Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 29.8s

Alternatives: 19

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -4.7402707401647905e+206
  2. Ec = 2.4713090812853925e+143
  3. Vef = 1.968554807268004e+289
  4. EDonor = -1.366784818928451e+158
  5. mu = -2.339572837681989e-245
  6. KbT = -3.699564692487034e-256
  7. NaChar = -7.924008455161047e+206
  8. Ev = 1.3126634661998606e+209
  9. EAccept = -0.0021634837304081024

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 67.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{if}\;EAccept \leq -3.1 \cdot 10^{-269}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 6.6 \cdot 10^{-254}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EAccept \leq 1.5 \cdot 10^{-172}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 2.06 \cdot 10^{-112}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;EAccept \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EAccept \leq 1.15 \cdot 10^{+24}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;EAccept \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_2
         (+
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))))
   (if (<= EAccept -3.1e-269)
     t_2
     (if (<= EAccept 6.6e-254)
       t_1
       (if (<= EAccept 1.5e-172)
         t_2
         (if (<= EAccept 2.06e-112)
           t_0
           (if (<= EAccept 4.8e-72)
             t_2
             (if (<= EAccept 3.2e-32)
               t_1
               (if (<= EAccept 1.15e+24)
                 t_2
                 (if (<= EAccept 7.5e+86)
                   t_0
                   (+
                    (/
                     NdChar
                     (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
                    (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	double t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_2 = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (EAccept <= -3.1e-269) {
		tmp = t_2;
	} else if (EAccept <= 6.6e-254) {
		tmp = t_1;
	} else if (EAccept <= 1.5e-172) {
		tmp = t_2;
	} else if (EAccept <= 2.06e-112) {
		tmp = t_0;
	} else if (EAccept <= 4.8e-72) {
		tmp = t_2;
	} else if (EAccept <= 3.2e-32) {
		tmp = t_1;
	} else if (EAccept <= 1.15e+24) {
		tmp = t_2;
	} else if (EAccept <= 7.5e+86) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    t_1 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_2 = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    if (eaccept <= (-3.1d-269)) then
        tmp = t_2
    else if (eaccept <= 6.6d-254) then
        tmp = t_1
    else if (eaccept <= 1.5d-172) then
        tmp = t_2
    else if (eaccept <= 2.06d-112) then
        tmp = t_0
    else if (eaccept <= 4.8d-72) then
        tmp = t_2
    else if (eaccept <= 3.2d-32) then
        tmp = t_1
    else if (eaccept <= 1.15d+24) then
        tmp = t_2
    else if (eaccept <= 7.5d+86) then
        tmp = t_0
    else
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_2 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	double tmp;
	if (EAccept <= -3.1e-269) {
		tmp = t_2;
	} else if (EAccept <= 6.6e-254) {
		tmp = t_1;
	} else if (EAccept <= 1.5e-172) {
		tmp = t_2;
	} else if (EAccept <= 2.06e-112) {
		tmp = t_0;
	} else if (EAccept <= 4.8e-72) {
		tmp = t_2;
	} else if (EAccept <= 3.2e-32) {
		tmp = t_1;
	} else if (EAccept <= 1.15e+24) {
		tmp = t_2;
	} else if (EAccept <= 7.5e+86) {
		tmp = t_0;
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	t_1 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_2 = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	tmp = 0
	if EAccept <= -3.1e-269:
		tmp = t_2
	elif EAccept <= 6.6e-254:
		tmp = t_1
	elif EAccept <= 1.5e-172:
		tmp = t_2
	elif EAccept <= 2.06e-112:
		tmp = t_0
	elif EAccept <= 4.8e-72:
		tmp = t_2
	elif EAccept <= 3.2e-32:
		tmp = t_1
	elif EAccept <= 1.15e+24:
		tmp = t_2
	elif EAccept <= 7.5e+86:
		tmp = t_0
	else:
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_2 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))))
	tmp = 0.0
	if (EAccept <= -3.1e-269)
		tmp = t_2;
	elseif (EAccept <= 6.6e-254)
		tmp = t_1;
	elseif (EAccept <= 1.5e-172)
		tmp = t_2;
	elseif (EAccept <= 2.06e-112)
		tmp = t_0;
	elseif (EAccept <= 4.8e-72)
		tmp = t_2;
	elseif (EAccept <= 3.2e-32)
		tmp = t_1;
	elseif (EAccept <= 1.15e+24)
		tmp = t_2;
	elseif (EAccept <= 7.5e+86)
		tmp = t_0;
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_2 = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	tmp = 0.0;
	if (EAccept <= -3.1e-269)
		tmp = t_2;
	elseif (EAccept <= 6.6e-254)
		tmp = t_1;
	elseif (EAccept <= 1.5e-172)
		tmp = t_2;
	elseif (EAccept <= 2.06e-112)
		tmp = t_0;
	elseif (EAccept <= 4.8e-72)
		tmp = t_2;
	elseif (EAccept <= 3.2e-32)
		tmp = t_1;
	elseif (EAccept <= 1.15e+24)
		tmp = t_2;
	elseif (EAccept <= 7.5e+86)
		tmp = t_0;
	else
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -3.1e-269], t$95$2, If[LessEqual[EAccept, 6.6e-254], t$95$1, If[LessEqual[EAccept, 1.5e-172], t$95$2, If[LessEqual[EAccept, 2.06e-112], t$95$0, If[LessEqual[EAccept, 4.8e-72], t$95$2, If[LessEqual[EAccept, 3.2e-32], t$95$1, If[LessEqual[EAccept, 1.15e+24], t$95$2, If[LessEqual[EAccept, 7.5e+86], t$95$0, N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if EAccept < -3.09999999999999967e-269 or 6.60000000000000033e-254 < EAccept < 1.49999999999999992e-172 or 2.06000000000000004e-112 < EAccept < 4.8e-72 or 3.2000000000000002e-32 < EAccept < 1.15e24

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 68.9%

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

   6. Taylor expanded in EDonor around 0 60.6%

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

   if -3.09999999999999967e-269 < EAccept < 6.60000000000000033e-254 or 4.8e-72 < EAccept < 3.2000000000000002e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 57.4%

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

   6. Taylor expanded in mu around inf 35.6%

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

      1. associate-/l* 35.6%

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

   8. Simplified 35.6%

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

   9. Taylor expanded in KbT around 0 68.3%

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

       1. associate--l+ 68.3%

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

       2. sub-neg 68.3%

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

       3. associate-+r+ 68.3%

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

       4. mul-1-neg 68.3%

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

       5. mul-1-neg 68.3%

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

       6. associate-+r+ 68.3%

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

       7. sub-neg 68.3%

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

       8. associate--l+ 68.3%

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

       9. +-commutative 68.3%

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

   11. Simplified 68.3%

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

   if 1.49999999999999992e-172 < EAccept < 2.06000000000000004e-112 or 1.15e24 < EAccept < 7.4999999999999997e86

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 76.8%

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

   if 7.4999999999999997e86 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 83.2%

