Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 31.2s

Alternatives: 27

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -6.063700608248466e-166
  2. Ec = -2.1778139239327518e-141
  3. Vef = 9.425710852496089e+29
  4. EDonor = 1.7185038993628508e+44
  5. mu = 1.000825157944548e-137
  6. KbT = -7.29200624515342e-287
  7. NaChar = 2.4436237326328943e-165
  8. Ev = 7.063583616336124e-9
  9. EAccept = -4.7708005851231495e-108

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

5. Final simplification 99.9%

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

Alternative 2: 64.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{if}\;mu \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq 6.6 \cdot 10^{+64}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{elif}\;mu \leq 2.5 \cdot 10^{+132}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;mu \leq 8.2 \cdot 10^{+164} \lor \neg \left(mu \leq 3 \cdot 10^{+180}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{\left(EAccept + \left(Vef + Ev\right)\right) - mu}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NdChar (+ (exp (/ mu KbT)) 1.0))
          (/ NaChar (- -1.0 (exp (/ mu (- KbT))))))))
   (if (<= mu -4.6e-5)
     t_0
     (if (<= mu 6.6e+64)
       (+
        (/ NaChar (+ (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)) 1.0))
        (/ NdChar (+ (+ (/ (+ Vef (+ EDonor (- mu Ec))) KbT) 1.0) 1.0)))
       (if (<= mu 2.5e+132)
         (+
          (/ NdChar (+ (exp (/ Vef KbT)) 1.0))
          (/ NaChar (+ (exp (/ Ev KbT)) 1.0)))
         (if (or (<= mu 8.2e+164) (not (<= mu 3e+180)))
           t_0
           (+
            (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0))
            (/ (* KbT NaChar) (- (+ EAccept (+ Vef Ev)) mu)))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - exp((mu / -KbT))));
	double tmp;
	if (mu <= -4.6e-5) {
		tmp = t_0;
	} else if (mu <= 6.6e+64) {
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else if (mu <= 2.5e+132) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((Ev / KbT)) + 1.0));
	} else if ((mu <= 8.2e+164) || !(mu <= 3e+180)) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (exp((mu / kbt)) + 1.0d0)) - (nachar / ((-1.0d0) - exp((mu / -kbt))))
    if (mu <= (-4.6d-5)) then
        tmp = t_0
    else if (mu <= 6.6d+64) then
        tmp = (nachar / (exp(((vef - (mu - (ev + eaccept))) / kbt)) + 1.0d0)) + (ndchar / ((((vef + (edonor + (mu - ec))) / kbt) + 1.0d0) + 1.0d0))
    else if (mu <= 2.5d+132) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (exp((ev / kbt)) + 1.0d0))
    else if ((mu <= 8.2d+164) .or. (.not. (mu <= 3d+180))) then
        tmp = t_0
    else
        tmp = (ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)) + ((kbt * nachar) / ((eaccept + (vef + ev)) - mu))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (Math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - Math.exp((mu / -KbT))));
	double tmp;
	if (mu <= -4.6e-5) {
		tmp = t_0;
	} else if (mu <= 6.6e+64) {
		tmp = (NaChar / (Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else if (mu <= 2.5e+132) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (Math.exp((Ev / KbT)) + 1.0));
	} else if ((mu <= 8.2e+164) || !(mu <= 3e+180)) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - math.exp((mu / -KbT))))
	tmp = 0
	if mu <= -4.6e-5:
		tmp = t_0
	elif mu <= 6.6e+64:
		tmp = (NaChar / (math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0))
	elif mu <= 2.5e+132:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (math.exp((Ev / KbT)) + 1.0))
	elif (mu <= 8.2e+164) or not (mu <= 3e+180):
		tmp = t_0
	else:
		tmp = (NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(mu / Float64(-KbT))))))
	tmp = 0.0
	if (mu <= -4.6e-5)
		tmp = t_0;
	elseif (mu <= 6.6e+64)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Float64(Float64(Vef + Float64(EDonor + Float64(mu - Ec))) / KbT) + 1.0) + 1.0)));
	elseif (mu <= 2.5e+132)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)));
	elseif ((mu <= 8.2e+164) || !(mu <= 3e+180))
		tmp = t_0;
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0)) + Float64(Float64(KbT * NaChar) / Float64(Float64(EAccept + Float64(Vef + Ev)) - mu)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - exp((mu / -KbT))));
	tmp = 0.0;
	if (mu <= -4.6e-5)
		tmp = t_0;
	elseif (mu <= 6.6e+64)
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	elseif (mu <= 2.5e+132)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((Ev / KbT)) + 1.0));
	elseif ((mu <= 8.2e+164) || ~((mu <= 3e+180)))
		tmp = t_0;
	else
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -4.6e-5], t$95$0, If[LessEqual[mu, 6.6e+64], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(Vef + N[(EDonor + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 2.5e+132], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[mu, 8.2e+164], N[Not[LessEqual[mu, 3e+180]], $MachinePrecision]], t$95$0, N[(N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if mu < -4.6e-5 or 2.5000000000000001e132 < mu < 8.20000000000000032e164 or 3.00000000000000003e180 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 90.7%

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

   6. Taylor expanded in mu around inf 78.3%

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

      1. associate-*r/ 51.0%

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

      2. mul-1-neg 51.0%

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

   8. Simplified 78.3%

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

   if -4.6e-5 < mu < 6.59999999999999976e64

   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%

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

   5. Taylor expanded in KbT around inf 69.7%

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

      1. +-commutative 69.7%

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

      2. associate-+r+ 69.7%

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

      3. associate--l- 69.7%

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

      4. neg-mul-1 69.7%

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

      5. unsub-neg 69.7%

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

      6. associate--l- 69.7%

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

      7. +-commutative 69.7%

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

      8. associate--r+ 69.7%

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

      9. associate--r+ 69.7%

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

   7. Simplified 69.7%

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

   if 6.59999999999999976e64 < mu < 2.5000000000000001e132

   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%

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

   5. Taylor expanded in Vef around inf 84.2%

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

   6. Taylor expanded in Ev around inf 75.6%

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

   if 8.20000000000000032e164 < mu < 3.00000000000000003e180

   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%

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

   5. Taylor expanded in KbT around inf 84.1%

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

   6. Taylor expanded in KbT around 0 84.1%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -4.6 \cdot 10^{-5}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq 6.6 \cdot 10^{+64}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{elif}\;mu \leq 2.5 \cdot 10^{+132}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1}\\ \mathbf{elif}\;mu \leq 8.2 \cdot 10^{+164} \lor \neg \left(mu \leq 3 \cdot 10^{+180}\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{\left(EAccept + \left(Vef + Ev\right)\right) - mu}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;mu \leq -2.8 \cdot 10^{+177}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;mu \leq -9 \cdot 10^{-232}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq 3.9 \cdot 10^{-267}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;mu \leq 6.5 \cdot 10^{+188}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NdChar (+ (exp (/ mu KbT)) 1.0))
          (/ NaChar (- -1.0 (exp (/ mu (- KbT)))))))
        (t_1
         (+
          (/ NaChar (+ (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)) 1.0))
          (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)))))
   (if (<= mu -2.8e+177)
     t_0
     (if (<= mu -9e-232)
       t_1
       (if (<= mu 3.9e-267)
         (-
          (/ NdChar (+ (exp (/ Ec (- KbT))) 1.0))
          (/ NaChar (- -1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))
         (if (<= mu 6.5e+188) t_1 t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - exp((mu / -KbT))));
	double t_1 = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / (exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (mu <= -2.8e+177) {
		tmp = t_0;
	} else if (mu <= -9e-232) {
		tmp = t_1;
	} else if (mu <= 3.9e-267) {
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) - (NaChar / (-1.0 - exp((((Vef + Ev) - mu) / KbT))));
	} else if (mu <= 6.5e+188) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / (exp((mu / kbt)) + 1.0d0)) - (nachar / ((-1.0d0) - exp((mu / -kbt))))
    t_1 = (nachar / (exp(((vef - (mu - (ev + eaccept))) / kbt)) + 1.0d0)) + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    if (mu <= (-2.8d+177)) then
        tmp = t_0
    else if (mu <= (-9d-232)) then
        tmp = t_1
    else if (mu <= 3.9d-267) then
        tmp = (ndchar / (exp((ec / -kbt)) + 1.0d0)) - (nachar / ((-1.0d0) - exp((((vef + ev) - mu) / kbt))))
    else if (mu <= 6.5d+188) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (Math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - Math.exp((mu / -KbT))));
	double t_1 = (NaChar / (Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	double tmp;
	if (mu <= -2.8e+177) {
		tmp = t_0;
	} else if (mu <= -9e-232) {
		tmp = t_1;
	} else if (mu <= 3.9e-267) {
		tmp = (NdChar / (Math.exp((Ec / -KbT)) + 1.0)) - (NaChar / (-1.0 - Math.exp((((Vef + Ev) - mu) / KbT))));
	} else if (mu <= 6.5e+188) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - math.exp((mu / -KbT))))
	t_1 = (NaChar / (math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	tmp = 0
	if mu <= -2.8e+177:
		tmp = t_0
	elif mu <= -9e-232:
		tmp = t_1
	elif mu <= 3.9e-267:
		tmp = (NdChar / (math.exp((Ec / -KbT)) + 1.0)) - (NaChar / (-1.0 - math.exp((((Vef + Ev) - mu) / KbT))))
	elif mu <= 6.5e+188:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(mu / Float64(-KbT))))))
	t_1 = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)))
	tmp = 0.0
	if (mu <= -2.8e+177)
		tmp = t_0;
	elseif (mu <= -9e-232)
		tmp = t_1;
	elseif (mu <= 3.9e-267)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Ec / Float64(-KbT))) + 1.0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	elseif (mu <= 6.5e+188)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - exp((mu / -KbT))));
	t_1 = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / (exp((EDonor / KbT)) + 1.0));
	tmp = 0.0;
	if (mu <= -2.8e+177)
		tmp = t_0;
	elseif (mu <= -9e-232)
		tmp = t_1;
	elseif (mu <= 3.9e-267)
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) - (NaChar / (-1.0 - exp((((Vef + Ev) - mu) / KbT))));
	elseif (mu <= 6.5e+188)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -2.8e+177], t$95$0, If[LessEqual[mu, -9e-232], t$95$1, If[LessEqual[mu, 3.9e-267], N[(N[(NdChar / N[(N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 6.5e+188], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -2.80000000000000002e177 or 6.49999999999999953e188 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 95.2%

