[(EAccept + Ev), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -6.2000000000000004e37 or 3.44999999999999999e-26 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.8%

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

   6. Taylor expanded in EAccept around 0 66.3%

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

   if -6.2000000000000004e37 < NdChar < 3.44999999999999999e-26

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 58.7%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} \cdot NaChar \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -6.2 \cdot 10^{+37} \lor \neg \left(NdChar \leq 3.45 \cdot 10^{-26}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -7000 \lor \neg \left(NdChar \leq 4.2 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -7000.0) (not (<= NdChar 4.2e-23)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (* NaChar 0.5))
   (+
    (* NaChar (/ 1.0 (+ 1.0 (exp (/ (+ Vef (- (+ EAccept Ev) mu)) KbT)))))
    (* NdChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -7000.0) || !(NdChar <= 4.2e-23)) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-7000.0d0)) .or. (.not. (ndchar <= 4.2d-23))) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar * 0.5d0)
    else
        tmp = (nachar * (1.0d0 / (1.0d0 + exp(((vef + ((eaccept + ev) - mu)) / kbt))))) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -7000.0) || !(NdChar <= 4.2e-23)) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar * (1.0 / (1.0 + Math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -7000.0) or not (NdChar <= 4.2e-23):
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NaChar * (1.0 / (1.0 + math.exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -7000.0) || !(NdChar <= 4.2e-23))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar * Float64(1.0 / Float64(1.0 + exp(Float64(Float64(Vef + Float64(Float64(EAccept + Ev) - mu)) / KbT))))) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -7000.0) || ~((NdChar <= 4.2e-23)))
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	else
		tmp = (NaChar * (1.0 / (1.0 + exp(((Vef + ((EAccept + Ev) - mu)) / KbT))))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -7000.0], N[Not[LessEqual[NdChar, 4.2e-23]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar * N[(1.0 / N[(1.0 + N[Exp[N[(N[(Vef + N[(N[(EAccept + Ev), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -7e3 or 4.2000000000000002e-23 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 59.7%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 59.7%

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

   7. Simplified 59.7%

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

   if -7e3 < NdChar < 4.2000000000000002e-23

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.9%

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

      2. associate-/r/ 100.0%

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

      3. div-inv 100.0%

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

      4. div-inv 100.0%

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

      5. associate-+r- 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in KbT around inf 58.9%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} \cdot NaChar \]
3. Recombined 2 regimes into one program.

4. Final simplification 59.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -7000 \lor \neg \left(NdChar \leq 4.2 \cdot 10^{-23}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NaChar \cdot \frac{1}{1 + e^{\frac{Vef + \left(\left(EAccept + Ev\right) - mu\right)}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 46.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.02 \cdot 10^{+193} \lor \neg \left(NaChar \leq 3.3 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.02e+193) (not (<= NaChar 3.3e-32)))
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* NdChar 0.5))
   (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (* 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 ((NaChar <= -1.02e+193) || !(NaChar <= 3.3e-32)) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (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 ((nachar <= (-1.02d+193)) .or. (.not. (nachar <= 3.3d-32))) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (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 ((NaChar <= -1.02e+193) || !(NaChar <= 3.3e-32)) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.02e+193) or not (NaChar <= 3.3e-32):
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.02e+193) || !(NaChar <= 3.3e-32))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + 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 ((NaChar <= -1.02e+193) || ~((NaChar <= 3.3e-32)))
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	else
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.02e+193], N[Not[LessEqual[NaChar, 3.3e-32]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.02000000000000004e193 or 3.30000000000000025e-32 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 64.8%

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

   6. Taylor expanded in KbT around inf 45.8%

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

   if -1.02000000000000004e193 < NaChar < 3.30000000000000025e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 58.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 58.9%