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

4. Final simplification 67.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -3.1 \cdot 10^{-269}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 6.6 \cdot 10^{-254}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.5 \cdot 10^{-172}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 2.06 \cdot 10^{-112}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 4.8 \cdot 10^{-72}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.2 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 1.15 \cdot 10^{+24}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 7.5 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_3 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_4 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + t_0\\ \mathbf{if}\;NaChar \leq -8 \cdot 10^{-20}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NaChar \leq -1.25 \cdot 10^{-126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + t_0\\ \mathbf{elif}\;NaChar \leq -8.2 \cdot 10^{-141}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{-256}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{-207}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NaChar \leq 4.7 \cdot 10^{-132}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 1.95 \cdot 10^{-90}:\\ \;\;\;\;t_4\\ \mathbf{elif}\;NaChar \leq 4.2 \cdot 10^{-30}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}{NdChar}}\\ \mathbf{elif}\;NaChar \leq 3.1 \cdot 10^{+290}:\\ \;\;\;\;t_3\\ \mathbf{else}:\\ \;\;\;\;t_4\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT))))))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT))))))
        (t_3 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_4 (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) t_0)))
   (if (<= NaChar -8e-20)
     t_3
     (if (<= NaChar -1.25e-126)
       (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) t_0)
       (if (<= NaChar -8.2e-141)
         t_2
         (if (<= NaChar 1.65e-256)
           t_1
           (if (<= NaChar 1.1e-207)
             t_3
             (if (<= NaChar 4.7e-132)
               t_1
               (if (<= NaChar 1.95e-90)
                 t_4
                 (if (<= NaChar 4.2e-30)
                   t_2
                   (if (<= NaChar 1.1e+216)
                     (+
                      (/
                       NaChar
                       (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
                      (/
                       1.0
                       (/
                        (-
                         (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
                         (/ Ec KbT))
                        NdChar)))
                     (if (<= NaChar 3.1e+290) t_3 t_4))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((-Ec / KbT)));
	double t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	double t_3 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_4 = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	double tmp;
	if (NaChar <= -8e-20) {
		tmp = t_3;
	} else if (NaChar <= -1.25e-126) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + t_0;
	} else if (NaChar <= -8.2e-141) {
		tmp = t_2;
	} else if (NaChar <= 1.65e-256) {
		tmp = t_1;
	} else if (NaChar <= 1.1e-207) {
		tmp = t_3;
	} else if (NaChar <= 4.7e-132) {
		tmp = t_1;
	} else if (NaChar <= 1.95e-90) {
		tmp = t_4;
	} else if (NaChar <= 4.2e-30) {
		tmp = t_2;
	} else if (NaChar <= 1.1e+216) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar));
	} else if (NaChar <= 3.1e+290) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((-ec / kbt)))
    t_1 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    t_2 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    t_3 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_4 = (nachar / (1.0d0 + exp((ev / kbt)))) + t_0
    if (nachar <= (-8d-20)) then
        tmp = t_3
    else if (nachar <= (-1.25d-126)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + t_0
    else if (nachar <= (-8.2d-141)) then
        tmp = t_2
    else if (nachar <= 1.65d-256) then
        tmp = t_1
    else if (nachar <= 1.1d-207) then
        tmp = t_3
    else if (nachar <= 4.7d-132) then
        tmp = t_1
    else if (nachar <= 1.95d-90) then
        tmp = t_4
    else if (nachar <= 4.2d-30) then
        tmp = t_2
    else if (nachar <= 1.1d+216) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (1.0d0 / (((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)) / ndchar))
    else if (nachar <= 3.1d+290) then
        tmp = t_3
    else
        tmp = t_4
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((-Ec / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double t_2 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	double t_3 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_4 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + t_0;
	double tmp;
	if (NaChar <= -8e-20) {
		tmp = t_3;
	} else if (NaChar <= -1.25e-126) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + t_0;
	} else if (NaChar <= -8.2e-141) {
		tmp = t_2;
	} else if (NaChar <= 1.65e-256) {
		tmp = t_1;
	} else if (NaChar <= 1.1e-207) {
		tmp = t_3;
	} else if (NaChar <= 4.7e-132) {
		tmp = t_1;
	} else if (NaChar <= 1.95e-90) {
		tmp = t_4;
	} else if (NaChar <= 4.2e-30) {
		tmp = t_2;
	} else if (NaChar <= 1.1e+216) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar));
	} else if (NaChar <= 3.1e+290) {
		tmp = t_3;
	} else {
		tmp = t_4;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((-Ec / KbT)))
	t_1 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	t_2 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	t_3 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_4 = (NaChar / (1.0 + math.exp((Ev / KbT)))) + t_0
	tmp = 0
	if NaChar <= -8e-20:
		tmp = t_3
	elif NaChar <= -1.25e-126:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + t_0
	elif NaChar <= -8.2e-141:
		tmp = t_2
	elif NaChar <= 1.65e-256:
		tmp = t_1
	elif NaChar <= 1.1e-207:
		tmp = t_3
	elif NaChar <= 4.7e-132:
		tmp = t_1
	elif NaChar <= 1.95e-90:
		tmp = t_4
	elif NaChar <= 4.2e-30:
		tmp = t_2
	elif NaChar <= 1.1e+216:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar))
	elif NaChar <= 3.1e+290:
		tmp = t_3
	else:
		tmp = t_4
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / KbT)))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))))
	t_3 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_4 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + t_0)
	tmp = 0.0
	if (NaChar <= -8e-20)
		tmp = t_3;
	elseif (NaChar <= -1.25e-126)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + t_0);
	elseif (NaChar <= -8.2e-141)
		tmp = t_2;
	elseif (NaChar <= 1.65e-256)
		tmp = t_1;
	elseif (NaChar <= 1.1e-207)
		tmp = t_3;
	elseif (NaChar <= 4.7e-132)
		tmp = t_1;
	elseif (NaChar <= 1.95e-90)
		tmp = t_4;
	elseif (NaChar <= 4.2e-30)
		tmp = t_2;
	elseif (NaChar <= 1.1e+216)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(1.0 / Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT)) / NdChar)));
	elseif (NaChar <= 3.1e+290)
		tmp = t_3;
	else
		tmp = t_4;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((-Ec / KbT)));
	t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	t_2 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	t_3 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_4 = (NaChar / (1.0 + exp((Ev / KbT)))) + t_0;
	tmp = 0.0;
	if (NaChar <= -8e-20)
		tmp = t_3;
	elseif (NaChar <= -1.25e-126)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + t_0;
	elseif (NaChar <= -8.2e-141)
		tmp = t_2;
	elseif (NaChar <= 1.65e-256)
		tmp = t_1;
	elseif (NaChar <= 1.1e-207)
		tmp = t_3;
	elseif (NaChar <= 4.7e-132)
		tmp = t_1;
	elseif (NaChar <= 1.95e-90)
		tmp = t_4;
	elseif (NaChar <= 4.2e-30)
		tmp = t_2;
	elseif (NaChar <= 1.1e+216)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar));
	elseif (NaChar <= 3.1e+290)
		tmp = t_3;
	else
		tmp = t_4;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]}, If[LessEqual[NaChar, -8e-20], t$95$3, If[LessEqual[NaChar, -1.25e-126], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[NaChar, -8.2e-141], t$95$2, If[LessEqual[NaChar, 1.65e-256], t$95$1, If[LessEqual[NaChar, 1.1e-207], t$95$3, If[LessEqual[NaChar, 4.7e-132], t$95$1, If[LessEqual[NaChar, 1.95e-90], t$95$4, If[LessEqual[NaChar, 4.2e-30], t$95$2, If[LessEqual[NaChar, 1.1e+216], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 3.1e+290], t$95$3, t$95$4]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if NaChar < -7.99999999999999956e-20 or 1.65e-256 < NaChar < 1.0999999999999999e-207 or 1.1e216 < NaChar < 3.1000000000000001e290

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 62.4%

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

   6. Taylor expanded in mu around inf 44.9%

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

      1. associate-/l* 44.1%

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

   8. Simplified 44.1%

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

   9. Taylor expanded in KbT around 0 83.6%

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

       1. associate--l+ 83.6%

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

       2. sub-neg 83.6%

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

       3. associate-+r+ 83.6%

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

       4. mul-1-neg 83.6%

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

       5. mul-1-neg 83.6%

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

       6. associate-+r+ 83.6%

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

       7. sub-neg 83.6%

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

       8. associate--l+ 83.6%

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

       9. +-commutative 83.6%

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

   11. Simplified 83.6%

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

   if -7.99999999999999956e-20 < NaChar < -1.25000000000000001e-126

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 90.9%

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

   6. Taylor expanded in Ec around inf 75.5%

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

      1. associate-*r/ 60.2%

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

      2. mul-1-neg 60.2%

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

   8. Simplified 75.5%

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

   if -1.25000000000000001e-126 < NaChar < -8.20000000000000005e-141 or 1.95000000000000002e-90 < NaChar < 4.2000000000000004e-30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 76.1%

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

   6. Taylor expanded in mu around inf 70.8%

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

      1. associate-*r/ 70.8%

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

      2. mul-1-neg 70.8%

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

   8. Simplified 70.8%

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

   if -8.20000000000000005e-141 < NaChar < 1.65e-256 or 1.0999999999999999e-207 < NaChar < 4.7000000000000002e-132

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 93.7%

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

   6. Taylor expanded in Ev around 0 87.5%

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

   if 4.7000000000000002e-132 < NaChar < 1.95000000000000002e-90 or 3.1000000000000001e290 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 65.1%

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

   6. Taylor expanded in Ec around inf 61.3%

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

      1. associate-*r/ 61.3%

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

      2. mul-1-neg 61.3%

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

   8. Simplified 61.3%

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

   if 4.2000000000000004e-30 < NaChar < 1.1e216

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. div-inv 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+r- 99.8%

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

      7. associate-+l- 99.8%

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

      8. +-commutative 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 70.9%

      \[\leadsto \frac{1}{\frac{\color{blue}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}}{NdChar}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -8 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.25 \cdot 10^{-126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -8.2 \cdot 10^{-141}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{-256}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{-207}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.7 \cdot 10^{-132}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.95 \cdot 10^{-90}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.2 \cdot 10^{-30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}{NdChar}}\\ \mathbf{elif}\;NaChar \leq 3.1 \cdot 10^{+290}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.2 \cdot 10^{-18}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-125}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -5.6 \cdot 10^{-147}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{-256}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 9 \cdot 10^{-206}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{-17} \lor \neg \left(NaChar \leq 7.5 \cdot 10^{+242}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}{NdChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))
   (if (<= NaChar -2.2e-18)
     t_1
     (if (<= NaChar -2.3e-125)
       (+
        (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
       (if (<= NaChar -5.6e-147)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
         (if (<= NaChar 1.65e-256)
           t_0
           (if (<= NaChar 9e-206)
             t_1
             (if (<= NaChar 5.5e-135)
               t_0
               (if (or (<= NaChar 1.1e-17) (not (<= NaChar 7.5e+242)))
                 (+
                  (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
                  (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
                 (+
                  (/
                   NaChar
                   (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
                  (/
                   1.0
                   (/
                    (-
                     (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
                     (/ Ec KbT))
                    NdChar))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (NaChar <= -2.2e-18) {
		tmp = t_1;
	} else if (NaChar <= -2.3e-125) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	} else if (NaChar <= -5.6e-147) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (NaChar <= 1.65e-256) {
		tmp = t_0;
	} else if (NaChar <= 9e-206) {
		tmp = t_1;
	} else if (NaChar <= 5.5e-135) {
		tmp = t_0;
	} else if ((NaChar <= 1.1e-17) || !(NaChar <= 7.5e+242)) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    t_1 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    if (nachar <= (-2.2d-18)) then
        tmp = t_1
    else if (nachar <= (-2.3d-125)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    else if (nachar <= (-5.6d-147)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (nachar <= 1.65d-256) then
        tmp = t_0
    else if (nachar <= 9d-206) then
        tmp = t_1
    else if (nachar <= 5.5d-135) then
        tmp = t_0
    else if ((nachar <= 1.1d-17) .or. (.not. (nachar <= 7.5d+242))) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (1.0d0 / (((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)) / ndchar))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (NaChar <= -2.2e-18) {
		tmp = t_1;
	} else if (NaChar <= -2.3e-125) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	} else if (NaChar <= -5.6e-147) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (NaChar <= 1.65e-256) {
		tmp = t_0;
	} else if (NaChar <= 9e-206) {
		tmp = t_1;
	} else if (NaChar <= 5.5e-135) {
		tmp = t_0;
	} else if ((NaChar <= 1.1e-17) || !(NaChar <= 7.5e+242)) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	t_1 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	tmp = 0
	if NaChar <= -2.2e-18:
		tmp = t_1
	elif NaChar <= -2.3e-125:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	elif NaChar <= -5.6e-147:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif NaChar <= 1.65e-256:
		tmp = t_0
	elif NaChar <= 9e-206:
		tmp = t_1
	elif NaChar <= 5.5e-135:
		tmp = t_0
	elif (NaChar <= 1.1e-17) or not (NaChar <= 7.5e+242):
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.2e-18)
		tmp = t_1;
	elseif (NaChar <= -2.3e-125)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	elseif (NaChar <= -5.6e-147)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (NaChar <= 1.65e-256)
		tmp = t_0;
	elseif (NaChar <= 9e-206)
		tmp = t_1;
	elseif (NaChar <= 5.5e-135)
		tmp = t_0;
	elseif ((NaChar <= 1.1e-17) || !(NaChar <= 7.5e+242))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(1.0 / Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT)) / NdChar)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.2e-18)
		tmp = t_1;
	elseif (NaChar <= -2.3e-125)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	elseif (NaChar <= -5.6e-147)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (NaChar <= 1.65e-256)
		tmp = t_0;
	elseif (NaChar <= 9e-206)
		tmp = t_1;
	elseif (NaChar <= 5.5e-135)
		tmp = t_0;
	elseif ((NaChar <= 1.1e-17) || ~((NaChar <= 7.5e+242)))
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.2e-18], t$95$1, If[LessEqual[NaChar, -2.3e-125], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -5.6e-147], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.65e-256], t$95$0, If[LessEqual[NaChar, 9e-206], t$95$1, If[LessEqual[NaChar, 5.5e-135], t$95$0, If[Or[LessEqual[NaChar, 1.1e-17], N[Not[LessEqual[NaChar, 7.5e+242]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if NaChar < -2.1999999999999998e-18 or 1.65e-256 < NaChar < 8.9999999999999996e-206