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

   6. Taylor expanded in mu around inf 88.5%

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

      1. associate-*r/ 52.0%

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

      2. mul-1-neg 52.0%

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

   8. Simplified 88.5%

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

   if -2.80000000000000002e177 < mu < -8.99999999999999933e-232 or 3.89999999999999977e-267 < mu < 6.49999999999999953e188

   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%

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

   5. Taylor expanded in EDonor around inf 82.6%

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

   if -8.99999999999999933e-232 < mu < 3.89999999999999977e-267

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Ec around inf 82.2%

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

      1. associate-*r/ 82.2%

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

      2. mul-1-neg 82.2%

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

   7. Simplified 82.2%

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

   8. Taylor expanded in EAccept around 0 71.4%

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

4. Final simplification 82.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -2.8 \cdot 10^{+177}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -9 \cdot 10^{-232}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;mu \leq 3.9 \cdot 10^{-267}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;mu \leq 6.5 \cdot 10^{+188}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 69.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}\\ t_1 := \frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{if}\;mu \leq -2.25 \cdot 10^{+141}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;mu \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} - \frac{NaChar}{-1 - t\_0}\\ \mathbf{elif}\;mu \leq 2.3 \cdot 10^{+128}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{t\_0 + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- (+ Vef Ev) mu) KbT)))
        (t_1
         (-
          (/ NdChar (+ (exp (/ mu KbT)) 1.0))
          (/ NaChar (- -1.0 (exp (/ mu (- KbT))))))))
   (if (<= mu -2.25e+141)
     t_1
     (if (<= mu -1e-308)
       (- (/ NdChar (+ (exp (/ Ec (- KbT))) 1.0)) (/ NaChar (- -1.0 t_0)))
       (if (<= mu 2.3e+128)
         (+ (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) (/ NaChar (+ t_0 1.0)))
         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 = exp((((Vef + Ev) - mu) / KbT));
	double t_1 = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - exp((mu / -KbT))));
	double tmp;
	if (mu <= -2.25e+141) {
		tmp = t_1;
	} else if (mu <= -1e-308) {
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	} else if (mu <= 2.3e+128) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (t_0 + 1.0));
	} 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 = exp((((vef + ev) - mu) / kbt))
    t_1 = (ndchar / (exp((mu / kbt)) + 1.0d0)) - (nachar / ((-1.0d0) - exp((mu / -kbt))))
    if (mu <= (-2.25d+141)) then
        tmp = t_1
    else if (mu <= (-1d-308)) then
        tmp = (ndchar / (exp((ec / -kbt)) + 1.0d0)) - (nachar / ((-1.0d0) - t_0))
    else if (mu <= 2.3d+128) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (t_0 + 1.0d0))
    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 = Math.exp((((Vef + Ev) - mu) / KbT));
	double t_1 = (NdChar / (Math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - Math.exp((mu / -KbT))));
	double tmp;
	if (mu <= -2.25e+141) {
		tmp = t_1;
	} else if (mu <= -1e-308) {
		tmp = (NdChar / (Math.exp((Ec / -KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	} else if (mu <= 2.3e+128) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (t_0 + 1.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp((((Vef + Ev) - mu) / KbT))
	t_1 = (NdChar / (math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - math.exp((mu / -KbT))))
	tmp = 0
	if mu <= -2.25e+141:
		tmp = t_1
	elif mu <= -1e-308:
		tmp = (NdChar / (math.exp((Ec / -KbT)) + 1.0)) - (NaChar / (-1.0 - t_0))
	elif mu <= 2.3e+128:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (t_0 + 1.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(mu / Float64(-KbT))))))
	tmp = 0.0
	if (mu <= -2.25e+141)
		tmp = t_1;
	elseif (mu <= -1e-308)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Ec / Float64(-KbT))) + 1.0)) - Float64(NaChar / Float64(-1.0 - t_0)));
	elseif (mu <= 2.3e+128)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(t_0 + 1.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp((((Vef + Ev) - mu) / KbT));
	t_1 = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - exp((mu / -KbT))));
	tmp = 0.0;
	if (mu <= -2.25e+141)
		tmp = t_1;
	elseif (mu <= -1e-308)
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	elseif (mu <= 2.3e+128)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (t_0 + 1.0));
	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[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -2.25e+141], t$95$1, If[LessEqual[mu, -1e-308], N[(N[(NdChar / N[(N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 2.3e+128], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 3 regimes

2. if mu < -2.2500000000000001e141 or 2.29999999999999998e128 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 90.7%

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

   6. Taylor expanded in mu around inf 81.2%

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

      1. associate-*r/ 49.8%

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

      2. mul-1-neg 49.8%

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

   8. Simplified 81.2%

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

   if -2.2500000000000001e141 < mu < -9.9999999999999991e-309

   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%

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

   5. Taylor expanded in Ec around inf 80.5%

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

      1. associate-*r/ 80.5%

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

      2. mul-1-neg 80.5%

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

   7. Simplified 80.5%

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

   8. Taylor expanded in EAccept around 0 71.3%

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

   if -9.9999999999999991e-309 < mu < 2.29999999999999998e128

   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%

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

   5. Taylor expanded in Vef around inf 78.7%

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

   6. Taylor expanded in EAccept around 0 72.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -2.25 \cdot 10^{+141}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \mathbf{elif}\;mu \leq -1 \cdot 10^{-308}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;mu \leq 2.3 \cdot 10^{+128}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{mu}{-KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 65.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ t_1 := \frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{if}\;NaChar \leq -6 \cdot 10^{-36}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{-187}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0))
          (/ NaChar (- (+ 2.0 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT)))))
        (t_1
         (+
          (/ NaChar (+ (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)) 1.0))
          (/ NdChar (+ (+ (/ (+ Vef (+ EDonor (- mu Ec))) KbT) 1.0) 1.0)))))
   (if (<= NaChar -6e-36)
     t_1
     (if (<= NaChar 1.9e-187)
       t_0
       (if (<= NaChar 1.8e-90)
         (+
          (/ NdChar (+ (exp (/ Vef KbT)) 1.0))
          (/ NaChar (+ (exp (/ mu (- KbT))) 1.0)))
         (if (<= NaChar 4.5e+21) t_0 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 = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / ((2.0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	double t_1 = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	double tmp;
	if (NaChar <= -6e-36) {
		tmp = t_1;
	} else if (NaChar <= 1.9e-187) {
		tmp = t_0;
	} else if (NaChar <= 1.8e-90) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((mu / -KbT)) + 1.0));
	} else if (NaChar <= 4.5e+21) {
		tmp = t_0;
	} 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 = (ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)) + (nachar / ((2.0d0 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    t_1 = (nachar / (exp(((vef - (mu - (ev + eaccept))) / kbt)) + 1.0d0)) + (ndchar / ((((vef + (edonor + (mu - ec))) / kbt) + 1.0d0) + 1.0d0))
    if (nachar <= (-6d-36)) then
        tmp = t_1
    else if (nachar <= 1.9d-187) then
        tmp = t_0
    else if (nachar <= 1.8d-90) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (exp((mu / -kbt)) + 1.0d0))
    else if (nachar <= 4.5d+21) then
        tmp = t_0
    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 = (NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / ((2.0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	double t_1 = (NaChar / (Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	double tmp;
	if (NaChar <= -6e-36) {
		tmp = t_1;
	} else if (NaChar <= 1.9e-187) {
		tmp = t_0;
	} else if (NaChar <= 1.8e-90) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (Math.exp((mu / -KbT)) + 1.0));
	} else if (NaChar <= 4.5e+21) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / ((2.0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	t_1 = (NaChar / (math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0))
	tmp = 0
	if NaChar <= -6e-36:
		tmp = t_1
	elif NaChar <= 1.9e-187:
		tmp = t_0
	elif NaChar <= 1.8e-90:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (math.exp((mu / -KbT)) + 1.0))
	elif NaChar <= 4.5e+21:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Float64(Float64(Vef + Float64(EDonor + Float64(mu - Ec))) / KbT) + 1.0) + 1.0)))
	tmp = 0.0
	if (NaChar <= -6e-36)
		tmp = t_1;
	elseif (NaChar <= 1.9e-187)
		tmp = t_0;
	elseif (NaChar <= 1.8e-90)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(mu / Float64(-KbT))) + 1.0)));
	elseif (NaChar <= 4.5e+21)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / ((2.0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	t_1 = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	tmp = 0.0;
	if (NaChar <= -6e-36)
		tmp = t_1;
	elseif (NaChar <= 1.9e-187)
		tmp = t_0;
	elseif (NaChar <= 1.8e-90)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((mu / -KbT)) + 1.0));
	elseif (NaChar <= 4.5e+21)
		tmp = t_0;
	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[(N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(Vef + N[(EDonor + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6e-36], t$95$1, If[LessEqual[NaChar, 1.9e-187], t$95$0, If[LessEqual[NaChar, 1.8e-90], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.5e+21], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -6.0000000000000003e-36 or 4.5e21 < 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%