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

   7. Simplified 58.9%

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

   8. Taylor expanded in EDonor around 0 52.5%

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

      1. +-commutative 52.5%

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

   10. Simplified 52.5%

       \[\leadsto \color{blue}{\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}} + NaChar \cdot 0.5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 50.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.02 \cdot 10^{+193} \lor \neg \left(NaChar \leq 3.3 \cdot 10^{-32}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 46.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5500:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -5500.0)
   (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar (+ 1.0 (/ EDonor KbT))))
   (if (<= NaChar 1.85e-32)
     (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (* NaChar 0.5))
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* NdChar 0.5)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -5500.0) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NaChar <= 1.85e-32) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-5500.0d0)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + (edonor / kbt)))
    else if (nachar <= 1.85d-32) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar * 0.5d0)
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -5500.0) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)));
	} else if (NaChar <= 1.85e-32) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -5500.0:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)))
	elif NaChar <= 1.85e-32:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -5500.0)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(EDonor / KbT))));
	elseif (NaChar <= 1.85e-32)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -5500.0)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + (EDonor / KbT)));
	elseif (NaChar <= 1.85e-32)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar * 0.5);
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -5500.0], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.85e-32], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -5500

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 69.1%

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

   6. Taylor expanded in KbT around inf 45.4%

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

      1. associate-+r+ 31.8%

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

   8. Simplified 45.4%

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

   9. Taylor expanded in EDonor around inf 46.2%

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

   if -5500 < NaChar < 1.85e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 61.6%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in EDonor around 0 54.9%

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

      1. +-commutative 54.9%

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

   10. Simplified 54.9%

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

   if 1.85e-32 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 70.7%

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

   6. Taylor expanded in KbT around inf 47.6%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5500:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.85 \cdot 10^{-32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 48.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -6.8 \cdot 10^{+254}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{KbT}{\frac{Vef}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Vef -6.8e+254)
   (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ KbT (/ Vef NdChar)))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (* 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 (Vef <= -6.8e+254) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (KbT / (Vef / NdChar));
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (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 (vef <= (-6.8d+254)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (kbt / (vef / ndchar))
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (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 (Vef <= -6.8e+254) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (KbT / (Vef / NdChar));
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Vef <= -6.8e+254:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (KbT / (Vef / NdChar))
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Vef <= -6.8e+254)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(KbT / Float64(Vef / NdChar)));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + 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 (Vef <= -6.8e+254)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (KbT / (Vef / NdChar));
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Vef, -6.8e+254], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT / N[(Vef / NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -6.8000000000000001e254

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 100.0%

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

   6. Taylor expanded in KbT around inf 53.3%

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

      1. associate-+r+ 29.6%

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

   8. Simplified 53.3%

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

   9. Taylor expanded in Vef around inf 45.5%

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

       1. associate-/l* 50.1%

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

   11. Simplified 50.1%

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

   if -6.8000000000000001e254 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 52.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 52.8%

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

   7. Simplified 52.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{NaChar \cdot 0.5} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -6.8 \cdot 10^{+254}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{KbT}{\frac{Vef}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 35.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 2.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;EAccept \leq 1.95 \cdot 10^{+123}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\left(\frac{Vef}{KbT} + \left(\frac{Ev}{KbT} + 2\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 2.8e-93)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (* NdChar 0.5))
   (if (<= EAccept 1.95e+123)
     (+
      (/
       NdChar
       (+
        1.0
        (- (+ (+ 1.0 (/ EDonor KbT)) (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
      (/ NaChar (- (+ (/ Vef KbT) (+ (/ Ev KbT) 2.0)) (/ mu KbT))))
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* NdChar 0.5)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 2.8e-93) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar * 0.5);
	} else if (EAccept <= 1.95e+123) {
		tmp = (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar / (((Vef / KbT) + ((Ev / KbT) + 2.0)) - (mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= 2.8d-93) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar * 0.5d0)
    else if (eaccept <= 1.95d+123) then
        tmp = (ndchar / (1.0d0 + (((1.0d0 + (edonor / kbt)) + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))) + (nachar / (((vef / kbt) + ((ev / kbt) + 2.0d0)) - (mu / kbt)))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 2.8e-93) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar * 0.5);
	} else if (EAccept <= 1.95e+123) {
		tmp = (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar / (((Vef / KbT) + ((Ev / KbT) + 2.0)) - (mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 2.8e-93:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar * 0.5)
	elif EAccept <= 1.95e+123:
		tmp = (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar / (((Vef / KbT) + ((Ev / KbT) + 2.0)) - (mu / KbT)))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 2.8e-93)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar * 0.5));
	elseif (EAccept <= 1.95e+123)
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(Float64(Float64(1.0 + Float64(EDonor / KbT)) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)))) + Float64(NaChar / Float64(Float64(Float64(Vef / KbT) + Float64(Float64(Ev / KbT) + 2.0)) - Float64(mu / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 2.8e-93)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar * 0.5);
	elseif (EAccept <= 1.95e+123)
		tmp = (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar / (((Vef / KbT) + ((Ev / KbT) + 2.0)) - (mu / KbT)));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 2.8e-93], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 1.95e+123], N[(N[(NdChar / N[(1.0 + N[(N[(N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 2.79999999999999998e-93

