Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 30.5s

Alternatives: 23

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{NdChar}{\mathsf{expm1}\left(\log \left(2 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}\right)\right)} + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NdChar (expm1 (log (+ 2.0 (exp (/ (+ Vef (+ mu (- EDonor Ec))) KbT))))))
  (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / expm1(log((2.0 + exp(((Vef + (mu + (EDonor - Ec))) / KbT)))))) + (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT))));
}

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / Math.expm1(Math.log((2.0 + Math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)))))) + (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT))));
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NdChar / math.expm1(math.log((2.0 + math.exp(((Vef + (mu + (EDonor - Ec))) / KbT)))))) + (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT))))

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NdChar / expm1(log(Float64(2.0 + exp(Float64(Float64(Vef + Float64(mu + Float64(EDonor - Ec))) / KbT)))))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))))
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NdChar / N[(Exp[N[Log[N[(2.0 + N[Exp[N[(N[(Vef + N[(mu + N[(EDonor - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $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%

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

   1. expm1-log1p-u 99.8%

      \[\leadsto \frac{NdChar}{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}\right)\right)}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} \]

   2. log1p-udef 100.0%

      \[\leadsto \frac{NdChar}{\mathsf{expm1}\left(\color{blue}{\log \left(1 + \left(1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}\right)\right)}\right)} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} \]

   3. associate-+r+ 100.0%

      \[\leadsto \frac{NdChar}{\mathsf{expm1}\left(\log \color{blue}{\left(\left(1 + 1\right) + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}\right)}\right)} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} \]

   4. metadata-eval 100.0%

      \[\leadsto \frac{NdChar}{\mathsf{expm1}\left(\log \left(\color{blue}{2} + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}\right)\right)} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} \]

   5. associate-+l- 100.0%

      \[\leadsto \frac{NdChar}{\mathsf{expm1}\left(\log \left(2 + e^{\frac{\color{blue}{Vef - \left(Ec - \left(EDonor + mu\right)\right)}}{KbT}}\right)\right)} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} \]

   6. associate--r+ 100.0%

      \[\leadsto \frac{NdChar}{\mathsf{expm1}\left(\log \left(2 + e^{\frac{Vef - \color{blue}{\left(\left(Ec - EDonor\right) - mu\right)}}{KbT}}\right)\right)} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} \]

5. Applied egg-rr 100.0%

   \[\leadsto \frac{NdChar}{\color{blue}{\mathsf{expm1}\left(\log \left(2 + e^{\frac{Vef - \left(\left(Ec - EDonor\right) - mu\right)}{KbT}}\right)\right)}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) + \left(EAccept - mu\right)}{KbT}}} \]

6. Final simplification 100.0%

   \[\leadsto \frac{NdChar}{\mathsf{expm1}\left(\log \left(2 + e^{\frac{Vef + \left(mu + \left(EDonor - Ec\right)\right)}{KbT}}\right)\right)} + \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} \]