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

   5. Taylor expanded in KbT around inf 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-+r+ 77.3%

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

      3. associate--l- 77.3%

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

      4. neg-mul-1 77.3%

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

      5. unsub-neg 77.3%

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

      6. associate--l- 77.3%

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

      7. +-commutative 77.3%

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

      8. associate--r+ 77.3%

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

      9. associate--r+ 77.3%

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

   7. Simplified 77.3%

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

   if -6.0000000000000003e-36 < NaChar < 1.90000000000000013e-187 or 1.7999999999999999e-90 < NaChar < 4.5e21

   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%

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

   5. Taylor expanded in KbT around inf 65.0%

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

   6. Taylor expanded in EAccept around 0 65.5%

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

   if 1.90000000000000013e-187 < NaChar < 1.7999999999999999e-90

   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%

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

   5. Taylor expanded in Vef around inf 88.0%

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

   6. Taylor expanded in mu around inf 76.0%

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

      1. associate-*r/ 76.0%

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

      2. mul-1-neg 76.0%

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

   8. Simplified 76.0%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6 \cdot 10^{-36}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{-187}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{mu}{-KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq 4.5 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 77.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}\\ \mathbf{if}\;EDonor \leq -8.5 \cdot 10^{-25} \lor \neg \left(EDonor \leq 1.6 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{NaChar}{t\_0 + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} - \frac{NaChar}{-1 - t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT))))
   (if (or (<= EDonor -8.5e-25) (not (<= EDonor 1.6e+88)))
     (+ (/ NaChar (+ t_0 1.0)) (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)))
     (- (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) (/ NaChar (- -1.0 t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((Vef - (mu - (Ev + EAccept))) / KbT));
	double tmp;
	if ((EDonor <= -8.5e-25) || !(EDonor <= 1.6e+88)) {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (exp((EDonor / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(((vef - (mu - (ev + eaccept))) / kbt))
    if ((edonor <= (-8.5d-25)) .or. (.not. (edonor <= 1.6d+88))) then
        tmp = (nachar / (t_0 + 1.0d0)) + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    else
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) - (nachar / ((-1.0d0) - t_0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT));
	double tmp;
	if ((EDonor <= -8.5e-25) || !(EDonor <= 1.6e+88)) {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))
	tmp = 0
	if (EDonor <= -8.5e-25) or not (EDonor <= 1.6e+88):
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	else:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT))
	tmp = 0.0
	if ((EDonor <= -8.5e-25) || !(EDonor <= 1.6e+88))
		tmp = Float64(Float64(NaChar / Float64(t_0 + 1.0)) + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) - Float64(NaChar / Float64(-1.0 - t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((Vef - (mu - (Ev + EAccept))) / KbT));
	tmp = 0.0;
	if ((EDonor <= -8.5e-25) || ~((EDonor <= 1.6e+88)))
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (exp((EDonor / KbT)) + 1.0));
	else
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[EDonor, -8.5e-25], N[Not[LessEqual[EDonor, 1.6e+88]], $MachinePrecision]], N[(N[(NaChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -8.49999999999999981e-25 or 1.5999999999999999e88 < EDonor

   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%

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

   5. Taylor expanded in EDonor around inf 84.5%

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

   if -8.49999999999999981e-25 < EDonor < 1.5999999999999999e88

   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%

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

   5. Taylor expanded in Vef around inf 79.1%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -8.5 \cdot 10^{-25} \lor \neg \left(EDonor \leq 1.6 \cdot 10^{+88}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 77.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}\\ \mathbf{if}\;EDonor \leq -5.8 \cdot 10^{+64} \lor \neg \left(EDonor \leq 5.5 \cdot 10^{+165}\right):\\ \;\;\;\;\frac{NaChar}{t\_0 + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT))))
   (if (or (<= EDonor -5.8e+64) (not (<= EDonor 5.5e+165)))
     (+ (/ NaChar (+ t_0 1.0)) (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)))
     (- (/ NdChar (+ (exp (/ mu KbT)) 1.0)) (/ NaChar (- -1.0 t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((Vef - (mu - (Ev + EAccept))) / KbT));
	double tmp;
	if ((EDonor <= -5.8e+64) || !(EDonor <= 5.5e+165)) {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (exp((EDonor / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(((vef - (mu - (ev + eaccept))) / kbt))
    if ((edonor <= (-5.8d+64)) .or. (.not. (edonor <= 5.5d+165))) then
        tmp = (nachar / (t_0 + 1.0d0)) + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    else
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) - (nachar / ((-1.0d0) - t_0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT));
	double tmp;
	if ((EDonor <= -5.8e+64) || !(EDonor <= 5.5e+165)) {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))
	tmp = 0
	if (EDonor <= -5.8e+64) or not (EDonor <= 5.5e+165):
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	else:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT))
	tmp = 0.0
	if ((EDonor <= -5.8e+64) || !(EDonor <= 5.5e+165))
		tmp = Float64(Float64(NaChar / Float64(t_0 + 1.0)) + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) - Float64(NaChar / Float64(-1.0 - t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((Vef - (mu - (Ev + EAccept))) / KbT));
	tmp = 0.0;
	if ((EDonor <= -5.8e+64) || ~((EDonor <= 5.5e+165)))
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / (exp((EDonor / KbT)) + 1.0));
	else
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) - (NaChar / (-1.0 - t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[Or[LessEqual[EDonor, -5.8e+64], N[Not[LessEqual[EDonor, 5.5e+165]], $MachinePrecision]], N[(N[(NaChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -5.79999999999999986e64 or 5.4999999999999998e165 < EDonor

   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%

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

   5. Taylor expanded in EDonor around inf 89.6%

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

   if -5.79999999999999986e64 < EDonor < 5.4999999999999998e165

   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%

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

   5. Taylor expanded in mu around inf 79.4%

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

4. Final simplification 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -5.8 \cdot 10^{+64} \lor \neg \left(EDonor \leq 5.5 \cdot 10^{+165}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 64.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 10^{-10}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 5.6 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 1e-10)
   (+
    (/ NdChar (+ (exp (/ Vef KbT)) 1.0))
    (/ NaChar (+ (exp (/ (- (+ Vef Ev) mu) KbT)) 1.0)))
   (if (<= EAccept 5.6e+126)
     (+
      (/ NaChar (+ (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)) 1.0))
      (/ NdChar (+ (+ (/ (+ Vef (+ EDonor (- mu Ec))) KbT) 1.0) 1.0)))
     (+
      (/ NdChar (+ (exp (/ mu KbT)) 1.0))
      (/ NaChar (+ (exp (/ EAccept KbT)) 1.0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 1e-10) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else if (EAccept <= 5.6e+126) {
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / (exp((EAccept / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= 1d-10) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (exp((((vef + ev) - mu) / kbt)) + 1.0d0))
    else if (eaccept <= 5.6d+126) then
        tmp = (nachar / (exp(((vef - (mu - (ev + eaccept))) / kbt)) + 1.0d0)) + (ndchar / ((((vef + (edonor + (mu - ec))) / kbt) + 1.0d0) + 1.0d0))
    else
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + (nachar / (exp((eaccept / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 1e-10) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (Math.exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	} else if (EAccept <= 5.6e+126) {
		tmp = (NaChar / (Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + (NaChar / (Math.exp((EAccept / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 1e-10:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (math.exp((((Vef + Ev) - mu) / KbT)) + 1.0))
	elif EAccept <= 5.6e+126:
		tmp = (NaChar / (math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0))
	else:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + (NaChar / (math.exp((EAccept / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 1e-10)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)) + 1.0)));
	elseif (EAccept <= 5.6e+126)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Float64(Float64(Vef + Float64(EDonor + Float64(mu - Ec))) / KbT) + 1.0) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 1e-10)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + Ev) - mu) / KbT)) + 1.0));
	elseif (EAccept <= 5.6e+126)
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	else
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + (NaChar / (exp((EAccept / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 1e-10], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 5.6e+126], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(Vef + N[(EDonor + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 1.00000000000000004e-10

   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%

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

   5. Taylor expanded in Vef around inf 71.3%

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

   6. Taylor expanded in EAccept around 0 67.8%

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

   if 1.00000000000000004e-10 < EAccept < 5.60000000000000018e126

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 60.0%

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

      1. +-commutative 60.0%

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

      2. associate-+r+ 60.0%

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

      3. associate--l- 60.0%

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

      4. neg-mul-1 60.0%

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

      5. unsub-neg 60.0%

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

      6. associate--l- 60.0%

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

      7. +-commutative 60.0%

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

      8. associate--r+ 60.0%

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

      9. associate--r+ 60.0%

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

   7. Simplified 60.0%

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

   if 5.60000000000000018e126 < 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%