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 71.4%

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

   6. Taylor expanded in KbT around inf 37.5%

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

   if 2.79999999999999998e-93 < EAccept < 1.94999999999999996e123

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.2%

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

      1. +-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in KbT around inf 36.1%

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

      1. associate-+r+ 36.1%

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

   10. Simplified 36.1%

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

   11. Taylor expanded in EAccept around 0 36.1%

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

       1. associate-+r+ 36.1%

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

       2. +-commutative 36.1%

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

   13. Simplified 36.1%

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

   if 1.94999999999999996e123 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 83.7%

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

   6. Taylor expanded in KbT around inf 59.5%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 2.8 \cdot 10^{-93}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;EAccept \leq 1.95 \cdot 10^{+123}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + \frac{NaChar}{\left(\frac{Vef}{KbT} + \left(\frac{Ev}{KbT} + 2\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 1.5 \cdot 10^{-243}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;EAccept \leq 2.3 \cdot 10^{+123}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 1.5e-243)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (* NdChar 0.5))
   (if (<= EAccept 2.3e+123)
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (* NaChar 0.5))
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* NdChar 0.5)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 1.5e-243) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar * 0.5);
	} else if (EAccept <= 2.3e+123) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= 1.5d-243) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar * 0.5d0)
    else if (eaccept <= 2.3d+123) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar * 0.5d0)
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 1.5e-243) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar * 0.5);
	} else if (EAccept <= 2.3e+123) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar * 0.5);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 1.5e-243:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar * 0.5)
	elif EAccept <= 2.3e+123:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar * 0.5)
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 1.5e-243)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar * 0.5));
	elseif (EAccept <= 2.3e+123)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 1.5e-243)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar * 0.5);
	elseif (EAccept <= 2.3e+123)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar * 0.5);
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 1.5e-243], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 2.3e+123], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 1.5000000000000001e-243

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 70.1%

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

   6. Taylor expanded in KbT around inf 37.8%

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

   if 1.5000000000000001e-243 < EAccept < 2.2999999999999999e123

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 51.9%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 51.9%

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

   7. Simplified 51.9%

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

   8. Taylor expanded in EDonor around inf 44.4%

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

   if 2.2999999999999999e123 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 83.7%

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

   6. Taylor expanded in KbT around inf 59.5%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 1.5 \cdot 10^{-243}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + NdChar \cdot 0.5\\ \mathbf{elif}\;EAccept \leq 2.3 \cdot 10^{+123}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 35.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+255}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)} + \frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \frac{KbT + Vef \cdot \frac{KbT}{mu}}{KbT \cdot \frac{KbT}{mu}}\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Vef -4.2e+255)
   (+
    (/
     NaChar
     (+
      1.0
      (- (+ 1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))) (/ mu KbT))))
    (/
     NdChar
     (+
      1.0
      (-
       (+
        (+ 1.0 (/ EDonor KbT))
        (/ (+ KbT (* Vef (/ KbT mu))) (* KbT (/ KbT mu))))
       (/ Ec KbT)))))
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (* NdChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Vef <= -4.2e+255) {
		tmp = (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))) + (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((KbT + (Vef * (KbT / mu))) / (KbT * (KbT / mu)))) - (Ec / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (vef <= (-4.2d+255)) then
        tmp = (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))) + (ndchar / (1.0d0 + (((1.0d0 + (edonor / kbt)) + ((kbt + (vef * (kbt / mu))) / (kbt * (kbt / mu)))) - (ec / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Vef <= -4.2e+255) {
		tmp = (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))) + (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((KbT + (Vef * (KbT / mu))) / (KbT * (KbT / mu)))) - (Ec / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Vef <= -4.2e+255:
		tmp = (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))) + (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((KbT + (Vef * (KbT / mu))) / (KbT * (KbT / mu)))) - (Ec / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Vef <= -4.2e+255)
		tmp = Float64(Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT)))) + Float64(NdChar / Float64(1.0 + Float64(Float64(Float64(1.0 + Float64(EDonor / KbT)) + Float64(Float64(KbT + Float64(Vef * Float64(KbT / mu))) / Float64(KbT * Float64(KbT / mu)))) - Float64(Ec / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Vef <= -4.2e+255)
		tmp = (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))) + (NdChar / (1.0 + (((1.0 + (EDonor / KbT)) + ((KbT + (Vef * (KbT / mu))) / (KbT * (KbT / mu)))) - (Ec / KbT))));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Vef, -4.2e+255], N[(N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[(N[(N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT + N[(Vef * N[(KbT / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(KbT * N[(KbT / mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < -4.2e255