Alternative 2: 71.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}}\\ t_2 := t_1 + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;Ev \leq -3.9 \cdot 10^{+175}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -3 \cdot 10^{+66}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq -2.5 \cdot 10^{-47}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Ev \leq -4.45 \cdot 10^{-197}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;Ev \leq 1.6 \cdot 10^{-52}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))))
        (t_1 (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor mu)) KbT)))))
        (t_2 (+ t_1 (/ NaChar (+ 1.0 (exp (/ Vef KbT)))))))
   (if (<= Ev -3.9e+175)
     (+ t_1 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= Ev -3e+66)
       t_2
       (if (<= Ev -2.5e-47)
         t_0
         (if (<= Ev -4.45e-197)
           t_2
           (if (<= Ev 1.6e-52)
             t_0
             (+ t_1 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	double t_1 = NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + exp((Vef / KbT))));
	double tmp;
	if (Ev <= -3.9e+175) {
		tmp = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Ev <= -3e+66) {
		tmp = t_2;
	} else if (Ev <= -2.5e-47) {
		tmp = t_0;
	} else if (Ev <= -4.45e-197) {
		tmp = t_2;
	} else if (Ev <= 1.6e-52) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    t_1 = ndchar / (1.0d0 + exp((((vef - ec) + (edonor + mu)) / kbt)))
    t_2 = t_1 + (nachar / (1.0d0 + exp((vef / kbt))))
    if (ev <= (-3.9d+175)) then
        tmp = t_1 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (ev <= (-3d+66)) then
        tmp = t_2
    else if (ev <= (-2.5d-47)) then
        tmp = t_0
    else if (ev <= (-4.45d-197)) then
        tmp = t_2
    else if (ev <= 1.6d-52) then
        tmp = t_0
    else
        tmp = t_1 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double t_1 = NdChar / (1.0 + Math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)));
	double t_2 = t_1 + (NaChar / (1.0 + Math.exp((Vef / KbT))));
	double tmp;
	if (Ev <= -3.9e+175) {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Ev <= -3e+66) {
		tmp = t_2;
	} else if (Ev <= -2.5e-47) {
		tmp = t_0;
	} else if (Ev <= -4.45e-197) {
		tmp = t_2;
	} else if (Ev <= 1.6e-52) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	t_1 = NdChar / (1.0 + math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))
	t_2 = t_1 + (NaChar / (1.0 + math.exp((Vef / KbT))))
	tmp = 0
	if Ev <= -3.9e+175:
		tmp = t_1 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Ev <= -3e+66:
		tmp = t_2
	elif Ev <= -2.5e-47:
		tmp = t_0
	elif Ev <= -4.45e-197:
		tmp = t_2
	elif Ev <= 1.6e-52:
		tmp = t_0
	else:
		tmp = t_1 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	t_1 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef - Ec) + Float64(EDonor + mu)) / KbT))))
	t_2 = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))))
	tmp = 0.0
	if (Ev <= -3.9e+175)
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Ev <= -3e+66)
		tmp = t_2;
	elseif (Ev <= -2.5e-47)
		tmp = t_0;
	elseif (Ev <= -4.45e-197)
		tmp = t_2;
	elseif (Ev <= 1.6e-52)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	t_1 = NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)));
	t_2 = t_1 + (NaChar / (1.0 + exp((Vef / KbT))));
	tmp = 0.0;
	if (Ev <= -3.9e+175)
		tmp = t_1 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Ev <= -3e+66)
		tmp = t_2;
	elseif (Ev <= -2.5e-47)
		tmp = t_0;
	elseif (Ev <= -4.45e-197)
		tmp = t_2;
	elseif (Ev <= 1.6e-52)
		tmp = t_0;
	else
		tmp = t_1 + (NaChar / (1.0 + exp((EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef - Ec), $MachinePrecision] + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -3.9e+175], N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -3e+66], t$95$2, If[LessEqual[Ev, -2.5e-47], t$95$0, If[LessEqual[Ev, -4.45e-197], t$95$2, If[LessEqual[Ev, 1.6e-52], t$95$0, N[(t$95$1 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if Ev < -3.89999999999999972e175

   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%

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

   4. Taylor expanded in Ev around inf 95.9%

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

   if -3.89999999999999972e175 < Ev < -3.00000000000000002e66 or -2.50000000000000006e-47 < Ev < -4.4500000000000001e-197

   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%

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

   4. Taylor expanded in Vef around inf 80.4%

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

   if -3.00000000000000002e66 < Ev < -2.50000000000000006e-47 or -4.4500000000000001e-197 < Ev < 1.60000000000000005e-52

   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%

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

   4. Taylor expanded in mu around inf 82.8%

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

   if 1.60000000000000005e-52 < 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%