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

   5. Taylor expanded in mu around inf 71.8%

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

   6. Taylor expanded in EAccept around inf 71.8%

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

4. Final simplification 67.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 10^{-10}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + Ev\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;EAccept \leq 5.6 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -4.8 \cdot 10^{-35} \lor \neg \left(NaChar \leq 4.9 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -4.8e-35) (not (<= NaChar 4.9e+23)))
   (+
    (/ NaChar (+ (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)) 1.0))
    (/ NdChar (+ (+ (/ (+ Vef (+ EDonor (- mu Ec))) KbT) 1.0) 1.0)))
   (-
    (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0))
    (/
     NaChar
     (+
      -1.0
      (+
       (/ mu KbT)
       (- -1.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -4.8e-35) || !(NaChar <= 4.9e+23)) {
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else {
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-4.8d-35)) .or. (.not. (nachar <= 4.9d+23))) then
        tmp = (nachar / (exp(((vef - (mu - (ev + eaccept))) / kbt)) + 1.0d0)) + (ndchar / ((((vef + (edonor + (mu - ec))) / kbt) + 1.0d0) + 1.0d0))
    else
        tmp = (ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)) - (nachar / ((-1.0d0) + ((mu / kbt) + ((-1.0d0) - ((eaccept / kbt) + ((vef / kbt) + (ev / kbt)))))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -4.8e-35) || !(NaChar <= 4.9e+23)) {
		tmp = (NaChar / (Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -4.8e-35) or not (NaChar <= 4.9e+23):
		tmp = (NaChar / (math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0))
	else:
		tmp = (NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -4.8e-35) || !(NaChar <= 4.9e+23))
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Float64(Float64(Vef + Float64(EDonor + Float64(mu - Ec))) / KbT) + 1.0) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0)) - Float64(NaChar / Float64(-1.0 + Float64(Float64(mu / KbT) + Float64(-1.0 - Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))))))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -4.8e-35) || ~((NaChar <= 4.9e+23)))
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	else
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) - (NaChar / (-1.0 + ((mu / KbT) + (-1.0 - ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT)))))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -4.8e-35], N[Not[LessEqual[NaChar, 4.9e+23]], $MachinePrecision]], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(Vef + N[(EDonor + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 + N[(N[(mu / KbT), $MachinePrecision] + N[(-1.0 - N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.8000000000000003e-35 or 4.9000000000000003e23 < 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%

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

   5. Taylor expanded in KbT around inf 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-+r+ 77.3%

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

      3. associate--l- 77.3%

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

      4. neg-mul-1 77.3%

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

      5. unsub-neg 77.3%

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

      6. associate--l- 77.3%

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

      7. +-commutative 77.3%

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

      8. associate--r+ 77.3%

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

      9. associate--r+ 77.3%

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

   7. Simplified 77.3%

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

   if -4.8000000000000003e-35 < NaChar < 4.9000000000000003e23

   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%

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

   5. Taylor expanded in KbT around inf 63.3%

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

4. Final simplification 70.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.8 \cdot 10^{-35} \lor \neg \left(NaChar \leq 4.9 \cdot 10^{+23}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} - \frac{NaChar}{-1 + \left(\frac{mu}{KbT} + \left(-1 - \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 53.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1}\\ t_1 := t\_0 + KbT \cdot \frac{NaChar}{Vef}\\ t_2 := \frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -5.1 \cdot 10^{-175}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -1.05 \cdot 10^{-199}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NaChar \leq -4.5 \cdot 10^{-246}:\\ \;\;\;\;t\_0 + NaChar \cdot \frac{KbT}{EAccept}\\ \mathbf{elif}\;NaChar \leq 2.65 \cdot 10^{-76}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0)))
        (t_1 (+ t_0 (* KbT (/ NaChar Vef))))
        (t_2
         (-
          (/ NdChar 2.0)
          (/ NaChar (- -1.0 (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)))))))
   (if (<= NaChar -1e-68)
     t_2
     (if (<= NaChar -5.1e-175)
       t_1
       (if (<= NaChar -1.05e-199)
         t_2
         (if (<= NaChar -4.5e-246)
           (+ t_0 (* NaChar (/ KbT EAccept)))
           (if (<= NaChar 2.65e-76) t_1 t_2)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0);
	double t_1 = t_0 + (KbT * (NaChar / Vef));
	double t_2 = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	double tmp;
	if (NaChar <= -1e-68) {
		tmp = t_2;
	} else if (NaChar <= -5.1e-175) {
		tmp = t_1;
	} else if (NaChar <= -1.05e-199) {
		tmp = t_2;
	} else if (NaChar <= -4.5e-246) {
		tmp = t_0 + (NaChar * (KbT / EAccept));
	} else if (NaChar <= 2.65e-76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)
    t_1 = t_0 + (kbt * (nachar / vef))
    t_2 = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef - (mu - (ev + eaccept))) / kbt))))
    if (nachar <= (-1d-68)) then
        tmp = t_2
    else if (nachar <= (-5.1d-175)) then
        tmp = t_1
    else if (nachar <= (-1.05d-199)) then
        tmp = t_2
    else if (nachar <= (-4.5d-246)) then
        tmp = t_0 + (nachar * (kbt / eaccept))
    else if (nachar <= 2.65d-76) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0);
	double t_1 = t_0 + (KbT * (NaChar / Vef));
	double t_2 = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	double tmp;
	if (NaChar <= -1e-68) {
		tmp = t_2;
	} else if (NaChar <= -5.1e-175) {
		tmp = t_1;
	} else if (NaChar <= -1.05e-199) {
		tmp = t_2;
	} else if (NaChar <= -4.5e-246) {
		tmp = t_0 + (NaChar * (KbT / EAccept));
	} else if (NaChar <= 2.65e-76) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)
	t_1 = t_0 + (KbT * (NaChar / Vef))
	t_2 = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))))
	tmp = 0
	if NaChar <= -1e-68:
		tmp = t_2
	elif NaChar <= -5.1e-175:
		tmp = t_1
	elif NaChar <= -1.05e-199:
		tmp = t_2
	elif NaChar <= -4.5e-246:
		tmp = t_0 + (NaChar * (KbT / EAccept))
	elif NaChar <= 2.65e-76:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0))
	t_1 = Float64(t_0 + Float64(KbT * Float64(NaChar / Vef)))
	t_2 = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)))))
	tmp = 0.0
	if (NaChar <= -1e-68)
		tmp = t_2;
	elseif (NaChar <= -5.1e-175)
		tmp = t_1;
	elseif (NaChar <= -1.05e-199)
		tmp = t_2;
	elseif (NaChar <= -4.5e-246)
		tmp = Float64(t_0 + Float64(NaChar * Float64(KbT / EAccept)));
	elseif (NaChar <= 2.65e-76)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0);
	t_1 = t_0 + (KbT * (NaChar / Vef));
	t_2 = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	tmp = 0.0;
	if (NaChar <= -1e-68)
		tmp = t_2;
	elseif (NaChar <= -5.1e-175)
		tmp = t_1;
	elseif (NaChar <= -1.05e-199)
		tmp = t_2;
	elseif (NaChar <= -4.5e-246)
		tmp = t_0 + (NaChar * (KbT / EAccept));
	elseif (NaChar <= 2.65e-76)
		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[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(KbT * N[(NaChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1e-68], t$95$2, If[LessEqual[NaChar, -5.1e-175], t$95$1, If[LessEqual[NaChar, -1.05e-199], t$95$2, If[LessEqual[NaChar, -4.5e-246], N[(t$95$0 + N[(NaChar * N[(KbT / EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.65e-76], t$95$1, t$95$2]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.00000000000000007e-68 or -5.10000000000000054e-175 < NaChar < -1.05000000000000001e-199 or 2.65e-76 < 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%

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

   5. Taylor expanded in mu around inf 80.9%

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

   6. Taylor expanded in mu around 0 58.9%

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

   if -1.00000000000000007e-68 < NaChar < -5.10000000000000054e-175 or -4.49999999999999999e-246 < NaChar < 2.65e-76