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.6%

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

      1. +-commutative 55.6%

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

   7. Simplified 55.6%

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

   8. Taylor expanded in KbT around inf 31.0%

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

      1. associate-+r+ 31.0%

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

   10. Simplified 31.0%

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

       1. +-commutative 31.0%

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

       2. clear-num 31.0%

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

       3. frac-add 35.6%

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

       4. *-un-lft-identity 35.6%

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

   12. Applied egg-rr 35.6%

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

   if -4.2e255 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.8%

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

   6. Taylor expanded in KbT around inf 42.3%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4.2 \cdot 10^{+255}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)} + \frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \frac{KbT + Vef \cdot \frac{KbT}{mu}}{KbT \cdot \frac{KbT}{mu}}\right) - \frac{Ec}{KbT}\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 30.1% accurate, 5.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)}\\ t_1 := 1 + \frac{EDonor}{KbT}\\ \mathbf{if}\;KbT \leq -2 \cdot 10^{+105}:\\ \;\;\;\;NdChar \cdot 0.5 + NaChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.6 \cdot 10^{-226}:\\ \;\;\;\;t_0 + \frac{NdChar}{t_1}\\ \mathbf{elif}\;KbT \leq 9.2 \cdot 10^{+142}:\\ \;\;\;\;t_0 + \frac{NdChar}{1 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(t_1 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (/
          NaChar
          (+
           1.0
           (-
            (+ 1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
            (/ mu KbT)))))
        (t_1 (+ 1.0 (/ EDonor KbT))))
   (if (<= KbT -2e+105)
     (+ (* NdChar 0.5) (* NaChar 0.5))
     (if (<= KbT 1.6e-226)
       (+ t_0 (/ NdChar t_1))
       (if (<= KbT 9.2e+142)
         (+ t_0 (/ NdChar (- 1.0 (/ Ec KbT))))
         (+
          (/ NdChar (+ 1.0 (- (+ t_1 (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
          (* 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 t_0 = NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	double t_1 = 1.0 + (EDonor / KbT);
	double tmp;
	if (KbT <= -2e+105) {
		tmp = (NdChar * 0.5) + (NaChar * 0.5);
	} else if (KbT <= 1.6e-226) {
		tmp = t_0 + (NdChar / t_1);
	} else if (KbT <= 9.2e+142) {
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)));
	} else {
		tmp = (NdChar / (1.0 + ((t_1 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))
    t_1 = 1.0d0 + (edonor / kbt)
    if (kbt <= (-2d+105)) then
        tmp = (ndchar * 0.5d0) + (nachar * 0.5d0)
    else if (kbt <= 1.6d-226) then
        tmp = t_0 + (ndchar / t_1)
    else if (kbt <= 9.2d+142) then
        tmp = t_0 + (ndchar / (1.0d0 - (ec / kbt)))
    else
        tmp = (ndchar / (1.0d0 + ((t_1 + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))) + (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 t_0 = NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	double t_1 = 1.0 + (EDonor / KbT);
	double tmp;
	if (KbT <= -2e+105) {
		tmp = (NdChar * 0.5) + (NaChar * 0.5);
	} else if (KbT <= 1.6e-226) {
		tmp = t_0 + (NdChar / t_1);
	} else if (KbT <= 9.2e+142) {
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)));
	} else {
		tmp = (NdChar / (1.0 + ((t_1 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))
	t_1 = 1.0 + (EDonor / KbT)
	tmp = 0
	if KbT <= -2e+105:
		tmp = (NdChar * 0.5) + (NaChar * 0.5)
	elif KbT <= 1.6e-226:
		tmp = t_0 + (NdChar / t_1)
	elif KbT <= 9.2e+142:
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)))
	else:
		tmp = (NdChar / (1.0 + ((t_1 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT))))
	t_1 = Float64(1.0 + Float64(EDonor / KbT))
	tmp = 0.0
	if (KbT <= -2e+105)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar * 0.5));
	elseif (KbT <= 1.6e-226)
		tmp = Float64(t_0 + Float64(NdChar / t_1));
	elseif (KbT <= 9.2e+142)
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 - Float64(Ec / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(Float64(t_1 + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)));
	t_1 = 1.0 + (EDonor / KbT);
	tmp = 0.0;
	if (KbT <= -2e+105)
		tmp = (NdChar * 0.5) + (NaChar * 0.5);
	elseif (KbT <= 1.6e-226)
		tmp = t_0 + (NdChar / t_1);
	elseif (KbT <= 9.2e+142)
		tmp = t_0 + (NdChar / (1.0 - (Ec / KbT)));
	else
		tmp = (NdChar / (1.0 + ((t_1 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * 0.5);
	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[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -2e+105], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.6e-226], N[(t$95$0 + N[(NdChar / t$95$1), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 9.2e+142], N[(t$95$0 + N[(NdChar / N[(1.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[(N[(t$95$1 + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -1.9999999999999999e105