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

   4. Taylor expanded in EAccept around inf 69.0%

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

4. Final simplification 79.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -3.9 \cdot 10^{+175}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -3 \cdot 10^{+66}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ev \leq -2.5 \cdot 10^{-47}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Ev \leq -4.45 \cdot 10^{-197}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;Ev \leq 1.6 \cdot 10^{-52}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 3: 63.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + e^{\frac{Vef}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ t_2 := \frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{\left(2 + \frac{\frac{KbT \cdot EAccept + KbT \cdot \frac{KbT \cdot \left(Vef + Ev\right)}{KbT}}{KbT}}{KbT}\right) - \frac{mu}{KbT}}\\ \mathbf{if}\;mu \leq -1.55 \cdot 10^{+87}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;mu \leq -1.1 \cdot 10^{-34}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;mu \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq -2.05 \cdot 10^{-140}:\\ \;\;\;\;\frac{NaChar}{t_0} + \frac{NdChar}{t_0}\\ \mathbf{elif}\;mu \leq 6.7 \cdot 10^{-276}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}}\\ \mathbf{elif}\;mu \leq 5.2 \cdot 10^{+62}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ 1.0 (exp (/ Vef KbT))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- mu) KbT))))))
        (t_2
         (+
          (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor mu)) KbT))))
          (/
           NaChar
           (-
            (+
             2.0
             (/
              (/ (+ (* KbT EAccept) (* KbT (/ (* KbT (+ Vef Ev)) KbT))) KbT)
              KbT))
            (/ mu KbT))))))
   (if (<= mu -1.55e+87)
     t_1
     (if (<= mu -1.1e-34)
       t_2
       (if (<= mu -1.25e-73)
         (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
         (if (<= mu -2.05e-140)
           (+ (/ NaChar t_0) (/ NdChar t_0))
           (if (<= mu 6.7e-276)
             (+
              (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
              (/ NdChar (- 2.0 (/ (- (- (- Ec EDonor) mu) Vef) KbT))))
             (if (<= mu 5.2e+62) t_2 t_1))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + exp((Vef / KbT));
	double t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	double t_2 = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / ((2.0 + ((((KbT * EAccept) + (KbT * ((KbT * (Vef + Ev)) / KbT))) / KbT) / KbT)) - (mu / KbT)));
	double tmp;
	if (mu <= -1.55e+87) {
		tmp = t_1;
	} else if (mu <= -1.1e-34) {
		tmp = t_2;
	} else if (mu <= -1.25e-73) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else if (mu <= -2.05e-140) {
		tmp = (NaChar / t_0) + (NdChar / t_0);
	} else if (mu <= 6.7e-276) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT)));
	} else if (mu <= 5.2e+62) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 1.0d0 + exp((vef / kbt))
    t_1 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    t_2 = (ndchar / (1.0d0 + exp((((vef - ec) + (edonor + mu)) / kbt)))) + (nachar / ((2.0d0 + ((((kbt * eaccept) + (kbt * ((kbt * (vef + ev)) / kbt))) / kbt) / kbt)) - (mu / kbt)))
    if (mu <= (-1.55d+87)) then
        tmp = t_1
    else if (mu <= (-1.1d-34)) then
        tmp = t_2
    else if (mu <= (-1.25d-73)) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else if (mu <= (-2.05d-140)) then
        tmp = (nachar / t_0) + (ndchar / t_0)
    else if (mu <= 6.7d-276) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / (2.0d0 - ((((ec - edonor) - mu) - vef) / kbt)))
    else if (mu <= 5.2d+62) then
        tmp = t_2
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 1.0 + Math.exp((Vef / KbT));
	double t_1 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	double t_2 = (NdChar / (1.0 + Math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / ((2.0 + ((((KbT * EAccept) + (KbT * ((KbT * (Vef + Ev)) / KbT))) / KbT) / KbT)) - (mu / KbT)));
	double tmp;
	if (mu <= -1.55e+87) {
		tmp = t_1;
	} else if (mu <= -1.1e-34) {
		tmp = t_2;
	} else if (mu <= -1.25e-73) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else if (mu <= -2.05e-140) {
		tmp = (NaChar / t_0) + (NdChar / t_0);
	} else if (mu <= 6.7e-276) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT)));
	} else if (mu <= 5.2e+62) {
		tmp = t_2;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 1.0 + math.exp((Vef / KbT))
	t_1 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	t_2 = (NdChar / (1.0 + math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / ((2.0 + ((((KbT * EAccept) + (KbT * ((KbT * (Vef + Ev)) / KbT))) / KbT) / KbT)) - (mu / KbT)))
	tmp = 0
	if mu <= -1.55e+87:
		tmp = t_1
	elif mu <= -1.1e-34:
		tmp = t_2
	elif mu <= -1.25e-73:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	elif mu <= -2.05e-140:
		tmp = (NaChar / t_0) + (NdChar / t_0)
	elif mu <= 6.7e-276:
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT)))
	elif mu <= 5.2e+62:
		tmp = t_2
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(1.0 + exp(Float64(Vef / KbT)))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef - Ec) + Float64(EDonor + mu)) / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(Float64(Float64(KbT * EAccept) + Float64(KbT * Float64(Float64(KbT * Float64(Vef + Ev)) / KbT))) / KbT) / KbT)) - Float64(mu / KbT))))
	tmp = 0.0
	if (mu <= -1.55e+87)
		tmp = t_1;
	elseif (mu <= -1.1e-34)
		tmp = t_2;
	elseif (mu <= -1.25e-73)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	elseif (mu <= -2.05e-140)
		tmp = Float64(Float64(NaChar / t_0) + Float64(NdChar / t_0));
	elseif (mu <= 6.7e-276)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / Float64(2.0 - Float64(Float64(Float64(Float64(Ec - EDonor) - mu) - Vef) / KbT))));
	elseif (mu <= 5.2e+62)
		tmp = t_2;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 1.0 + exp((Vef / KbT));
	t_1 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	t_2 = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / ((2.0 + ((((KbT * EAccept) + (KbT * ((KbT * (Vef + Ev)) / KbT))) / KbT) / KbT)) - (mu / KbT)));
	tmp = 0.0;
	if (mu <= -1.55e+87)
		tmp = t_1;
	elseif (mu <= -1.1e-34)
		tmp = t_2;
	elseif (mu <= -1.25e-73)
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	elseif (mu <= -2.05e-140)
		tmp = (NaChar / t_0) + (NdChar / t_0);
	elseif (mu <= 6.7e-276)
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT)));
	elseif (mu <= 5.2e+62)
		tmp = t_2;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef - Ec), $MachinePrecision] + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(N[(N[(KbT * EAccept), $MachinePrecision] + N[(KbT * N[(N[(KbT * N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[mu, -1.55e+87], t$95$1, If[LessEqual[mu, -1.1e-34], t$95$2, If[LessEqual[mu, -1.25e-73], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, -2.05e-140], N[(N[(NaChar / t$95$0), $MachinePrecision] + N[(NdChar / t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 6.7e-276], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 - N[(N[(N[(N[(Ec - EDonor), $MachinePrecision] - mu), $MachinePrecision] - Vef), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[mu, 5.2e+62], t$95$2, t$95$1]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if mu < -1.55e87 or 5.19999999999999968e62 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 90.6%