   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%

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

   5. Taylor expanded in KbT around inf 66.0%

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

   6. Taylor expanded in Vef around inf 54.4%

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

      1. associate-/l* 55.1%

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

   8. Simplified 55.1%

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

   if -1.05000000000000001e-199 < NaChar < -4.49999999999999999e-246

   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%

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

   5. Taylor expanded in KbT around inf 76.4%

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

   6. Taylor expanded in EAccept around inf 63.9%

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

      1. *-commutative 63.9%

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

      2. associate-/l* 63.8%

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

   8. Applied egg-rr 63.8%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1 \cdot 10^{-68}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -5.1 \cdot 10^{-175}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + KbT \cdot \frac{NaChar}{Vef}\\ \mathbf{elif}\;NaChar \leq -1.05 \cdot 10^{-199}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -4.5 \cdot 10^{-246}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + NaChar \cdot \frac{KbT}{EAccept}\\ \mathbf{elif}\;NaChar \leq 2.65 \cdot 10^{-76}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + KbT \cdot \frac{NaChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.7% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1}\\ t_1 := \frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1}\\ t_2 := t\_1 + \frac{NaChar}{2}\\ \mathbf{if}\;NdChar \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;NdChar \leq -5.1 \cdot 10^{-166}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 6.8 \cdot 10^{-23}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(1 - \frac{Ec}{KbT}\right) + 1}\\ \mathbf{elif}\;NdChar \leq 46000000:\\ \;\;\;\;t\_1 + KbT \cdot \frac{NaChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)) 1.0)))
        (t_1 (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0)))
        (t_2 (+ t_1 (/ NaChar 2.0))))
   (if (<= NdChar -4.5e+24)
     t_2
     (if (<= NdChar -5.1e-166)
       (+ t_0 (/ NdChar (+ (/ Vef KbT) 2.0)))
       (if (<= NdChar 6.8e-23)
         (+ t_0 (/ NdChar (+ (- 1.0 (/ Ec KbT)) 1.0)))
         (if (<= NdChar 46000000.0) (+ t_1 (* KbT (/ NaChar Vef))) 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 / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0);
	double t_1 = NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0);
	double t_2 = t_1 + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -4.5e+24) {
		tmp = t_2;
	} else if (NdChar <= -5.1e-166) {
		tmp = t_0 + (NdChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= 6.8e-23) {
		tmp = t_0 + (NdChar / ((1.0 - (Ec / KbT)) + 1.0));
	} else if (NdChar <= 46000000.0) {
		tmp = t_1 + (KbT * (NaChar / Vef));
	} 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 / (exp(((vef - (mu - (ev + eaccept))) / kbt)) + 1.0d0)
    t_1 = ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)
    t_2 = t_1 + (nachar / 2.0d0)
    if (ndchar <= (-4.5d+24)) then
        tmp = t_2
    else if (ndchar <= (-5.1d-166)) then
        tmp = t_0 + (ndchar / ((vef / kbt) + 2.0d0))
    else if (ndchar <= 6.8d-23) then
        tmp = t_0 + (ndchar / ((1.0d0 - (ec / kbt)) + 1.0d0))
    else if (ndchar <= 46000000.0d0) then
        tmp = t_1 + (kbt * (nachar / vef))
    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 / (Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0);
	double t_1 = NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0);
	double t_2 = t_1 + (NaChar / 2.0);
	double tmp;
	if (NdChar <= -4.5e+24) {
		tmp = t_2;
	} else if (NdChar <= -5.1e-166) {
		tmp = t_0 + (NdChar / ((Vef / KbT) + 2.0));
	} else if (NdChar <= 6.8e-23) {
		tmp = t_0 + (NdChar / ((1.0 - (Ec / KbT)) + 1.0));
	} else if (NdChar <= 46000000.0) {
		tmp = t_1 + (KbT * (NaChar / Vef));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)
	t_1 = NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)
	t_2 = t_1 + (NaChar / 2.0)
	tmp = 0
	if NdChar <= -4.5e+24:
		tmp = t_2
	elif NdChar <= -5.1e-166:
		tmp = t_0 + (NdChar / ((Vef / KbT) + 2.0))
	elif NdChar <= 6.8e-23:
		tmp = t_0 + (NdChar / ((1.0 - (Ec / KbT)) + 1.0))
	elif NdChar <= 46000000.0:
		tmp = t_1 + (KbT * (NaChar / Vef))
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)) + 1.0))
	t_1 = Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0))
	t_2 = Float64(t_1 + Float64(NaChar / 2.0))
	tmp = 0.0
	if (NdChar <= -4.5e+24)
		tmp = t_2;
	elseif (NdChar <= -5.1e-166)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(Vef / KbT) + 2.0)));
	elseif (NdChar <= 6.8e-23)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(1.0 - Float64(Ec / KbT)) + 1.0)));
	elseif (NdChar <= 46000000.0)
		tmp = Float64(t_1 + Float64(KbT * Float64(NaChar / Vef)));
	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 / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0);
	t_1 = NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0);
	t_2 = t_1 + (NaChar / 2.0);
	tmp = 0.0;
	if (NdChar <= -4.5e+24)
		tmp = t_2;
	elseif (NdChar <= -5.1e-166)
		tmp = t_0 + (NdChar / ((Vef / KbT) + 2.0));
	elseif (NdChar <= 6.8e-23)
		tmp = t_0 + (NdChar / ((1.0 - (Ec / KbT)) + 1.0));
	elseif (NdChar <= 46000000.0)
		tmp = t_1 + (KbT * (NaChar / Vef));
	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[(N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -4.5e+24], t$95$2, If[LessEqual[NdChar, -5.1e-166], N[(t$95$0 + N[(NdChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 6.8e-23], N[(t$95$0 + N[(NdChar / N[(N[(1.0 - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 46000000.0], N[(t$95$1 + N[(KbT * N[(NaChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NdChar < -4.50000000000000019e24 or 4.6e7 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 56.5%

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

   if -4.50000000000000019e24 < NdChar < -5.1000000000000002e-166

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 79.2%

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

   6. Taylor expanded in Vef around 0 71.8%

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

      1. +-commutative 43.6%

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

   8. Simplified 71.8%

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

   if -5.1000000000000002e-166 < NdChar < 6.8000000000000001e-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%

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

   5. Taylor expanded in Ec around inf 83.7%

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

      1. associate-*r/ 83.7%

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

      2. mul-1-neg 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in Ec around 0 74.4%

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

      1. neg-mul-1 74.4%

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

      2. unsub-neg 74.4%

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

   10. Simplified 74.4%

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

   if 6.8000000000000001e-23 < NdChar < 4.6e7

   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%

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

   5. Taylor expanded in KbT around inf 67.2%

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

   6. Taylor expanded in Vef around inf 83.8%

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

      1. associate-/l* 83.8%

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

   8. Simplified 83.8%

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

4. Final simplification 65.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq -5.1 \cdot 10^{-166}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 6.8 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(1 - \frac{Ec}{KbT}\right) + 1}\\ \mathbf{elif}\;NdChar \leq 46000000:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + KbT \cdot \frac{NaChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 65.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -4 \cdot 10^{-35} \lor \neg \left(NaChar \leq 4.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{\left(EAccept + \left(Vef + Ev\right)\right) - mu}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -4e-35) (not (<= NaChar 4.8e-15)))
   (+
    (/ NaChar (+ (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)) 1.0))
    (/ NdChar (+ (+ (/ (+ Vef (+ EDonor (- mu Ec))) KbT) 1.0) 1.0)))
   (+
    (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0))
    (/ (* KbT NaChar) (- (+ EAccept (+ Vef Ev)) mu)))))

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 <= -4e-35) || !(NaChar <= 4.8e-15)) {
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else {
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu));
	}
	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 <= (-4d-35)) .or. (.not. (nachar <= 4.8d-15))) then
        tmp = (nachar / (exp(((vef - (mu - (ev + eaccept))) / kbt)) + 1.0d0)) + (ndchar / ((((vef + (edonor + (mu - ec))) / kbt) + 1.0d0) + 1.0d0))
    else
        tmp = (ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)) + ((kbt * nachar) / ((eaccept + (vef + ev)) - mu))
    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 <= -4e-35) || !(NaChar <= 4.8e-15)) {
		tmp = (NaChar / (Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -4e-35) or not (NaChar <= 4.8e-15):
		tmp = (NaChar / (math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0))
	else:
		tmp = (NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -4e-35) || !(NaChar <= 4.8e-15))
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Float64(Float64(Vef + Float64(EDonor + Float64(mu - Ec))) / KbT) + 1.0) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0)) + Float64(Float64(KbT * NaChar) / Float64(Float64(EAccept + Float64(Vef + Ev)) - mu)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -4e-35) || ~((NaChar <= 4.8e-15)))
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	else
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -4e-35], N[Not[LessEqual[NaChar, 4.8e-15]], $MachinePrecision]], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(Vef + N[(EDonor + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.00000000000000003e-35 or 4.7999999999999999e-15 < 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%

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

   5. Taylor expanded in KbT around inf 75.6%

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

      1. +-commutative 75.6%

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

      2. associate-+r+ 75.6%

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

      3. associate--l- 75.6%

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

      4. neg-mul-1 75.6%

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

      5. unsub-neg 75.6%

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

      6. associate--l- 75.6%

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

      7. +-commutative 75.6%

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

      8. associate--r+ 75.6%

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

      9. associate--r+ 75.6%

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

   7. Simplified 75.6%

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

   if -4.00000000000000003e-35 < NaChar < 4.7999999999999999e-15

   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%

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

   5. Taylor expanded in KbT around inf 63.6%

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

   6. Taylor expanded in KbT around 0 63.3%

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

4. Final simplification 69.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4 \cdot 10^{-35} \lor \neg \left(NaChar \leq 4.8 \cdot 10^{-15}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{\left(EAccept + \left(Vef + Ev\right)\right) - mu}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 66.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -6 \cdot 10^{-36} \lor \neg \left(NaChar \leq 1.65 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -6e-36) (not (<= NaChar 1.65e+22)))
   (+
    (/ NaChar (+ (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)) 1.0))
    (/ NdChar (+ (+ (/ (+ Vef (+ EDonor (- mu Ec))) KbT) 1.0) 1.0)))
   (+
    (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0))
    (/ NaChar (- (+ 2.0 (+ (/ Vef KbT) (/ Ev KbT))) (/ mu KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -6e-36) || !(NaChar <= 1.65e+22)) {
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else {
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / ((2.0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-6d-36)) .or. (.not. (nachar <= 1.65d+22))) then
        tmp = (nachar / (exp(((vef - (mu - (ev + eaccept))) / kbt)) + 1.0d0)) + (ndchar / ((((vef + (edonor + (mu - ec))) / kbt) + 1.0d0) + 1.0d0))
    else
        tmp = (ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)) + (nachar / ((2.0d0 + ((vef / kbt) + (ev / kbt))) - (mu / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -6e-36) || !(NaChar <= 1.65e+22)) {
		tmp = (NaChar / (Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	} else {
		tmp = (NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / ((2.0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -6e-36) or not (NaChar <= 1.65e+22):
		tmp = (NaChar / (math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0))
	else:
		tmp = (NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / ((2.0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -6e-36) || !(NaChar <= 1.65e+22))
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Float64(Float64(Vef + Float64(EDonor + Float64(mu - Ec))) / KbT) + 1.0) + 1.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(Vef / KbT) + Float64(Ev / KbT))) - Float64(mu / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -6e-36) || ~((NaChar <= 1.65e+22)))
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((((Vef + (EDonor + (mu - Ec))) / KbT) + 1.0) + 1.0));
	else
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / ((2.0 + ((Vef / KbT) + (Ev / KbT))) - (mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -6e-36], N[Not[LessEqual[NaChar, 1.65e+22]], $MachinePrecision]], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(N[(Vef + N[(EDonor + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision] + 1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -6.0000000000000003e-36 or 1.6499999999999999e22 < 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%