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.7%

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

   6. Taylor expanded in mu around inf 45.1%

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

      1. associate-/l* 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in KbT around 0 84.3%

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

       1. associate--l+ 84.3%

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

       2. sub-neg 84.3%

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

       3. associate-+r+ 84.3%

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

       4. mul-1-neg 84.3%

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

       5. mul-1-neg 84.3%

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

       6. associate-+r+ 84.3%

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

       7. sub-neg 84.3%

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

       8. associate--l+ 84.3%

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

       9. +-commutative 84.3%

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

   11. Simplified 84.3%

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

   if -2.1999999999999998e-18 < NaChar < -2.2999999999999999e-125

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 90.9%

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

   6. Taylor expanded in Ec around inf 75.5%

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

      1. associate-*r/ 60.2%

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

      2. mul-1-neg 60.2%

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

   8. Simplified 75.5%

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

   if -2.2999999999999999e-125 < NaChar < -5.6000000000000001e-147

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 100.0%

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

   6. Taylor expanded in mu around inf 79.7%

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

      1. associate-*r/ 79.7%

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

      2. mul-1-neg 79.7%

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

   8. Simplified 79.7%

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

   if -5.6000000000000001e-147 < NaChar < 1.65e-256 or 8.9999999999999996e-206 < NaChar < 5.4999999999999999e-135

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 93.5%

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

   6. Taylor expanded in Ev around 0 87.1%

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

   if 5.4999999999999999e-135 < NaChar < 1.1e-17 or 7.49999999999999961e242 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 66.8%

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

   6. Taylor expanded in EDonor around 0 63.4%

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

   if 1.1e-17 < NaChar < 7.49999999999999961e242

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. div-inv 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+r- 99.8%

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

      7. associate-+l- 99.8%

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

      8. +-commutative 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 70.3%

      \[\leadsto \frac{1}{\frac{\color{blue}{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}}{NdChar}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.2 \cdot 10^{-18}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-125}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -5.6 \cdot 10^{-147}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{-256}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 9 \cdot 10^{-206}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 5.5 \cdot 10^{-135}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{-17} \lor \neg \left(NaChar \leq 7.5 \cdot 10^{+242}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}{NdChar}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -1.55 \cdot 10^{-127}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -8.8 \cdot 10^{-142}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{-256}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 1.15 \cdot 10^{-202}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{-134}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 3.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))
   (if (<= NaChar -2.4e-20)
     t_1
     (if (<= NaChar -1.55e-127)
       (+
        (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
       (if (<= NaChar -8.8e-142)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
         (if (<= NaChar 1.65e-256)
           t_0
           (if (<= NaChar 1.15e-202)
             t_1
             (if (<= NaChar 1.1e-134)
               t_0
               (if (<= NaChar 3.6e-13)
                 (+
                  (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
                  (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
                 (+
                  (/
                   NaChar
                   (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
                  (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (NaChar <= -2.4e-20) {
		tmp = t_1;
	} else if (NaChar <= -1.55e-127) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	} else if (NaChar <= -8.8e-142) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (NaChar <= 1.65e-256) {
		tmp = t_0;
	} else if (NaChar <= 1.15e-202) {
		tmp = t_1;
	} else if (NaChar <= 1.1e-134) {
		tmp = t_0;
	} else if (NaChar <= 3.6e-13) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    t_1 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    if (nachar <= (-2.4d-20)) then
        tmp = t_1
    else if (nachar <= (-1.55d-127)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    else if (nachar <= (-8.8d-142)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (nachar <= 1.65d-256) then
        tmp = t_0
    else if (nachar <= 1.15d-202) then
        tmp = t_1
    else if (nachar <= 1.1d-134) then
        tmp = t_0
    else if (nachar <= 3.6d-13) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (NaChar <= -2.4e-20) {
		tmp = t_1;
	} else if (NaChar <= -1.55e-127) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	} else if (NaChar <= -8.8e-142) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (NaChar <= 1.65e-256) {
		tmp = t_0;
	} else if (NaChar <= 1.15e-202) {
		tmp = t_1;
	} else if (NaChar <= 1.1e-134) {
		tmp = t_0;
	} else if (NaChar <= 3.6e-13) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	t_1 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	tmp = 0
	if NaChar <= -2.4e-20:
		tmp = t_1
	elif NaChar <= -1.55e-127:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	elif NaChar <= -8.8e-142:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif NaChar <= 1.65e-256:
		tmp = t_0
	elif NaChar <= 1.15e-202:
		tmp = t_1
	elif NaChar <= 1.1e-134:
		tmp = t_0
	elif NaChar <= 3.6e-13:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.4e-20)
		tmp = t_1;
	elseif (NaChar <= -1.55e-127)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	elseif (NaChar <= -8.8e-142)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (NaChar <= 1.65e-256)
		tmp = t_0;
	elseif (NaChar <= 1.15e-202)
		tmp = t_1;
	elseif (NaChar <= 1.1e-134)
		tmp = t_0;
	elseif (NaChar <= 3.6e-13)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.4e-20)
		tmp = t_1;
	elseif (NaChar <= -1.55e-127)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	elseif (NaChar <= -8.8e-142)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (NaChar <= 1.65e-256)
		tmp = t_0;
	elseif (NaChar <= 1.15e-202)
		tmp = t_1;
	elseif (NaChar <= 1.1e-134)
		tmp = t_0;
	elseif (NaChar <= 3.6e-13)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.4e-20], t$95$1, If[LessEqual[NaChar, -1.55e-127], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -8.8e-142], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.65e-256], t$95$0, If[LessEqual[NaChar, 1.15e-202], t$95$1, If[LessEqual[NaChar, 1.1e-134], t$95$0, If[LessEqual[NaChar, 3.6e-13], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if NaChar < -2.39999999999999993e-20 or 1.65e-256 < NaChar < 1.1499999999999999e-202

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.7%

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

   6. Taylor expanded in mu around inf 45.1%

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

      1. associate-/l* 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in KbT around 0 84.3%

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

       1. associate--l+ 84.3%

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

       2. sub-neg 84.3%

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

       3. associate-+r+ 84.3%

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

       4. mul-1-neg 84.3%

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

       5. mul-1-neg 84.3%

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

       6. associate-+r+ 84.3%

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

       7. sub-neg 84.3%

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

       8. associate--l+ 84.3%

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

       9. +-commutative 84.3%

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

   11. Simplified 84.3%

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

   if -2.39999999999999993e-20 < NaChar < -1.55e-127

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 90.9%

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

   6. Taylor expanded in Ec around inf 75.5%

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

      1. associate-*r/ 60.2%

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

      2. mul-1-neg 60.2%

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

   8. Simplified 75.5%

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

   if -1.55e-127 < NaChar < -8.80000000000000066e-142

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 100.0%

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

   6. Taylor expanded in mu around inf 79.7%

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

      1. associate-*r/ 79.7%

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

      2. mul-1-neg 79.7%

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

   8. Simplified 79.7%

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

   if -8.80000000000000066e-142 < NaChar < 1.65e-256 or 1.1499999999999999e-202 < NaChar < 1.1e-134