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

   5. Taylor expanded in mu around inf 79.8%

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

      1. associate-*r/ 41.3%

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

      2. mul-1-neg 41.3%

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

   7. Simplified 79.8%

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

   if -1.55e87 < mu < -1.0999999999999999e-34 or 6.69999999999999983e-276 < mu < 5.19999999999999968e62

   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%

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

   4. Taylor expanded in KbT around inf 71.7%

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

      1. frac-add 64.9%

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

      2. associate-/r* 70.6%

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

      3. *-commutative 70.6%

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

      4. *-commutative 70.6%

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

   6. Applied egg-rr 70.6%

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

      1. frac-add 70.5%

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

      2. associate-/r* 74.0%

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

      3. *-commutative 74.0%

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

      4. *-commutative 74.0%

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

      5. distribute-lft-out 75.2%

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

   8. Applied egg-rr 75.2%

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

   if -1.0999999999999999e-34 < mu < -1.25e-73

   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%

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

   4. Taylor expanded in EAccept around inf 73.1%

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

   5. Taylor expanded in KbT around inf 59.3%

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

      1. associate--l+ 59.3%

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

      2. sub-neg 59.3%

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

      3. mul-1-neg 59.3%

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

      4. +-commutative 59.3%

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

      5. associate-+r+ 59.3%

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

      6. +-commutative 59.3%

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

      7. associate-+r+ 59.3%

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

      8. mul-1-neg 59.3%

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

      9. neg-sub0 59.3%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 59.3%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 59.3%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 59.3%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 59.3%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 59.3%