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 83.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in KbT around inf 70.5%

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

   if -1.9999999999999999e105 < KbT < 1.59999999999999991e-226

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 50.0%

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

      1. +-commutative 50.0%

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

   7. Simplified 50.0%

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

   8. Taylor expanded in KbT around inf 18.8%

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

      1. associate-+r+ 18.8%

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

   10. Simplified 18.8%

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

   11. Taylor expanded in EDonor around inf 24.9%

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

   if 1.59999999999999991e-226 < KbT < 9.20000000000000009e142

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 49.8%

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

      1. +-commutative 49.8%

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

   7. Simplified 49.8%

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

   8. Taylor expanded in KbT around inf 13.2%

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

      1. associate-+r+ 13.2%

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

   10. Simplified 13.2%

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

   11. Taylor expanded in Ec around inf 27.3%

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

       1. neg-mul-1 27.3%

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

       2. distribute-neg-frac 27.3%

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

   13. Simplified 27.3%

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

   if 9.20000000000000009e142 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in KbT around inf 59.9%

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

      1. associate-+r+ 56.2%

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

   10. Simplified 59.9%

       \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)}} + NaChar \cdot 0.5 \]
3. Recombined 4 regimes into one program.

4. Final simplification 38.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -2 \cdot 10^{+105}:\\ \;\;\;\;NdChar \cdot 0.5 + NaChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 1.6 \cdot 10^{-226}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;KbT \leq 9.2 \cdot 10^{+142}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)} + \frac{NdChar}{1 - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 30.3% accurate, 5.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{EDonor}{KbT}\\ \mathbf{if}\;KbT \leq -3.3 \cdot 10^{+105}:\\ \;\;\;\;NdChar \cdot 0.5 + NaChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)} + \frac{NdChar}{t_0}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(t_0 + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + NaChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ EDonor KbT))))
   (if (<= KbT -3.3e+105)
     (+ (* NdChar 0.5) (* NaChar 0.5))
     (if (<= KbT 4.8e+70)
       (+
        (/
         NaChar
         (+
          1.0
          (-
           (+ 1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))
           (/ mu KbT))))
        (/ NdChar t_0))
       (+
        (/ NdChar (+ 1.0 (- (+ t_0 (+ (/ Vef KbT) (/ mu KbT))) (/ Ec KbT))))
        (* 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 t_0 = 1.0 + (EDonor / KbT);
	double tmp;
	if (KbT <= -3.3e+105) {
		tmp = (NdChar * 0.5) + (NaChar * 0.5);
	} else if (KbT <= 4.8e+70) {
		tmp = (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))) + (NdChar / t_0);
	} else {
		tmp = (NdChar / (1.0 + ((t_0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (edonor / kbt)
    if (kbt <= (-3.3d+105)) then
        tmp = (ndchar * 0.5d0) + (nachar * 0.5d0)
    else if (kbt <= 4.8d+70) then
        tmp = (nachar / (1.0d0 + ((1.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))) - (mu / kbt)))) + (ndchar / t_0)
    else
        tmp = (ndchar / (1.0d0 + ((t_0 + ((vef / kbt) + (mu / kbt))) - (ec / kbt)))) + (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 t_0 = 1.0 + (EDonor / KbT);
	double tmp;
	if (KbT <= -3.3e+105) {
		tmp = (NdChar * 0.5) + (NaChar * 0.5);
	} else if (KbT <= 4.8e+70) {
		tmp = (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))) + (NdChar / t_0);
	} else {