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 93.5%

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

   6. Taylor expanded in Ev around 0 87.1%

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

   if 1.1e-134 < NaChar < 3.5999999999999998e-13

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 70.8%

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

   6. Taylor expanded in EDonor around 0 66.1%

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

   if 3.5999999999999998e-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%

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

   5. Taylor expanded in EDonor around inf 82.9%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.4 \cdot 10^{-20}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.55 \cdot 10^{-127}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -8.8 \cdot 10^{-142}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{-256}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.15 \cdot 10^{-202}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.1 \cdot 10^{-134}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 3.6 \cdot 10^{-13}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.4 \cdot 10^{-19}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq -1 \cdot 10^{-125}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -9.2 \cdot 10^{-148}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.5 \cdot 10^{-256}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 9 \cdot 10^{-135}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 1.75 \cdot 10^{-12}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_2 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))))
   (if (<= NaChar -1.4e-19)
     t_1
     (if (<= NaChar -1e-125)
       (+
        (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
        (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT)))))
       (if (<= NaChar -9.2e-148)
         (+ t_2 (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
         (if (<= NaChar 1.5e-256)
           t_0
           (if (<= NaChar 8.5e-207)
             t_1
             (if (<= NaChar 9e-135)
               t_0
               (if (<= NaChar 1.75e-12)
                 (+
                  (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
                  (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))))
                 (+ t_2 (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_2 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (NaChar <= -1.4e-19) {
		tmp = t_1;
	} else if (NaChar <= -1e-125) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	} else if (NaChar <= -9.2e-148) {
		tmp = t_2 + (NdChar / (1.0 + exp((mu / KbT))));
	} else if (NaChar <= 1.5e-256) {
		tmp = t_0;
	} else if (NaChar <= 8.5e-207) {
		tmp = t_1;
	} else if (NaChar <= 9e-135) {
		tmp = t_0;
	} else if (NaChar <= 1.75e-12) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = t_2 + (NdChar / (1.0 + exp((EDonor / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    t_1 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_2 = nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))
    if (nachar <= (-1.4d-19)) then
        tmp = t_1
    else if (nachar <= (-1d-125)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    else if (nachar <= (-9.2d-148)) then
        tmp = t_2 + (ndchar / (1.0d0 + exp((mu / kbt))))
    else if (nachar <= 1.5d-256) then
        tmp = t_0
    else if (nachar <= 8.5d-207) then
        tmp = t_1
    else if (nachar <= 9d-135) then
        tmp = t_0
    else if (nachar <= 1.75d-12) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt))))
    else
        tmp = t_2 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_2 = NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	double tmp;
	if (NaChar <= -1.4e-19) {
		tmp = t_1;
	} else if (NaChar <= -1e-125) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	} else if (NaChar <= -9.2e-148) {
		tmp = t_2 + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else if (NaChar <= 1.5e-256) {
		tmp = t_0;
	} else if (NaChar <= 8.5e-207) {
		tmp = t_1;
	} else if (NaChar <= 9e-135) {
		tmp = t_0;
	} else if (NaChar <= 1.75e-12) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT))));
	} else {
		tmp = t_2 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	t_1 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_2 = NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))
	tmp = 0
	if NaChar <= -1.4e-19:
		tmp = t_1
	elif NaChar <= -1e-125:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	elif NaChar <= -9.2e-148:
		tmp = t_2 + (NdChar / (1.0 + math.exp((mu / KbT))))
	elif NaChar <= 1.5e-256:
		tmp = t_0
	elif NaChar <= 8.5e-207:
		tmp = t_1
	elif NaChar <= 9e-135:
		tmp = t_0
	elif NaChar <= 1.75e-12:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT))))
	else:
		tmp = t_2 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.4e-19)
		tmp = t_1;
	elseif (NaChar <= -1e-125)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))));
	elseif (NaChar <= -9.2e-148)
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	elseif (NaChar <= 1.5e-256)
		tmp = t_0;
	elseif (NaChar <= 8.5e-207)
		tmp = t_1;
	elseif (NaChar <= 9e-135)
		tmp = t_0;
	elseif (NaChar <= 1.75e-12)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))));
	else
		tmp = Float64(t_2 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_2 = NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.4e-19)
		tmp = t_1;
	elseif (NaChar <= -1e-125)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	elseif (NaChar <= -9.2e-148)
		tmp = t_2 + (NdChar / (1.0 + exp((mu / KbT))));
	elseif (NaChar <= 1.5e-256)
		tmp = t_0;
	elseif (NaChar <= 8.5e-207)
		tmp = t_1;
	elseif (NaChar <= 9e-135)
		tmp = t_0;
	elseif (NaChar <= 1.75e-12)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT))));
	else
		tmp = t_2 + (NdChar / (1.0 + exp((EDonor / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.4e-19], t$95$1, If[LessEqual[NaChar, -1e-125], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -9.2e-148], N[(t$95$2 + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.5e-256], t$95$0, If[LessEqual[NaChar, 8.5e-207], t$95$1, If[LessEqual[NaChar, 9e-135], t$95$0, If[LessEqual[NaChar, 1.75e-12], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$2 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if NaChar < -1.40000000000000001e-19 or 1.4999999999999999e-256 < NaChar < 8.49999999999999962e-207

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.7%

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

   6. Taylor expanded in mu around inf 45.1%

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

      1. associate-/l* 44.0%

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

   8. Simplified 44.0%

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

   9. Taylor expanded in KbT around 0 84.3%

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

       1. associate--l+ 84.3%

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

       2. sub-neg 84.3%

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

       3. associate-+r+ 84.3%

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

       4. mul-1-neg 84.3%

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

       5. mul-1-neg 84.3%

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

       6. associate-+r+ 84.3%

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

       7. sub-neg 84.3%

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

       8. associate--l+ 84.3%

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

       9. +-commutative 84.3%

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

   11. Simplified 84.3%

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

   if -1.40000000000000001e-19 < NaChar < -1.00000000000000001e-125

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 90.9%

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

   6. Taylor expanded in Ec around inf 75.5%

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

      1. associate-*r/ 60.2%

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

      2. mul-1-neg 60.2%

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

   8. Simplified 75.5%

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

   if -1.00000000000000001e-125 < NaChar < -9.1999999999999999e-148

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 100.0%

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

   if -9.1999999999999999e-148 < NaChar < 1.4999999999999999e-256 or 8.49999999999999962e-207 < NaChar < 8.99999999999999975e-135

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 93.5%

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

   6. Taylor expanded in Ev around 0 87.1%

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

   if 8.99999999999999975e-135 < NaChar < 1.75e-12

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 70.8%

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

   6. Taylor expanded in EDonor around 0 66.1%

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

   if 1.75e-12 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 82.9%

      \[\leadsto \frac{NdChar}{1 + e^{\color{blue}{\frac{EDonor}{KbT}}}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 81.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.4 \cdot 10^{-19}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1 \cdot 10^{-125}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -9.2 \cdot 10^{-148}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.5 \cdot 10^{-256}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-207}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 9 \cdot 10^{-135}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.75 \cdot 10^{-12}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{if}\;NaChar \leq -1.75 \cdot 10^{-99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{-256}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq 2.5 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 4.5 \cdot 10^{-132}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{-86}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NaChar \leq 3.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.26 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}{NdChar}}\\ \mathbf{elif}\;NaChar \leq 2 \cdot 10^{+287}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))
          (/ NdChar (+ 1.0 (exp (/ (- Ec) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT)))))))
   (if (<= NaChar -1.75e-99)
     t_1
     (if (<= NaChar 1.65e-256)
       t_2
       (if (<= NaChar 2.5e-207)
         t_1
         (if (<= NaChar 4.5e-132)
           t_2
           (if (<= NaChar 1.3e-86)
             t_0
             (if (<= NaChar 3.8e-30)
               (+
                (/ NdChar (+ 1.0 (exp (/ mu KbT))))
                (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
               (if (<= NaChar 1.26e+216)
                 (+
                  (/
                   NaChar
                   (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
                  (/
                   1.0
                   (/
                    (-
                     (+ 2.0 (+ (/ EDonor KbT) (+ (/ Vef KbT) (/ mu KbT))))
                     (/ Ec KbT))
                    NdChar)))
                 (if (<= NaChar 2e+287) 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 = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	double t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_2 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double tmp;
	if (NaChar <= -1.75e-99) {
		tmp = t_1;
	} else if (NaChar <= 1.65e-256) {
		tmp = t_2;
	} else if (NaChar <= 2.5e-207) {
		tmp = t_1;
	} else if (NaChar <= 4.5e-132) {
		tmp = t_2;
	} else if (NaChar <= 1.3e-86) {
		tmp = t_0;
	} else if (NaChar <= 3.8e-30) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else if (NaChar <= 1.26e+216) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar));
	} else if (NaChar <= 2e+287) {
		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) :: t_2
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / (1.0d0 + exp((-ec / kbt))))
    t_1 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_2 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    if (nachar <= (-1.75d-99)) then
        tmp = t_1
    else if (nachar <= 1.65d-256) then
        tmp = t_2
    else if (nachar <= 2.5d-207) then
        tmp = t_1
    else if (nachar <= 4.5d-132) then
        tmp = t_2
    else if (nachar <= 1.3d-86) then
        tmp = t_0
    else if (nachar <= 3.8d-30) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else if (nachar <= 1.26d+216) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (1.0d0 / (((2.0d0 + ((edonor / kbt) + ((vef / kbt) + (mu / kbt)))) - (ec / kbt)) / ndchar))
    else if (nachar <= 2d+287) 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 = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / (1.0 + Math.exp((-Ec / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_2 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	double tmp;
	if (NaChar <= -1.75e-99) {
		tmp = t_1;
	} else if (NaChar <= 1.65e-256) {
		tmp = t_2;
	} else if (NaChar <= 2.5e-207) {
		tmp = t_1;
	} else if (NaChar <= 4.5e-132) {
		tmp = t_2;
	} else if (NaChar <= 1.3e-86) {
		tmp = t_0;
	} else if (NaChar <= 3.8e-30) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else if (NaChar <= 1.26e+216) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar));
	} else if (NaChar <= 2e+287) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / (1.0 + math.exp((-Ec / KbT))))
	t_1 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_2 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	tmp = 0
	if NaChar <= -1.75e-99:
		tmp = t_1
	elif NaChar <= 1.65e-256:
		tmp = t_2
	elif NaChar <= 2.5e-207:
		tmp = t_1
	elif NaChar <= 4.5e-132:
		tmp = t_2
	elif NaChar <= 1.3e-86:
		tmp = t_0
	elif NaChar <= 3.8e-30:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	elif NaChar <= 1.26e+216:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar))
	elif NaChar <= 2e+287:
		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(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Ec) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / KbT)))))
	tmp = 0.0
	if (NaChar <= -1.75e-99)
		tmp = t_1;
	elseif (NaChar <= 1.65e-256)
		tmp = t_2;
	elseif (NaChar <= 2.5e-207)
		tmp = t_1;
	elseif (NaChar <= 4.5e-132)
		tmp = t_2;
	elseif (NaChar <= 1.3e-86)
		tmp = t_0;
	elseif (NaChar <= 3.8e-30)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	elseif (NaChar <= 1.26e+216)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(1.0 / Float64(Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) + Float64(Float64(Vef / KbT) + Float64(mu / KbT)))) - Float64(Ec / KbT)) / NdChar)));
	elseif (NaChar <= 2e+287)
		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 = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / (1.0 + exp((-Ec / KbT))));
	t_1 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_2 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	tmp = 0.0;
	if (NaChar <= -1.75e-99)
		tmp = t_1;
	elseif (NaChar <= 1.65e-256)
		tmp = t_2;
	elseif (NaChar <= 2.5e-207)
		tmp = t_1;
	elseif (NaChar <= 4.5e-132)
		tmp = t_2;
	elseif (NaChar <= 1.3e-86)
		tmp = t_0;
	elseif (NaChar <= 3.8e-30)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	elseif (NaChar <= 1.26e+216)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (1.0 / (((2.0 + ((EDonor / KbT) + ((Vef / KbT) + (mu / KbT)))) - (Ec / KbT)) / NdChar));
	elseif (NaChar <= 2e+287)
		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[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[((-Ec) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.75e-99], t$95$1, If[LessEqual[NaChar, 1.65e-256], t$95$2, If[LessEqual[NaChar, 2.5e-207], t$95$1, If[LessEqual[NaChar, 4.5e-132], t$95$2, If[LessEqual[NaChar, 1.3e-86], t$95$0, If[LessEqual[NaChar, 3.8e-30], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.26e+216], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.0 / N[(N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision] / NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2e+287], t$95$1, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NaChar < -1.7499999999999999e-99 or 1.65e-256 < NaChar < 2.50000000000000007e-207 or 1.2599999999999999e216 < NaChar < 2.0000000000000002e287