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

      15. +-commutative 59.3%

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

      16. sub-neg 59.3%

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

      17. div-sub 59.6%

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

   7. Simplified 59.6%

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

   8. Taylor expanded in EDonor around inf 45.5%

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

      1. associate-/l* 45.5%

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

   10. Simplified 45.5%

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

   11. Taylor expanded in KbT around 0 73.2%

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

   if -1.25e-73 < mu < -2.0500000000000001e-140

   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%

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

   4. Taylor expanded in Vef around inf 91.7%

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

   5. Taylor expanded in EDonor around 0 91.7%

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

      1. +-commutative 39.1%

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

      2. associate--l+ 39.1%

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

   7. Simplified 91.7%

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

   8. Taylor expanded in Vef around inf 91.7%

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

   if -2.0500000000000001e-140 < mu < 6.69999999999999983e-276

   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%

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

   4. Taylor expanded in KbT around inf 77.9%

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

      1. associate--l+ 60.6%

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

      2. sub-neg 60.6%

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

      3. mul-1-neg 60.6%

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

      4. +-commutative 60.6%

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

      5. associate-+r+ 60.6%

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

      6. +-commutative 60.6%

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

      7. associate-+r+ 60.6%

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

      8. mul-1-neg 60.6%

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

      9. neg-sub0 60.6%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 60.6%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 62.7%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 62.7%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 62.7%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 62.7%

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

      15. +-commutative 62.7%

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

      16. sub-neg 62.7%

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

      17. div-sub 62.7%

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

   6. Simplified 80.1%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -1.55 \cdot 10^{+87}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{elif}\;mu \leq -1.1 \cdot 10^{-34}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{\left(2 + \frac{\frac{KbT \cdot EAccept + KbT \cdot \frac{KbT \cdot \left(Vef + Ev\right)}{KbT}}{KbT}}{KbT}\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;mu \leq -1.25 \cdot 10^{-73}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;mu \leq -2.05 \cdot 10^{-140}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;mu \leq 6.7 \cdot 10^{-276}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}}\\ \mathbf{elif}\;mu \leq 5.2 \cdot 10^{+62}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{\left(2 + \frac{\frac{KbT \cdot EAccept + KbT \cdot \frac{KbT \cdot \left(Vef + Ev\right)}{KbT}}{KbT}}{KbT}\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \end{array} \]

Alternative 4: 72.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{if}\;Vef \leq -4.7 \cdot 10^{+126}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;Vef \leq -6.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.3 \cdot 10^{+103}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
          (/ NdChar (+ 1.0 (exp (/ mu KbT)))))))
   (if (<= Vef -4.7e+126)
     t_0
     (if (<= Vef -6.2e-92)
       (+
        (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor mu)) KbT))))
        (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
       (if (<= Vef 2.3e+103)
         t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NdChar (+ 1.0 (exp (/ (+ Vef (- mu Ec)) KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	double tmp;
	if (Vef <= -4.7e+126) {
		tmp = t_0;
	} else if (Vef <= -6.2e-92) {
		tmp = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (Vef <= 2.3e+103) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    if (vef <= (-4.7d+126)) then
        tmp = t_0
    else if (vef <= (-6.2d-92)) then
        tmp = (ndchar / (1.0d0 + exp((((vef - ec) + (edonor + mu)) / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (vef <= 2.3d+103) then
        tmp = t_0
    else
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp(((vef + (mu - ec)) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	double tmp;
	if (Vef <= -4.7e+126) {
		tmp = t_0;
	} else if (Vef <= -6.2e-92) {
		tmp = (NdChar / (1.0 + Math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (Vef <= 2.3e+103) {
		tmp = t_0;
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp(((Vef + (mu - Ec)) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	tmp = 0
	if Vef <= -4.7e+126:
		tmp = t_0
	elif Vef <= -6.2e-92:
		tmp = (NdChar / (1.0 + math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif Vef <= 2.3e+103:
		tmp = t_0
	else:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp(((Vef + (mu - Ec)) / 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(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))))
	tmp = 0.0
	if (Vef <= -4.7e+126)
		tmp = t_0;
	elseif (Vef <= -6.2e-92)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef - Ec) + Float64(EDonor + mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (Vef <= 2.3e+103)
		tmp = t_0;
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(mu - Ec)) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	tmp = 0.0;
	if (Vef <= -4.7e+126)
		tmp = t_0;
	elseif (Vef <= -6.2e-92)
		tmp = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (Vef <= 2.3e+103)
		tmp = t_0;
	else
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / 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[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Vef, -4.7e+126], t$95$0, If[LessEqual[Vef, -6.2e-92], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef - Ec), $MachinePrecision] + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Vef, 2.3e+103], t$95$0, N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if Vef < -4.6999999999999999e126 or -6.2000000000000002e-92 < Vef < 2.30000000000000008e103