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

   5. Taylor expanded in KbT around inf 77.3%

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

      1. +-commutative 77.3%

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

      2. associate-+r+ 77.3%

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

      3. associate--l- 77.3%

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

      4. neg-mul-1 77.3%

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

      5. unsub-neg 77.3%

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

      6. associate--l- 77.3%

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

      7. +-commutative 77.3%

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

      8. associate--r+ 77.3%

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

      9. associate--r+ 77.3%

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

   7. Simplified 77.3%

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

   if -6.0000000000000003e-36 < NaChar < 1.6499999999999999e22

   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%

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

   5. Taylor expanded in KbT around inf 63.3%

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

   6. Taylor expanded in EAccept around 0 63.0%

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

4. Final simplification 70.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6 \cdot 10^{-36} \lor \neg \left(NaChar \leq 1.65 \cdot 10^{+22}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\left(\frac{Vef + \left(EDonor + \left(mu - Ec\right)\right)}{KbT} + 1\right) + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{\left(2 + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 61.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}\\ \mathbf{if}\;NaChar \leq -1.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT} + 2} - \frac{NaChar}{-1 - t\_0}\\ \mathbf{elif}\;NaChar \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{\left(EAccept + \left(Vef + Ev\right)\right) - mu}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t\_0 + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT))))
   (if (<= NaChar -1.3e-35)
     (- (/ NdChar (+ (/ mu KbT) 2.0)) (/ NaChar (- -1.0 t_0)))
     (if (<= NaChar 4.4e+21)
       (+
        (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0))
        (/ (* KbT NaChar) (- (+ EAccept (+ Vef Ev)) mu)))
       (+ (/ NaChar (+ t_0 1.0)) (/ NdChar (+ (/ Vef KbT) 2.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((Vef - (mu - (Ev + EAccept))) / KbT));
	double tmp;
	if (NaChar <= -1.3e-35) {
		tmp = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - t_0));
	} else if (NaChar <= 4.4e+21) {
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu));
	} else {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(((vef - (mu - (ev + eaccept))) / kbt))
    if (nachar <= (-1.3d-35)) then
        tmp = (ndchar / ((mu / kbt) + 2.0d0)) - (nachar / ((-1.0d0) - t_0))
    else if (nachar <= 4.4d+21) then
        tmp = (ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)) + ((kbt * nachar) / ((eaccept + (vef + ev)) - mu))
    else
        tmp = (nachar / (t_0 + 1.0d0)) + (ndchar / ((vef / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT));
	double tmp;
	if (NaChar <= -1.3e-35) {
		tmp = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - t_0));
	} else if (NaChar <= 4.4e+21) {
		tmp = (NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu));
	} else {
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))
	tmp = 0
	if NaChar <= -1.3e-35:
		tmp = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - t_0))
	elif NaChar <= 4.4e+21:
		tmp = (NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu))
	else:
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / ((Vef / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT))
	tmp = 0.0
	if (NaChar <= -1.3e-35)
		tmp = Float64(Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)) - Float64(NaChar / Float64(-1.0 - t_0)));
	elseif (NaChar <= 4.4e+21)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0)) + Float64(Float64(KbT * NaChar) / Float64(Float64(EAccept + Float64(Vef + Ev)) - mu)));
	else
		tmp = Float64(Float64(NaChar / Float64(t_0 + 1.0)) + Float64(NdChar / Float64(Float64(Vef / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((Vef - (mu - (Ev + EAccept))) / KbT));
	tmp = 0.0;
	if (NaChar <= -1.3e-35)
		tmp = (NdChar / ((mu / KbT) + 2.0)) - (NaChar / (-1.0 - t_0));
	elseif (NaChar <= 4.4e+21)
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + ((KbT * NaChar) / ((EAccept + (Vef + Ev)) - mu));
	else
		tmp = (NaChar / (t_0 + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[NaChar, -1.3e-35], N[(N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.4e+21], N[(N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.30000000000000002e-35

   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%

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

   5. Taylor expanded in mu around inf 77.4%

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

   6. Taylor expanded in mu around 0 67.1%

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

      1. +-commutative 67.1%

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

   8. Simplified 67.1%

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

   if -1.30000000000000002e-35 < NaChar < 4.4e21

   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%

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

   5. Taylor expanded in KbT around inf 63.3%

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

   6. Taylor expanded in KbT around 0 62.2%

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

   if 4.4e21 < 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%

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

   5. Taylor expanded in Vef around inf 88.9%

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

   6. Taylor expanded in Vef around 0 84.0%

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

      1. +-commutative 54.6%

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

   8. Simplified 84.0%

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

4. Final simplification 67.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.3 \cdot 10^{-35}:\\ \;\;\;\;\frac{NdChar}{\frac{mu}{KbT} + 2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{KbT \cdot NaChar}{\left(EAccept + \left(Vef + Ev\right)\right) - mu}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 60.7% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -5 \cdot 10^{+24} \lor \neg \left(NdChar \leq 0.000215\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -5e+24) (not (<= NdChar 0.000215)))
   (+
    (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0))
    (/ NaChar 2.0))
   (+
    (/ NaChar (+ (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)) 1.0))
    (/ NdChar (+ (/ Vef 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 ((NdChar <= -5e+24) || !(NdChar <= 0.000215)) {
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((Vef / 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 ((ndchar <= (-5d+24)) .or. (.not. (ndchar <= 0.000215d0))) then
        tmp = (ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else
        tmp = (nachar / (exp(((vef - (mu - (ev + eaccept))) / kbt)) + 1.0d0)) + (ndchar / ((vef / 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 ((NdChar <= -5e+24) || !(NdChar <= 0.000215)) {
		tmp = (NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -5e+24) or not (NdChar <= 0.000215):
		tmp = (NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (math.exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -5e+24) || !(NdChar <= 0.000215))
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Vef / 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 ((NdChar <= -5e+24) || ~((NdChar <= 0.000215)))
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / 2.0);
	else
		tmp = (NaChar / (exp(((Vef - (mu - (Ev + EAccept))) / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -5e+24], N[Not[LessEqual[NdChar, 0.000215]], $MachinePrecision]], N[(N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -5.00000000000000045e24 or 2.14999999999999995e-4 < NdChar

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 55.7%

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

   if -5.00000000000000045e24 < NdChar < 2.14999999999999995e-4

   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%

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

   5. Taylor expanded in Vef around inf 79.9%

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

   6. Taylor expanded in Vef around 0 70.3%

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

      1. +-commutative 46.5%

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

   8. Simplified 70.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -5 \cdot 10^{+24} \lor \neg \left(NdChar \leq 0.000215\right):\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 53.5% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5.3 \cdot 10^{-66} \lor \neg \left(NaChar \leq 1.9 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + KbT \cdot \frac{NaChar}{Vef}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -5.3e-66) (not (<= NaChar 1.9e-77)))
   (-
    (/ NdChar 2.0)
    (/ NaChar (- -1.0 (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)))))
   (+
    (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0))
    (* KbT (/ NaChar Vef)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -5.3e-66) || !(NaChar <= 1.9e-77)) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	} else {
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (KbT * (NaChar / Vef));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-5.3d-66)) .or. (.not. (nachar <= 1.9d-77))) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef - (mu - (ev + eaccept))) / kbt))))
    else
        tmp = (ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)) + (kbt * (nachar / vef))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -5.3e-66) || !(NaChar <= 1.9e-77)) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	} else {
		tmp = (NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (KbT * (NaChar / Vef));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -5.3e-66) or not (NaChar <= 1.9e-77):
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))))
	else:
		tmp = (NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (KbT * (NaChar / Vef))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -5.3e-66) || !(NaChar <= 1.9e-77))
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0)) + Float64(KbT * Float64(NaChar / Vef)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -5.3e-66) || ~((NaChar <= 1.9e-77)))
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	else
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (KbT * (NaChar / Vef));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -5.3e-66], N[Not[LessEqual[NaChar, 1.9e-77]], $MachinePrecision]], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NaChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -5.3000000000000004e-66 or 1.8999999999999999e-77 < 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%

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

   5. Taylor expanded in mu around inf 80.3%

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

   6. Taylor expanded in mu around 0 58.3%

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

   if -5.3000000000000004e-66 < NaChar < 1.8999999999999999e-77

   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%

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

   5. Taylor expanded in KbT around inf 64.6%

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

   6. Taylor expanded in Vef around inf 52.8%

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

      1. associate-/l* 53.4%

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

   8. Simplified 53.4%

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

4. Final simplification 56.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.3 \cdot 10^{-66} \lor \neg \left(NaChar \leq 1.9 \cdot 10^{-77}\right):\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + KbT \cdot \frac{NaChar}{Vef}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 56.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.75 \cdot 10^{-55} \lor \neg \left(NaChar \leq 0.205\right):\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -1.75e-55) (not (<= NaChar 0.205)))
   (-
    (/ NdChar 2.0)
    (/ NaChar (- -1.0 (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)))))
   (+
    (/ NdChar (+ (exp (/ (- (+ Vef (+ EDonor mu)) Ec) KbT)) 1.0))
    (/ NaChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.75e-55) || !(NaChar <= 0.205)) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	} else {
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-1.75d-55)) .or. (.not. (nachar <= 0.205d0))) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef - (mu - (ev + eaccept))) / kbt))))
    else
        tmp = (ndchar / (exp((((vef + (edonor + mu)) - ec) / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -1.75e-55) || !(NaChar <= 0.205)) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	} else {
		tmp = (NdChar / (Math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -1.75e-55) or not (NaChar <= 0.205):
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))))
	else:
		tmp = (NdChar / (math.exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -1.75e-55) || !(NaChar <= 0.205))
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Float64(Float64(Vef + Float64(EDonor + mu)) - Ec) / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -1.75e-55) || ~((NaChar <= 0.205)))
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	else
		tmp = (NdChar / (exp((((Vef + (EDonor + mu)) - Ec) / KbT)) + 1.0)) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -1.75e-55], N[Not[LessEqual[NaChar, 0.205]], $MachinePrecision]], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(N[(N[(Vef + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -1.75000000000000013e-55 or 0.204999999999999988 < 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%