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 61.8%

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

   6. Taylor expanded in mu around inf 43.9%

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

      1. associate-/l* 42.3%

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

   8. Simplified 42.3%

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

   9. Taylor expanded in KbT around 0 80.1%

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

       1. associate--l+ 80.1%

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

       2. sub-neg 80.1%

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

       3. associate-+r+ 80.1%

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

       4. mul-1-neg 80.1%

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

       5. mul-1-neg 80.1%

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

       6. associate-+r+ 80.1%

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

       7. sub-neg 80.1%

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

       8. associate--l+ 80.1%

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

       9. +-commutative 80.1%

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

   11. Simplified 80.1%

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

   if -1.7499999999999999e-99 < NaChar < 1.65e-256 or 2.50000000000000007e-207 < NaChar < 4.4999999999999999e-132

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 90.4%

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

   6. Taylor expanded in Ev around 0 83.6%

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

   if 4.4999999999999999e-132 < NaChar < 1.3000000000000001e-86 or 2.0000000000000002e287 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 65.1%

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

   6. Taylor expanded in Ec around inf 61.3%

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

      1. associate-*r/ 61.3%

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

      2. mul-1-neg 61.3%

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

   8. Simplified 61.3%

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

   if 1.3000000000000001e-86 < NaChar < 3.8000000000000003e-30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 69.8%

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

   6. Taylor expanded in mu around inf 68.5%

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

      1. associate-*r/ 68.5%

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

      2. mul-1-neg 68.5%

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

   8. Simplified 68.5%

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

   if 3.8000000000000003e-30 < NaChar < 1.2599999999999999e216

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

      1. clear-num 99.8%

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

      2. inv-pow 99.8%

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

      3. div-inv 99.8%

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

      4. div-inv 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-+r- 99.8%

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

      7. associate-+l- 99.8%

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

      8. +-commutative 99.8%

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

   6. Applied egg-rr 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in KbT around inf 70.9%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.75 \cdot 10^{-99}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.65 \cdot 10^{-256}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 2.5 \cdot 10^{-207}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.5 \cdot 10^{-132}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NaChar \leq 1.3 \cdot 10^{-86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 3.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.26 \cdot 10^{+216}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{1}{\frac{\left(2 + \left(\frac{EDonor}{KbT} + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}{NdChar}}\\ \mathbf{elif}\;NaChar \leq 2 \cdot 10^{+287}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{1 + e^{\frac{-Ec}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_1 := t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{if}\;EAccept \leq -1.52 \cdot 10^{-271}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EAccept \leq 2.2 \cdot 10^{-258}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.5 \cdot 10^{+24}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;EAccept \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))))
   (if (<= EAccept -1.52e-271)
     t_1
     (if (<= EAccept 2.2e-258)
       (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
       (if (<= EAccept 3.5e+24)
         t_1
         (if (<= EAccept 3.3e+86)
           (+
            (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
            (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
           (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	double tmp;
	if (EAccept <= -1.52e-271) {
		tmp = t_1;
	} else if (EAccept <= 2.2e-258) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (EAccept <= 3.5e+24) {
		tmp = t_1;
	} else if (EAccept <= 3.3e+86) {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_1 = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    if (eaccept <= (-1.52d-271)) then
        tmp = t_1
    else if (eaccept <= 2.2d-258) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else if (eaccept <= 3.5d+24) then
        tmp = t_1
    else if (eaccept <= 3.3d+86) then
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_1 = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double tmp;
	if (EAccept <= -1.52e-271) {
		tmp = t_1;
	} else if (EAccept <= 2.2e-258) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else if (EAccept <= 3.5e+24) {
		tmp = t_1;
	} else if (EAccept <= 3.3e+86) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_1 = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	tmp = 0
	if EAccept <= -1.52e-271:
		tmp = t_1
	elif EAccept <= 2.2e-258:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	elif EAccept <= 3.5e+24:
		tmp = t_1
	elif EAccept <= 3.3e+86:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	tmp = 0.0
	if (EAccept <= -1.52e-271)
		tmp = t_1;
	elseif (EAccept <= 2.2e-258)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	elseif (EAccept <= 3.5e+24)
		tmp = t_1;
	elseif (EAccept <= 3.3e+86)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_1 = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	tmp = 0.0;
	if (EAccept <= -1.52e-271)
		tmp = t_1;
	elseif (EAccept <= 2.2e-258)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	elseif (EAccept <= 3.5e+24)
		tmp = t_1;
	elseif (EAccept <= 3.3e+86)
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EAccept, -1.52e-271], t$95$1, If[LessEqual[EAccept, 2.2e-258], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 3.5e+24], t$95$1, If[LessEqual[EAccept, 3.3e+86], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if EAccept < -1.51999999999999988e-271 or 2.20000000000000015e-258 < EAccept < 3.5000000000000002e24

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 69.1%

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

   if -1.51999999999999988e-271 < EAccept < 2.20000000000000015e-258

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.4%

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

   6. Taylor expanded in mu around inf 32.5%

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

      1. associate-/l* 32.6%

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

   8. Simplified 32.6%

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

   9. Taylor expanded in KbT around 0 71.5%

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

       1. associate--l+ 71.5%

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

       2. sub-neg 71.5%

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

       3. associate-+r+ 71.5%

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

       4. mul-1-neg 71.5%

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

       5. mul-1-neg 71.5%

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

       6. associate-+r+ 71.5%

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

       7. sub-neg 71.5%

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

       8. associate--l+ 71.5%

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

       9. +-commutative 71.5%

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

   11. Simplified 71.5%

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

   if 3.5000000000000002e24 < EAccept < 3.2999999999999999e86

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 78.5%

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

   if 3.2999999999999999e86 < EAccept

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 83.2%

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

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -1.52 \cdot 10^{-271}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 2.2 \cdot 10^{-258}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.5 \cdot 10^{+24}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;EAccept \leq 3.3 \cdot 10^{+86}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 72.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ \mathbf{if}\;Ev \leq -1 \cdot 10^{+110}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -2.2 \cdot 10^{-222}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.35 \cdot 10^{-307}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))))
   (if (<= Ev -1e+110)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= Ev -2.2e-222)
       (+ t_0 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))
       (if (<= Ev -1.35e-307)
         (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))
         (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (Ev <= -1e+110) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Ev <= -2.2e-222) {
		tmp = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	} else if (Ev <= -1.35e-307) {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    if (ev <= (-1d+110)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (ev <= (-2.2d-222)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((vef / kbt))))
    else if (ev <= (-1.35d-307)) then
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    else
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double tmp;
	if (Ev <= -1e+110) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Ev <= -2.2e-222) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	} else if (Ev <= -1.35e-307) {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	} else {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	tmp = 0
	if Ev <= -1e+110:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Ev <= -2.2e-222:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	elif Ev <= -1.35e-307:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	else:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	tmp = 0.0
	if (Ev <= -1e+110)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Ev <= -2.2e-222)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	elseif (Ev <= -1.35e-307)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	tmp = 0.0;
	if (Ev <= -1e+110)
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Ev <= -2.2e-222)
		tmp = t_0 + (NaChar / (1.0 + exp((Vef / KbT))));
	elseif (Ev <= -1.35e-307)
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	else
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -1e+110], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -2.2e-222], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.35e-307], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -1e110

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 85.1%

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

   if -1e110 < Ev < -2.2e-222

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 79.0%

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

   if -2.2e-222 < Ev < -1.34999999999999993e-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%

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

   5. Taylor expanded in KbT around inf 66.5%

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

   6. Taylor expanded in mu around inf 35.9%

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

      1. associate-/l* 35.7%

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

   8. Simplified 35.7%

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

   9. Taylor expanded in KbT around 0 73.1%

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

       1. associate--l+ 73.1%

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

       2. sub-neg 73.1%

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

       3. associate-+r+ 73.1%

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

       4. mul-1-neg 73.1%

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

       5. mul-1-neg 73.1%

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

       6. associate-+r+ 73.1%

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

       7. sub-neg 73.1%

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

       8. associate--l+ 73.1%

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

       9. +-commutative 73.1%

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

   11. Simplified 73.1%

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

   if -1.34999999999999993e-307 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 76.6%