		tmp = (NdChar / (1.0 + ((t_0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + (EDonor / KbT)
	tmp = 0
	if KbT <= -3.3e+105:
		tmp = (NdChar * 0.5) + (NaChar * 0.5)
	elif KbT <= 4.8e+70:
		tmp = (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))) + (NdChar / t_0)
	else:
		tmp = (NdChar / (1.0 + ((t_0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + Float64(EDonor / KbT))
	tmp = 0.0
	if (KbT <= -3.3e+105)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar * 0.5));
	elseif (KbT <= 4.8e+70)
		tmp = Float64(Float64(NaChar / Float64(1.0 + Float64(Float64(1.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))) - Float64(mu / KbT)))) + Float64(NdChar / t_0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + Float64(Float64(t_0 + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) - Float64(Ec / KbT)))) + Float64(NaChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + (EDonor / KbT);
	tmp = 0.0;
	if (KbT <= -3.3e+105)
		tmp = (NdChar * 0.5) + (NaChar * 0.5);
	elseif (KbT <= 4.8e+70)
		tmp = (NaChar / (1.0 + ((1.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))) - (mu / KbT)))) + (NdChar / t_0);
	else
		tmp = (NdChar / (1.0 + ((t_0 + ((Vef / KbT) + (mu / KbT))) - (Ec / KbT)))) + (NaChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -3.3e+105], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4.8e+70], N[(N[(NaChar / N[(1.0 + N[(N[(1.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / t$95$0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[(N[(t$95$0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar * 0.5), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -3.29999999999999997e105

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 83.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 83.4%

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

   7. Simplified 83.4%

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

   8. Taylor expanded in KbT around inf 70.5%

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

   if -3.29999999999999997e105 < KbT < 4.79999999999999974e70

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 48.7%

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

      1. +-commutative 48.7%

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

   7. Simplified 48.7%

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

   8. Taylor expanded in KbT around inf 16.3%

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

      1. associate-+r+ 16.3%

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

   10. Simplified 16.3%

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

   11. Taylor expanded in EDonor around inf 22.3%

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

   if 4.79999999999999974e70 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.2%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
   6. Step-by-step derivation

      1. *-commutative 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in KbT around inf 50.1%

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

      1. associate-+r+ 46.7%

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

   10. Simplified 50.1%

       \[\leadsto \frac{NdChar}{1 + \color{blue}{\left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)}} + NaChar \cdot 0.5 \]
3. Recombined 3 regimes into one program.

4. Final simplification 36.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.3 \cdot 10^{+105}:\\ \;\;\;\;NdChar \cdot 0.5 + NaChar \cdot 0.5\\ \mathbf{elif}\;KbT \leq 4.8 \cdot 10^{+70}:\\ \;\;\;\;\frac{NaChar}{1 + \left(\left(1 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right) - \frac{mu}{KbT}\right)} + \frac{NdChar}{1 + \frac{EDonor}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + \left(\left(\left(1 + \frac{EDonor}{KbT}\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right) - \frac{Ec}{KbT}\right)} + NaChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 28.3% accurate, 32.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 50.1%

   \[\leadsto \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
6. Step-by-step derivation

   1. *-commutative 50.1%

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

7. Simplified 50.1%

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

8. Taylor expanded in KbT around inf 30.9%

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

9. Final simplification 30.9%

   \[\leadsto NdChar \cdot 0.5 + NaChar \cdot 0.5 \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024021 
(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))))))