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

   5. Taylor expanded in mu around inf 79.9%

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

   6. Taylor expanded in mu around 0 61.3%

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

   if -1.75000000000000013e-55 < NaChar < 0.204999999999999988

   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%

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

   5. Taylor expanded in KbT around inf 58.3%

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

4. Final simplification 59.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.75 \cdot 10^{-55} \lor \neg \left(NaChar \leq 0.205\right):\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{\left(Vef + \left(EDonor + mu\right)\right) - Ec}{KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 49.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -3.3 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.16 \cdot 10^{+98}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar -3.3e+21)
   (+ (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) (/ NaChar (+ (/ Ev KbT) 2.0)))
   (if (<= NdChar 1.16e+98)
     (-
      (/ NdChar 2.0)
      (/ NaChar (- -1.0 (exp (/ (- Vef (- mu (+ Ev EAccept))) KbT)))))
     (+ (/ NdChar (+ (exp (/ Ec (- KbT))) 1.0)) (/ NaChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -3.3e+21) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= 1.16e+98) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	} else {
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ndchar <= (-3.3d+21)) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / ((ev / kbt) + 2.0d0))
    else if (ndchar <= 1.16d+98) then
        tmp = (ndchar / 2.0d0) - (nachar / ((-1.0d0) - exp(((vef - (mu - (ev + eaccept))) / kbt))))
    else
        tmp = (ndchar / (exp((ec / -kbt)) + 1.0d0)) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -3.3e+21) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (NdChar <= 1.16e+98) {
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - Math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	} else {
		tmp = (NdChar / (Math.exp((Ec / -KbT)) + 1.0)) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= -3.3e+21:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0))
	elif NdChar <= 1.16e+98:
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - math.exp(((Vef - (mu - (Ev + EAccept))) / KbT))))
	else:
		tmp = (NdChar / (math.exp((Ec / -KbT)) + 1.0)) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= -3.3e+21)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (NdChar <= 1.16e+98)
		tmp = Float64(Float64(NdChar / 2.0) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Vef - Float64(mu - Float64(Ev + EAccept))) / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Ec / Float64(-KbT))) + 1.0)) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= -3.3e+21)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	elseif (NdChar <= 1.16e+98)
		tmp = (NdChar / 2.0) - (NaChar / (-1.0 - exp(((Vef - (mu - (Ev + EAccept))) / KbT))));
	else
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, -3.3e+21], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.16e+98], N[(N[(NdChar / 2.0), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(Vef - N[(mu - N[(Ev + EAccept), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -3.3e21

   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%

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

   5. Taylor expanded in Vef around inf 60.2%

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

   6. Taylor expanded in Ev around inf 50.4%

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

   7. Taylor expanded in Ev around 0 45.2%

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

   if -3.3e21 < NdChar < 1.15999999999999995e98

   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%

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

   5. Taylor expanded in mu around inf 79.5%

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

   6. Taylor expanded in mu around 0 59.7%

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

   if 1.15999999999999995e98 < NdChar

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 53.6%

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

   6. Taylor expanded in Ec around inf 43.9%

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

      1. associate-*r/ 67.3%

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

      2. mul-1-neg 67.3%

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

   8. Simplified 43.9%

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

4. Final simplification 53.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -3.3 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.16 \cdot 10^{+98}:\\ \;\;\;\;\frac{NdChar}{2} - \frac{NaChar}{-1 - e^{\frac{Vef - \left(mu - \left(Ev + EAccept\right)\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 42.1% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{-55} \lor \neg \left(NaChar \leq 2.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -4.5e-55) (not (<= NaChar 2.2e-13)))
   (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (/ NdChar (+ (/ Vef KbT) 2.0)))
   (+ (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) (/ NaChar (+ (/ Ev KbT) 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -4.5e-55) || !(NaChar <= 2.2e-13)) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	} else {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-4.5d-55)) .or. (.not. (nachar <= 2.2d-13))) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar / ((vef / kbt) + 2.0d0))
    else
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (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 <= -4.5e-55) || !(NaChar <= 2.2e-13)) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	} else {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -4.5e-55) or not (NaChar <= 2.2e-13):
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0))
	else:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -4.5e-55) || !(NaChar <= 2.2e-13))
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar / Float64(Float64(Vef / KbT) + 2.0)));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -4.5e-55) || ~((NaChar <= 2.2e-13)))
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar / ((Vef / KbT) + 2.0));
	else
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (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, -4.5e-55], N[Not[LessEqual[NaChar, 2.2e-13]], $MachinePrecision]], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.4999999999999997e-55 or 2.19999999999999997e-13 < 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%

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

   5. Taylor expanded in Vef around inf 75.9%

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

   6. Taylor expanded in Ev around inf 48.7%

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

   7. Taylor expanded in Vef around 0 45.1%

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

      1. +-commutative 45.1%

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

   9. Simplified 45.1%

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

   if -4.4999999999999997e-55 < NaChar < 2.19999999999999997e-13

   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%

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

   5. Taylor expanded in Vef around inf 61.8%

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

   6. Taylor expanded in Ev around inf 47.7%

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

   7. Taylor expanded in Ev around 0 45.4%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{-55} \lor \neg \left(NaChar \leq 2.2 \cdot 10^{-13}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + \frac{NdChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 36.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq 8.4 \cdot 10^{-262}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.4 \cdot 10^{-79}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{KbT \cdot NaChar}{EAccept}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT 8.4e-262)
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 2.0))
   (if (<= KbT 1.4e-79)
     (+ (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) (/ (* KbT NaChar) EAccept))
     (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (* NdChar 0.5)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= 8.4e-262) {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (KbT <= 1.4e-79) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + ((KbT * NaChar) / EAccept);
	} else {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= 8.4d-262) then
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else if (kbt <= 1.4d-79) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + ((kbt * nachar) / eaccept)
    else
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= 8.4e-262) {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (KbT <= 1.4e-79) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + ((KbT * NaChar) / EAccept);
	} else {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= 8.4e-262:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	elif KbT <= 1.4e-79:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + ((KbT * NaChar) / EAccept)
	else:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= 8.4e-262)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	elseif (KbT <= 1.4e-79)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(Float64(KbT * NaChar) / EAccept));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= 8.4e-262)
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	elseif (KbT <= 1.4e-79)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + ((KbT * NaChar) / EAccept);
	else
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, 8.4e-262], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.4e-79], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / EAccept), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < 8.3999999999999998e-262

   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%

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

   5. Taylor expanded in Ec around inf 70.2%

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

      1. associate-*r/ 70.2%

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

      2. mul-1-neg 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in EAccept around inf 54.0%

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

   9. Taylor expanded in Ec around 0 37.3%

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

   if 8.3999999999999998e-262 < KbT < 1.40000000000000006e-79

   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%

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

   5. Taylor expanded in KbT around inf 31.2%

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

   6. Taylor expanded in EAccept around inf 47.0%

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

   7. Taylor expanded in Vef around inf 41.3%

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

   if 1.40000000000000006e-79 < KbT

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Vef around inf 76.9%

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

   6. Taylor expanded in Ev around inf 57.4%

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

   7. Taylor expanded in Vef around 0 48.5%

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

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 8.4 \cdot 10^{-262}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.4 \cdot 10^{-79}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{KbT \cdot NaChar}{EAccept}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 37.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq 2.2 \cdot 10^{-307}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.5 \cdot 10^{-72}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{KbT \cdot NaChar}{EAccept}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT 2.2e-307)
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 2.0))
   (if (<= KbT 1.5e-72)
     (+ (/ NdChar (+ (exp (/ mu KbT)) 1.0)) (/ (* KbT NaChar) EAccept))
     (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (* NdChar 0.5)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= 2.2e-307) {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (KbT <= 1.5e-72) {
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + ((KbT * NaChar) / EAccept);
	} else {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= 2.2d-307) then
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    else if (kbt <= 1.5d-72) then
        tmp = (ndchar / (exp((mu / kbt)) + 1.0d0)) + ((kbt * nachar) / eaccept)
    else
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar * 0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= 2.2e-307) {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	} else if (KbT <= 1.5e-72) {
		tmp = (NdChar / (Math.exp((mu / KbT)) + 1.0)) + ((KbT * NaChar) / EAccept);
	} else {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= 2.2e-307:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	elif KbT <= 1.5e-72:
		tmp = (NdChar / (math.exp((mu / KbT)) + 1.0)) + ((KbT * NaChar) / EAccept)
	else:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= 2.2e-307)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	elseif (KbT <= 1.5e-72)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(mu / KbT)) + 1.0)) + Float64(Float64(KbT * NaChar) / EAccept));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar * 0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= 2.2e-307)
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	elseif (KbT <= 1.5e-72)
		tmp = (NdChar / (exp((mu / KbT)) + 1.0)) + ((KbT * NaChar) / EAccept);
	else
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, 2.2e-307], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.5e-72], N[(N[(NdChar / N[(N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(N[(KbT * NaChar), $MachinePrecision] / EAccept), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < 2.2e-307