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

4. Final simplification 78.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1 \cdot 10^{+110}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -2.2 \cdot 10^{-222}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.35 \cdot 10^{-307}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 64.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ t_2 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}}\\ t_3 := t_2 + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{if}\;NdChar \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NdChar \leq -1.46 \cdot 10^{-25}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -5.8 \cdot 10^{-60}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;NdChar \leq -4.4 \cdot 10^{-111}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -7.2 \cdot 10^{-207}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 1.15 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 1.7 \cdot 10^{+135}:\\ \;\;\;\;t_2 + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 4.4 \cdot 10^{+173}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ NdChar (+ (/ mu KbT) 2.0))))
        (t_2 (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)))))
        (t_3 (+ t_2 (/ NaChar (+ (/ Vef KbT) 2.0)))))
   (if (<= NdChar -1.9e+29)
     t_3
     (if (<= NdChar -1.46e-25)
       t_0
       (if (<= NdChar -5.8e-60)
         t_3
         (if (<= NdChar -4.4e-111)
           (/ NdChar (+ 1.0 (exp (/ mu KbT))))
           (if (<= NdChar -7.2e-207)
             t_1
             (if (<= NdChar 1.15e+34)
               t_0
               (if (<= NdChar 1.7e+135)
                 (+ t_2 (/ NaChar (+ 1.0 (+ 1.0 (/ Ev KbT)))))
                 (if (<= NdChar 4.4e+173) t_1 t_3))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	double t_2 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_3 = t_2 + (NaChar / ((Vef / KbT) + 2.0));
	double tmp;
	if (NdChar <= -1.9e+29) {
		tmp = t_3;
	} else if (NdChar <= -1.46e-25) {
		tmp = t_0;
	} else if (NdChar <= -5.8e-60) {
		tmp = t_3;
	} else if (NdChar <= -4.4e-111) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else if (NdChar <= -7.2e-207) {
		tmp = t_1;
	} else if (NdChar <= 1.15e+34) {
		tmp = t_0;
	} else if (NdChar <= 1.7e+135) {
		tmp = t_2 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	} else if (NdChar <= 4.4e+173) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((mu / kbt) + 2.0d0))
    t_2 = ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))
    t_3 = t_2 + (nachar / ((vef / kbt) + 2.0d0))
    if (ndchar <= (-1.9d+29)) then
        tmp = t_3
    else if (ndchar <= (-1.46d-25)) then
        tmp = t_0
    else if (ndchar <= (-5.8d-60)) then
        tmp = t_3
    else if (ndchar <= (-4.4d-111)) then
        tmp = ndchar / (1.0d0 + exp((mu / kbt)))
    else if (ndchar <= (-7.2d-207)) then
        tmp = t_1
    else if (ndchar <= 1.15d+34) then
        tmp = t_0
    else if (ndchar <= 1.7d+135) then
        tmp = t_2 + (nachar / (1.0d0 + (1.0d0 + (ev / kbt))))
    else if (ndchar <= 4.4d+173) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	double t_2 = NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	double t_3 = t_2 + (NaChar / ((Vef / KbT) + 2.0));
	double tmp;
	if (NdChar <= -1.9e+29) {
		tmp = t_3;
	} else if (NdChar <= -1.46e-25) {
		tmp = t_0;
	} else if (NdChar <= -5.8e-60) {
		tmp = t_3;
	} else if (NdChar <= -4.4e-111) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else if (NdChar <= -7.2e-207) {
		tmp = t_1;
	} else if (NdChar <= 1.15e+34) {
		tmp = t_0;
	} else if (NdChar <= 1.7e+135) {
		tmp = t_2 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	} else if (NdChar <= 4.4e+173) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	t_2 = NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))
	t_3 = t_2 + (NaChar / ((Vef / KbT) + 2.0))
	tmp = 0
	if NdChar <= -1.9e+29:
		tmp = t_3
	elif NdChar <= -1.46e-25:
		tmp = t_0
	elif NdChar <= -5.8e-60:
		tmp = t_3
	elif NdChar <= -4.4e-111:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	elif NdChar <= -7.2e-207:
		tmp = t_1
	elif NdChar <= 1.15e+34:
		tmp = t_0
	elif NdChar <= 1.7e+135:
		tmp = t_2 + (NaChar / (1.0 + (1.0 + (Ev / KbT))))
	elif NdChar <= 4.4e+173:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)))
	t_2 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT))))
	t_3 = Float64(t_2 + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)))
	tmp = 0.0
	if (NdChar <= -1.9e+29)
		tmp = t_3;
	elseif (NdChar <= -1.46e-25)
		tmp = t_0;
	elseif (NdChar <= -5.8e-60)
		tmp = t_3;
	elseif (NdChar <= -4.4e-111)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	elseif (NdChar <= -7.2e-207)
		tmp = t_1;
	elseif (NdChar <= 1.15e+34)
		tmp = t_0;
	elseif (NdChar <= 1.7e+135)
		tmp = Float64(t_2 + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(Ev / KbT)))));
	elseif (NdChar <= 4.4e+173)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	t_2 = NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)));
	t_3 = t_2 + (NaChar / ((Vef / KbT) + 2.0));
	tmp = 0.0;
	if (NdChar <= -1.9e+29)
		tmp = t_3;
	elseif (NdChar <= -1.46e-25)
		tmp = t_0;
	elseif (NdChar <= -5.8e-60)
		tmp = t_3;
	elseif (NdChar <= -4.4e-111)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	elseif (NdChar <= -7.2e-207)
		tmp = t_1;
	elseif (NdChar <= 1.15e+34)
		tmp = t_0;
	elseif (NdChar <= 1.7e+135)
		tmp = t_2 + (NaChar / (1.0 + (1.0 + (Ev / KbT))));
	elseif (NdChar <= 4.4e+173)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(t$95$2 + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -1.9e+29], t$95$3, If[LessEqual[NdChar, -1.46e-25], t$95$0, If[LessEqual[NdChar, -5.8e-60], t$95$3, If[LessEqual[NdChar, -4.4e-111], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, -7.2e-207], t$95$1, If[LessEqual[NdChar, 1.15e+34], t$95$0, If[LessEqual[NdChar, 1.7e+135], N[(t$95$2 + N[(NaChar / N[(1.0 + N[(1.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 4.4e+173], t$95$1, t$95$3]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if NdChar < -1.89999999999999985e29 or -1.46e-25 < NdChar < -5.7999999999999999e-60 or 4.4e173 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.9%

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

   6. Taylor expanded in Vef around 0 71.6%

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

   if -1.89999999999999985e29 < NdChar < -1.46e-25 or -7.1999999999999993e-207 < NdChar < 1.1499999999999999e34

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.5%

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

   6. Taylor expanded in mu around inf 49.1%

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

      1. associate-/l* 46.3%

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

   8. Simplified 46.3%

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

   9. Taylor expanded in KbT around 0 81.7%

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

       1. associate--l+ 81.7%

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

       2. sub-neg 81.7%

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

       3. associate-+r+ 81.7%

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

       4. mul-1-neg 81.7%

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

       5. mul-1-neg 81.7%

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

       6. associate-+r+ 81.7%

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

       7. sub-neg 81.7%

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

       8. associate--l+ 81.7%

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

       9. +-commutative 81.7%

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

   11. Simplified 81.7%

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

   if -5.7999999999999999e-60 < NdChar < -4.4e-111

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 71.2%

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

   6. Taylor expanded in Vef around inf 42.4%

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

   7. Taylor expanded in Vef around 0 23.3%

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

   8. Taylor expanded in NdChar around inf 71.2%

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

   if -4.4e-111 < NdChar < -7.1999999999999993e-207 or 1.70000000000000005e135 < NdChar < 4.4e173

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 78.3%

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

   6. Taylor expanded in mu around 0 74.2%

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

   if 1.1499999999999999e34 < NdChar < 1.70000000000000005e135

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in Ev around inf 76.9%

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

   6. Taylor expanded in Ev around 0 76.4%

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

4. Final simplification 76.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.9 \cdot 10^{+29}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -1.46 \cdot 10^{-25}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -5.8 \cdot 10^{-60}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -4.4 \cdot 10^{-111}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -7.2 \cdot 10^{-207}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.15 \cdot 10^{+34}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.7 \cdot 10^{+135}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{1 + \left(1 + \frac{Ev}{KbT}\right)}\\ \mathbf{elif}\;NdChar \leq 4.4 \cdot 10^{+173}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 66.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -8 \cdot 10^{+27} \lor \neg \left(NdChar \leq -1.65 \cdot 10^{-28} \lor \neg \left(NdChar \leq -2.8 \cdot 10^{-57}\right) \land \left(NdChar \leq 4.3 \cdot 10^{+33} \lor \neg \left(NdChar \leq 3.6 \cdot 10^{+130}\right) \land NdChar \leq 1.22 \cdot 10^{+177}\right)\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -8e+27)
         (not
          (or (<= NdChar -1.65e-28)
              (and (not (<= NdChar -2.8e-57))
                   (or (<= NdChar 4.3e+33)
                       (and (not (<= NdChar 3.6e+130))
                            (<= NdChar 1.22e+177)))))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
    (/ NaChar (+ (/ Vef KbT) 2.0)))
   (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -8e+27) || !((NdChar <= -1.65e-28) || (!(NdChar <= -2.8e-57) && ((NdChar <= 4.3e+33) || (!(NdChar <= 3.6e+130) && (NdChar <= 1.22e+177)))))) {
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else {
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-8d+27)) .or. (.not. (ndchar <= (-1.65d-28)) .or. (.not. (ndchar <= (-2.8d-57))) .and. (ndchar <= 4.3d+33) .or. (.not. (ndchar <= 3.6d+130)) .and. (ndchar <= 1.22d+177))) then
        tmp = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    else
        tmp = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -8e+27) || !((NdChar <= -1.65e-28) || (!(NdChar <= -2.8e-57) && ((NdChar <= 4.3e+33) || (!(NdChar <= 3.6e+130) && (NdChar <= 1.22e+177)))))) {
		tmp = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	} else {
		tmp = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -8e+27) or not ((NdChar <= -1.65e-28) or (not (NdChar <= -2.8e-57) and ((NdChar <= 4.3e+33) or (not (NdChar <= 3.6e+130) and (NdChar <= 1.22e+177))))):
		tmp = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	else:
		tmp = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -8e+27) || !((NdChar <= -1.65e-28) || (!(NdChar <= -2.8e-57) && ((NdChar <= 4.3e+33) || (!(NdChar <= 3.6e+130) && (NdChar <= 1.22e+177))))))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -8e+27) || ~(((NdChar <= -1.65e-28) || (~((NdChar <= -2.8e-57)) && ((NdChar <= 4.3e+33) || (~((NdChar <= 3.6e+130)) && (NdChar <= 1.22e+177)))))))
		tmp = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	else
		tmp = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -8e+27], N[Not[Or[LessEqual[NdChar, -1.65e-28], And[N[Not[LessEqual[NdChar, -2.8e-57]], $MachinePrecision], Or[LessEqual[NdChar, 4.3e+33], And[N[Not[LessEqual[NdChar, 3.6e+130]], $MachinePrecision], LessEqual[NdChar, 1.22e+177]]]]]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -8.0000000000000001e27 or -1.6500000000000001e-28 < NdChar < -2.7999999999999999e-57 or 4.30000000000000028e33 < NdChar < 3.6000000000000001e130 or 1.21999999999999999e177 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.2%

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

   6. Taylor expanded in Vef around 0 71.0%

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

   if -8.0000000000000001e27 < NdChar < -1.6500000000000001e-28 or -2.7999999999999999e-57 < NdChar < 4.30000000000000028e33 or 3.6000000000000001e130 < NdChar < 1.21999999999999999e177

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.6%

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

   6. Taylor expanded in mu around inf 45.4%

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

      1. associate-/l* 43.4%

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

   8. Simplified 43.4%

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

   9. Taylor expanded in KbT around 0 76.4%

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

       1. associate--l+ 76.4%

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

       2. sub-neg 76.4%

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

       3. associate-+r+ 76.4%

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

       4. mul-1-neg 76.4%

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

       5. mul-1-neg 76.4%

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

       6. associate-+r+ 76.4%

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

       7. sub-neg 76.4%

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

       8. associate--l+ 76.4%

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

       9. +-commutative 76.4%

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

   11. Simplified 76.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -8 \cdot 10^{+27} \lor \neg \left(NdChar \leq -1.65 \cdot 10^{-28} \lor \neg \left(NdChar \leq -2.8 \cdot 10^{-57}\right) \land \left(NdChar \leq 4.3 \cdot 10^{+33} \lor \neg \left(NdChar \leq 3.6 \cdot 10^{+130}\right) \land NdChar \leq 1.22 \cdot 10^{+177}\right)\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 66.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{if}\;NdChar \leq -4.6 \cdot 10^{+27}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq -7.5 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq -7 \cdot 10^{-56}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NdChar \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;NdChar \leq 1.2 \cdot 10^{+134} \lor \neg \left(NdChar \leq 4.4 \cdot 10^{+173}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT)))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT))))
          (/ NaChar (+ (/ Vef KbT) 2.0)))))
   (if (<= NdChar -4.6e+27)
     t_1
     (if (<= NdChar -7.5e-29)
       t_0
       (if (<= NdChar -7e-56)
         t_1
         (if (<= NdChar 1.1e+34)
           t_0
           (if (or (<= NdChar 1.2e+134) (not (<= NdChar 4.4e+173)))
             t_1
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
              (/ NdChar (+ (/ mu 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 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	double tmp;
	if (NdChar <= -4.6e+27) {
		tmp = t_1;
	} else if (NdChar <= -7.5e-29) {
		tmp = t_0;
	} else if (NdChar <= -7e-56) {
		tmp = t_1;
	} else if (NdChar <= 1.1e+34) {
		tmp = t_0;
	} else if ((NdChar <= 1.2e+134) || !(NdChar <= 4.4e+173)) {
		tmp = t_1;
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    t_1 = (ndchar / (1.0d0 + exp(((mu + (edonor + (vef - ec))) / kbt)))) + (nachar / ((vef / kbt) + 2.0d0))
    if (ndchar <= (-4.6d+27)) then
        tmp = t_1
    else if (ndchar <= (-7.5d-29)) then
        tmp = t_0
    else if (ndchar <= (-7d-56)) then
        tmp = t_1
    else if (ndchar <= 1.1d+34) then
        tmp = t_0
    else if ((ndchar <= 1.2d+134) .or. (.not. (ndchar <= 4.4d+173))) then
        tmp = t_1
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (ndchar / ((mu / 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 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double t_1 = (NdChar / (1.0 + Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	double tmp;
	if (NdChar <= -4.6e+27) {
		tmp = t_1;
	} else if (NdChar <= -7.5e-29) {
		tmp = t_0;
	} else if (NdChar <= -7e-56) {
		tmp = t_1;
	} else if (NdChar <= 1.1e+34) {
		tmp = t_0;
	} else if ((NdChar <= 1.2e+134) || !(NdChar <= 4.4e+173)) {
		tmp = t_1;
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	t_1 = (NdChar / (1.0 + math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0))
	tmp = 0
	if NdChar <= -4.6e+27:
		tmp = t_1
	elif NdChar <= -7.5e-29:
		tmp = t_0
	elif NdChar <= -7e-56:
		tmp = t_1
	elif NdChar <= 1.1e+34:
		tmp = t_0
	elif (NdChar <= 1.2e+134) or not (NdChar <= 4.4e+173):
		tmp = t_1
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)))) + Float64(NaChar / Float64(Float64(Vef / KbT) + 2.0)))
	tmp = 0.0
	if (NdChar <= -4.6e+27)
		tmp = t_1;
	elseif (NdChar <= -7.5e-29)
		tmp = t_0;
	elseif (NdChar <= -7e-56)
		tmp = t_1;
	elseif (NdChar <= 1.1e+34)
		tmp = t_0;
	elseif ((NdChar <= 1.2e+134) || !(NdChar <= 4.4e+173))
		tmp = t_1;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / Float64(Float64(mu / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	t_1 = (NdChar / (1.0 + exp(((mu + (EDonor + (Vef - Ec))) / KbT)))) + (NaChar / ((Vef / KbT) + 2.0));
	tmp = 0.0;
	if (NdChar <= -4.6e+27)
		tmp = t_1;
	elseif (NdChar <= -7.5e-29)
		tmp = t_0;
	elseif (NdChar <= -7e-56)
		tmp = t_1;
	elseif (NdChar <= 1.1e+34)
		tmp = t_0;
	elseif ((NdChar <= 1.2e+134) || ~((NdChar <= 4.4e+173)))
		tmp = t_1;
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / ((mu / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -4.6e+27], t$95$1, If[LessEqual[NdChar, -7.5e-29], t$95$0, If[LessEqual[NdChar, -7e-56], t$95$1, If[LessEqual[NdChar, 1.1e+34], t$95$0, If[Or[LessEqual[NdChar, 1.2e+134], N[Not[LessEqual[NdChar, 4.4e+173]], $MachinePrecision]], t$95$1, N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(mu / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -4.6000000000000001e27 or -7.50000000000000006e-29 < NdChar < -6.9999999999999996e-56 or 1.1000000000000001e34 < NdChar < 1.20000000000000003e134 or 4.4e173 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.3%

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

   6. Taylor expanded in Vef around 0 71.2%

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

   if -4.6000000000000001e27 < NdChar < -7.50000000000000006e-29 or -6.9999999999999996e-56 < NdChar < 1.1000000000000001e34

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 63.9%

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

   6. Taylor expanded in mu around inf 45.5%

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

      1. associate-/l* 43.3%

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

   8. Simplified 43.3%

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

   9. Taylor expanded in KbT around 0 75.9%

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

       1. associate--l+ 75.9%

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

       2. sub-neg 75.9%

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

       3. associate-+r+ 75.9%

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

       4. mul-1-neg 75.9%

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

       5. mul-1-neg 75.9%

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

       6. associate-+r+ 75.9%

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

       7. sub-neg 75.9%

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

       8. associate--l+ 75.9%

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

       9. +-commutative 75.9%

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

   11. Simplified 75.9%

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

   if 1.20000000000000003e134 < NdChar < 4.4e173

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 67.4%

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

   6. Taylor expanded in mu around 0 83.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq -7.5 \cdot 10^{-29}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq -7 \cdot 10^{-56}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{elif}\;NdChar \leq 1.1 \cdot 10^{+34}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;NdChar \leq 1.2 \cdot 10^{+134} \lor \neg \left(NdChar \leq 4.4 \cdot 10^{+173}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{\frac{mu}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 61.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;KbT \leq -8.8 \cdot 10^{-64}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq -9 \cdot 10^{-90}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.5 \cdot 10^{+109}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept (+ Vef Ev)) mu) KbT))))))
   (if (<= KbT -8.8e-64)
     t_0
     (if (<= KbT -9e-90)
       (/ NdChar (+ 1.0 (exp (/ mu KbT))))
       (if (<= KbT 2.5e+109)
         t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ Vef (+ EAccept (- Ev mu))) KbT))))
          (/ 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 t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -8.8e-64) {
		tmp = t_0;
	} else if (KbT <= -9e-90) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else if (KbT <= 2.5e+109) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (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) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((((eaccept + (vef + ev)) - mu) / kbt)))
    if (kbt <= (-8.8d-64)) then
        tmp = t_0
    else if (kbt <= (-9d-90)) then
        tmp = ndchar / (1.0d0 + exp((mu / kbt)))
    else if (kbt <= 2.5d+109) then
        tmp = t_0
    else
        tmp = (nachar / (1.0d0 + exp(((vef + (eaccept + (ev - mu))) / kbt)))) + (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 t_0 = NaChar / (1.0 + Math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	double tmp;
	if (KbT <= -8.8e-64) {
		tmp = t_0;
	} else if (KbT <= -9e-90) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else if (KbT <= 2.5e+109) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp((((EAccept + (Vef + Ev)) - mu) / KbT)))
	tmp = 0
	if KbT <= -8.8e-64:
		tmp = t_0
	elif KbT <= -9e-90:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	elif KbT <= 2.5e+109:
		tmp = t_0
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Float64(Vef + Ev)) - mu) / KbT))))
	tmp = 0.0
	if (KbT <= -8.8e-64)
		tmp = t_0;
	elseif (KbT <= -9e-90)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	elseif (KbT <= 2.5e+109)
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(EAccept + Float64(Ev - mu))) / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp((((EAccept + (Vef + Ev)) - mu) / KbT)));
	tmp = 0.0;
	if (KbT <= -8.8e-64)
		tmp = t_0;
	elseif (KbT <= -9e-90)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	elseif (KbT <= 2.5e+109)
		tmp = t_0;
	else
		tmp = (NaChar / (1.0 + exp(((Vef + (EAccept + (Ev - mu))) / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -8.8e-64], t$95$0, If[LessEqual[KbT, -9e-90], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 2.5e+109], t$95$0, N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(EAccept + N[(Ev - mu), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -8.7999999999999998e-64 or -9.00000000000000017e-90 < KbT < 2.5000000000000001e109