   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%

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

   5. Taylor expanded in Ec around inf 69.4%

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

      1. associate-*r/ 69.4%

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

      2. mul-1-neg 69.4%

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

   7. Simplified 69.4%

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

   8. Taylor expanded in EAccept around inf 52.7%

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

   9. Taylor expanded in Ec around 0 38.2%

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

   if 2.2e-307 < KbT < 1.5e-72

   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%

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

   5. Taylor expanded in KbT around inf 29.7%

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

   6. Taylor expanded in EAccept around inf 44.1%

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

   7. Taylor expanded in mu around inf 34.6%

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

   if 1.5e-72 < KbT

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in Vef around inf 78.7%

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

   6. Taylor expanded in Ev around inf 58.7%

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

   7. Taylor expanded in Vef around 0 49.6%

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

4. Final simplification 41.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq 2.2 \cdot 10^{-307}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.5 \cdot 10^{-72}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{mu}{KbT}} + 1} + \frac{KbT \cdot NaChar}{EAccept}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 40.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 3.65 \cdot 10^{-34}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar -4.5e+53)
   (+ (/ NdChar (+ (exp (/ EDonor KbT)) 1.0)) (/ NaChar 2.0))
   (if (<= NdChar 3.65e-34)
     (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (* NdChar 0.5))
     (+ (/ NdChar (+ (exp (/ Ec (- KbT))) 1.0)) (/ NaChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -4.5e+53) {
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	} else if (NdChar <= 3.65e-34) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) + (NaChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ndchar <= (-4.5d+53)) then
        tmp = (ndchar / (exp((edonor / kbt)) + 1.0d0)) + (nachar / 2.0d0)
    else if (ndchar <= 3.65d-34) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar * 0.5d0)
    else
        tmp = (ndchar / (exp((ec / -kbt)) + 1.0d0)) + (nachar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -4.5e+53) {
		tmp = (NdChar / (Math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	} else if (NdChar <= 3.65e-34) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	} else {
		tmp = (NdChar / (Math.exp((Ec / -KbT)) + 1.0)) + (NaChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= -4.5e+53:
		tmp = (NdChar / (math.exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0)
	elif NdChar <= 3.65e-34:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5)
	else:
		tmp = (NdChar / (math.exp((Ec / -KbT)) + 1.0)) + (NaChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= -4.5e+53)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)) + Float64(NaChar / 2.0));
	elseif (NdChar <= 3.65e-34)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Ec / Float64(-KbT))) + 1.0)) + Float64(NaChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= -4.5e+53)
		tmp = (NdChar / (exp((EDonor / KbT)) + 1.0)) + (NaChar / 2.0);
	elseif (NdChar <= 3.65e-34)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	else
		tmp = (NdChar / (exp((Ec / -KbT)) + 1.0)) + (NaChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, -4.5e+53], N[(N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 3.65e-34], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(Ec / (-KbT)), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -4.5000000000000002e53

   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%

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

   5. Taylor expanded in KbT around inf 56.4%

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

   6. Taylor expanded in EDonor around inf 46.4%

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

   if -4.5000000000000002e53 < NdChar < 3.64999999999999998e-34

   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%

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

   5. Taylor expanded in Vef around inf 78.9%

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

   6. Taylor expanded in Ev around inf 51.9%

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

   7. Taylor expanded in Vef around 0 42.2%

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

   if 3.64999999999999998e-34 < NdChar

   1. Initial program 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in KbT around inf 53.6%

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

   6. Taylor expanded in Ec around inf 41.4%

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

      1. associate-*r/ 67.3%

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

      2. mul-1-neg 67.3%

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

   8. Simplified 41.4%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.5 \cdot 10^{+53}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} + \frac{NaChar}{2}\\ \mathbf{elif}\;NdChar \leq 3.65 \cdot 10^{-34}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Ec}{-KbT}} + 1} + \frac{NaChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 39.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 4.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 5.2 \cdot 10^{+119}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 4.2e-185)
   (+ (/ NdChar (+ (exp (/ Vef KbT)) 1.0)) (/ NaChar (+ (/ Ev KbT) 2.0)))
   (if (<= EAccept 5.2e+119)
     (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (* NdChar 0.5))
     (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 4.2e-185) {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (EAccept <= 5.2e+119) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= 4.2d-185) then
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / ((ev / kbt) + 2.0d0))
    else if (eaccept <= 5.2d+119) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar * 0.5d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 4.2e-185) {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	} else if (EAccept <= 5.2e+119) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 4.2e-185:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0))
	elif EAccept <= 5.2e+119:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 4.2e-185)
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(Float64(Ev / KbT) + 2.0)));
	elseif (EAccept <= 5.2e+119)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 4.2e-185)
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / ((Ev / KbT) + 2.0));
	elseif (EAccept <= 5.2e+119)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 4.2e-185], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Ev / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 5.2e+119], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < 4.2e-185

   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%

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

   5. Taylor expanded in Vef around inf 71.6%

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

   6. Taylor expanded in Ev around inf 50.6%

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

   7. Taylor expanded in Ev around 0 43.4%

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

   if 4.2e-185 < EAccept < 5.2e119

   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%

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

   5. Taylor expanded in Vef around inf 65.2%

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

   6. Taylor expanded in Ev around inf 48.9%

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

   7. Taylor expanded in Vef around 0 38.6%

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

   if 5.2e119 < 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%

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

   5. Taylor expanded in Ec around inf 72.9%

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

      1. associate-*r/ 72.9%

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

      2. mul-1-neg 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in EAccept around inf 67.4%

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

   9. Taylor expanded in Ec around 0 47.4%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 4.2 \cdot 10^{-185}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{\frac{Ev}{KbT} + 2}\\ \mathbf{elif}\;EAccept \leq 5.2 \cdot 10^{+119}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 38.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq 1.22 \cdot 10^{+123}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept 1.22e+123)
   (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (* NdChar 0.5))
   (+ (/ NaChar (+ (exp (/ EAccept KbT)) 1.0)) (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 1.22e+123) {
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	} else {
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= 1.22d+123) then
        tmp = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar * 0.5d0)
    else
        tmp = (nachar / (exp((eaccept / kbt)) + 1.0d0)) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= 1.22e+123) {
		tmp = (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	} else {
		tmp = (NaChar / (Math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= 1.22e+123:
		tmp = (NaChar / (math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5)
	else:
		tmp = (NaChar / (math.exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= 1.22e+123)
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(Ev / KbT)) + 1.0)) + Float64(NdChar * 0.5));
	else
		tmp = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) + 1.0)) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= 1.22e+123)
		tmp = (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
	else
		tmp = (NaChar / (exp((EAccept / KbT)) + 1.0)) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, 1.22e+123], N[(N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EAccept < 1.22e123

   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%

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

   5. Taylor expanded in Vef around inf 69.7%

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

   6. Taylor expanded in Ev around inf 50.1%

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

   7. Taylor expanded in Vef around 0 37.5%

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

   if 1.22e123 < 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%

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

   5. Taylor expanded in Ec around inf 72.9%

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

      1. associate-*r/ 72.9%

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

      2. mul-1-neg 72.9%

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

   7. Simplified 72.9%

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

   8. Taylor expanded in EAccept around inf 67.4%

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

   9. Taylor expanded in Ec around 0 47.4%

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

4. Final simplification 38.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq 1.22 \cdot 10^{+123}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 36.4% accurate, 2.1× speedup

Math

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (/ NaChar (+ (exp (/ Ev KbT)) 1.0)) (* NdChar 0.5)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / (exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (nachar / (exp((ev / kbt)) + 1.0d0)) + (ndchar * 0.5d0)
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / (Math.exp((Ev / KbT)) + 1.0)) + (NdChar * 0.5);
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in Vef around inf 69.7%

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

6. Taylor expanded in Ev around inf 48.3%

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

7. Taylor expanded in Vef around 0 36.4%

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

8. Final simplification 36.4%

   \[\leadsto \frac{NaChar}{e^{\frac{Ev}{KbT}} + 1} + NdChar \cdot 0.5 \]
9. Add Preprocessing

Alternative 26: 28.3% accurate, 32.7× speedup

Math

\[\begin{array}{l} \\ \frac{NaChar}{2} + \frac{NdChar}{2} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (/ NaChar 2.0) (/ NdChar 2.0)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / 2.0) + (NdChar / 2.0);
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (nachar / 2.0d0) + (ndchar / 2.0d0)
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / 2.0) + (NdChar / 2.0);
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NaChar / 2.0) + (NdChar / 2.0)

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NaChar / 2.0) + Float64(NdChar / 2.0))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar / 2.0) + (NdChar / 2.0);
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.9%

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

3. Simplified 99.9%

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

5. Taylor expanded in KbT around inf 46.9%

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

6. Taylor expanded in KbT around inf 29.4%

   \[\leadsto \frac{NdChar}{\color{blue}{2}} + \frac{NaChar}{1 + 1} \]

7. Final simplification 29.4%

   \[\leadsto \frac{NaChar}{2} + \frac{NdChar}{2} \]
8. Add Preprocessing

Alternative 27: 18.5% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 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%

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

5. Taylor expanded in KbT around inf 50.7%

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

6. Taylor expanded in mu around inf 30.3%

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

7. Taylor expanded in KbT around inf 11.1%

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

8. Taylor expanded in NdChar around inf 16.4%

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

9. Final simplification 16.4%

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

Reproduce

herbie shell --seed 2024046 
(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))))))