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 51.6%

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

   6. Taylor expanded in mu around inf 32.6%

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

      1. associate-/l* 32.2%

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

   8. Simplified 32.2%

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

   9. Taylor expanded in KbT around 0 64.1%

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

       1. associate--l+ 64.1%

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

       2. sub-neg 64.1%

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

       3. associate-+r+ 64.1%

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

       4. mul-1-neg 64.1%

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

       5. mul-1-neg 64.1%

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

       6. associate-+r+ 64.1%

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

       7. sub-neg 64.1%

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

       8. associate--l+ 64.1%

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

       9. +-commutative 64.1%

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

   11. Simplified 64.1%

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

   if -8.7999999999999998e-64 < KbT < -9.00000000000000017e-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%

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

   5. Taylor expanded in mu around inf 88.4%

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

   6. Taylor expanded in Vef around inf 88.4%

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

   7. Taylor expanded in Vef around 0 74.6%

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

   8. Taylor expanded in NdChar around inf 88.4%

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

   if 2.5000000000000001e109 < KbT

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 74.9%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -8.8 \cdot 10^{-64}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq -9 \cdot 10^{-90}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;KbT \leq 2.5 \cdot 10^{+109}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef + \left(EAccept + \left(Ev - mu\right)\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 39.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.05 \cdot 10^{+105} \lor \neg \left(NaChar \leq 5.5 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.05e+105) (not (<= NaChar 5.5e-27)))
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (/ NdChar (+ 1.0 (exp (/ 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 <= -2.05e+105) || !(NaChar <= 5.5e-27)) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = NdChar / (1.0 + exp((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 <= (-2.05d+105)) .or. (.not. (nachar <= 5.5d-27))) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = ndchar / (1.0d0 + exp((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 <= -2.05e+105) || !(NaChar <= 5.5e-27)) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2.05e+105) or not (NaChar <= 5.5e-27):
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	else:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -2.05e+105) || !(NaChar <= 5.5e-27))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(NdChar / Float64(1.0 + exp(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 <= -2.05e+105) || ~((NaChar <= 5.5e-27)))
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	else
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -2.05e+105], N[Not[LessEqual[NaChar, 5.5e-27]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.0500000000000001e105 or 5.5000000000000002e-27 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 60.1%

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

   6. Taylor expanded in EAccept around inf 47.4%

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

   if -2.0500000000000001e105 < NaChar < 5.5000000000000002e-27

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 61.4%

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

   6. Taylor expanded in Vef around inf 42.8%

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

   7. Taylor expanded in Vef around 0 36.4%

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

   8. Taylor expanded in NdChar around inf 39.8%

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

4. Final simplification 43.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.05 \cdot 10^{+105} \lor \neg \left(NaChar \leq 5.5 \cdot 10^{-27}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 38.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -4.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 3.4 \cdot 10^{-214}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -4.3e-60)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (if (<= KbT 3.4e-214)
     (/ NdChar (+ 1.0 (exp (/ mu KbT))))
     (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ 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 (KbT <= -4.3e-60) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 3.4e-214) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (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 (kbt <= (-4.3d-60)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 3.4d-214) then
        tmp = ndchar / (1.0d0 + exp((mu / kbt)))
    else
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (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 (KbT <= -4.3e-60) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 3.4e-214) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -4.3e-60:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= 3.4e-214:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	else:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -4.3e-60)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 3.4e-214)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + 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 (KbT <= -4.3e-60)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 3.4e-214)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	else
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -4.3e-60], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 3.4e-214], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -4.3000000000000001e-60

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 52.6%

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

   6. Taylor expanded in EAccept around inf 44.1%

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

   if -4.3000000000000001e-60 < KbT < 3.3999999999999999e-214

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 68.2%

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

   6. Taylor expanded in Vef around inf 49.5%

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

   7. Taylor expanded in Vef around 0 38.6%

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

   8. Taylor expanded in NdChar around inf 44.6%

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

   if 3.3999999999999999e-214 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 48.9%

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

   6. Taylor expanded in Ev around inf 35.4%

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

4. Final simplification 40.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.3 \cdot 10^{-60}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 3.4 \cdot 10^{-214}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 59.7% accurate, 2.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 53.2%

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

6. Taylor expanded in mu around inf 30.5%

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

   1. associate-/l* 30.1%

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

8. Simplified 30.1%

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

9. Taylor expanded in KbT around 0 60.6%

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

    1. associate--l+ 60.6%

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

    2. sub-neg 60.6%

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

    3. associate-+r+ 60.6%

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

    4. mul-1-neg 60.6%

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

    5. mul-1-neg 60.6%

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

    6. associate-+r+ 60.6%

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

    7. sub-neg 60.6%

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

    8. associate--l+ 60.6%

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

    9. +-commutative 60.6%

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

11. Simplified 60.6%

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

12. Final simplification 60.6%

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

Alternative 17: 39.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -4.5 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;KbT \leq 8 \cdot 10^{+101}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -4.5e+106)
   (* 0.5 (+ NdChar NaChar))
   (if (<= KbT 8e+101)
     (/ NdChar (+ 1.0 (exp (/ mu KbT))))
     (+ (/ NdChar 2.0) (/ NaChar (+ (/ EAccept KbT) 2.0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -4.5e+106) {
		tmp = 0.5 * (NdChar + NaChar);
	} else if (KbT <= 8e+101) {
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-4.5d+106)) then
        tmp = 0.5d0 * (ndchar + nachar)
    else if (kbt <= 8d+101) then
        tmp = ndchar / (1.0d0 + exp((mu / kbt)))
    else
        tmp = (ndchar / 2.0d0) + (nachar / ((eaccept / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -4.5e+106) {
		tmp = 0.5 * (NdChar + NaChar);
	} else if (KbT <= 8e+101) {
		tmp = NdChar / (1.0 + Math.exp((mu / KbT)));
	} else {
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -4.5e+106:
		tmp = 0.5 * (NdChar + NaChar)
	elif KbT <= 8e+101:
		tmp = NdChar / (1.0 + math.exp((mu / KbT)))
	else:
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -4.5e+106)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	elseif (KbT <= 8e+101)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT))));
	else
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(Float64(EAccept / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -4.5e+106)
		tmp = 0.5 * (NdChar + NaChar);
	elseif (KbT <= 8e+101)
		tmp = NdChar / (1.0 + exp((mu / KbT)));
	else
		tmp = (NdChar / 2.0) + (NaChar / ((EAccept / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -4.5e+106], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 8e+101], N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(N[(EAccept / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -4.4999999999999997e106

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 64.9%

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

   6. Taylor expanded in Vef around inf 49.1%

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

   7. Taylor expanded in Vef around 0 46.9%

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

   8. Taylor expanded in KbT around inf 45.7%

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

      1. distribute-lft-out 45.7%

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

   10. Simplified 45.7%

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

   if -4.4999999999999997e106 < KbT < 7.9999999999999998e101

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 63.9%

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

   6. Taylor expanded in Vef around inf 40.5%

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

   7. Taylor expanded in Vef around 0 27.2%

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

   8. Taylor expanded in NdChar around inf 33.1%

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

   if 7.9999999999999998e101 < KbT

   1. Initial program 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in KbT around inf 73.0%

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

   6. Taylor expanded in EAccept around inf 61.4%

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

   7. Taylor expanded in EAccept around 0 60.5%

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

4. Final simplification 39.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.5 \cdot 10^{+106}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;KbT \leq 8 \cdot 10^{+101}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{\frac{EAccept}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 28.4% accurate, 25.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Vef \leq 1.32 \cdot 10^{+135}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Vef 1.32e+135)
   (* 0.5 (+ NdChar NaChar))
   (/ NaChar (+ (/ 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 (Vef <= 1.32e+135) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / ((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 (vef <= 1.32d+135) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = nachar / ((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 (Vef <= 1.32e+135) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = NaChar / ((Vef / KbT) + 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Vef <= 1.32e+135:
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = NaChar / ((Vef / KbT) + 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Vef <= 1.32e+135)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(NaChar / 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 (Vef <= 1.32e+135)
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = NaChar / ((Vef / KbT) + 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Vef, 1.32e+135], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[(Vef / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Vef < 1.32e135

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 70.0%

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

   6. Taylor expanded in Vef around inf 47.4%

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

   7. Taylor expanded in Vef around 0 38.0%

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

   8. Taylor expanded in KbT around inf 28.3%

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

      1. distribute-lft-out 28.3%

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

   10. Simplified 28.3%

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

   if 1.32e135 < Vef

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 40.3%

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

   6. Taylor expanded in Vef around inf 31.5%

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

   7. Taylor expanded in Vef around 0 16.1%

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

   8. Taylor expanded in NdChar around 0 28.7%

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

4. Final simplification 28.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq 1.32 \cdot 10^{+135}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{\frac{Vef}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 27.6% accurate, 45.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in mu around inf 66.4%

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

6. Taylor expanded in Vef around inf 45.4%

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

7. Taylor expanded in Vef around 0 35.4%

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

8. Taylor expanded in KbT around inf 26.4%

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

   1. distribute-lft-out 26.4%

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

10. Simplified 26.4%

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

11. Final simplification 26.4%

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

Reproduce

herbie shell --seed 2024011 
(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))))))