   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%

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

   4. Taylor expanded in mu around inf 78.5%

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

   if -4.6999999999999999e126 < Vef < -6.2000000000000002e-92

   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%

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

   4. Taylor expanded in EAccept around inf 79.3%

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

   if 2.30000000000000008e103 < 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%

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

   4. Taylor expanded in Vef around inf 93.1%

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

   5. Taylor expanded in EDonor around 0 93.0%

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

      1. +-commutative 28.9%

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

      2. associate--l+ 28.9%

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

   7. Simplified 93.0%

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

4. Final simplification 81.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Vef \leq -4.7 \cdot 10^{+126}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{elif}\;Vef \leq -6.2 \cdot 10^{-92}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;Vef \leq 2.3 \cdot 10^{+103}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}}\\ \end{array} \]

Alternative 5: 70.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}}\\ \mathbf{if}\;Ev \leq -1.4 \cdot 10^{+153}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.9 \cdot 10^{-145}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}}\\ \mathbf{elif}\;Ev \leq 1.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor mu)) KbT))))))
   (if (<= Ev -1.4e+153)
     (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= Ev -1.9e-145)
       (+
        (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
        (/ NdChar (+ 1.0 (exp (/ (+ Vef (- mu Ec)) KbT)))))
       (if (<= Ev 1.1e-58)
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
          (/ NdChar (+ 1.0 (exp (/ 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((((Vef - Ec) + (EDonor + mu)) / KbT)));
	double tmp;
	if (Ev <= -1.4e+153) {
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Ev <= -1.9e-145) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT))));
	} else if (Ev <= 1.1e-58) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + exp((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((((vef - ec) + (edonor + mu)) / kbt)))
    if (ev <= (-1.4d+153)) then
        tmp = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (ev <= (-1.9d-145)) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp(((vef + (mu - ec)) / kbt))))
    else if (ev <= 1.1d-58) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / (1.0d0 + exp((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((((Vef - Ec) + (EDonor + mu)) / KbT)));
	double tmp;
	if (Ev <= -1.4e+153) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Ev <= -1.9e-145) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp(((Vef + (mu - Ec)) / KbT))));
	} else if (Ev <= 1.1e-58) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((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((((Vef - Ec) + (EDonor + mu)) / KbT)))
	tmp = 0
	if Ev <= -1.4e+153:
		tmp = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Ev <= -1.9e-145:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp(((Vef + (mu - Ec)) / KbT))))
	elif Ev <= 1.1e-58:
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + math.exp((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(Float64(Vef - Ec) + Float64(EDonor + mu)) / KbT))))
	tmp = 0.0
	if (Ev <= -1.4e+153)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Ev <= -1.9e-145)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(mu - Ec)) / KbT)))));
	elseif (Ev <= 1.1e-58)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(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((((Vef - Ec) + (EDonor + mu)) / KbT)));
	tmp = 0.0;
	if (Ev <= -1.4e+153)
		tmp = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Ev <= -1.9e-145)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT))));
	elseif (Ev <= 1.1e-58)
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + exp((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[(N[(Vef - Ec), $MachinePrecision] + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[Ev, -1.4e+153], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -1.9e-145], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, 1.1e-58], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / 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 Ev < -1.39999999999999993e153

   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%

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

   4. Taylor expanded in Ev around inf 93.6%

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

   if -1.39999999999999993e153 < Ev < -1.9000000000000001e-145

   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%

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

   4. Taylor expanded in Vef around inf 77.0%

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

   5. Taylor expanded in EDonor around 0 74.9%

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

      1. +-commutative 29.0%

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

      2. associate--l+ 29.0%

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

   7. Simplified 74.9%

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

   if -1.9000000000000001e-145 < Ev < 1.10000000000000003e-58

   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%

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

   4. Taylor expanded in mu around inf 80.6%

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

   if 1.10000000000000003e-58 < 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%

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

   4. Taylor expanded in EAccept around inf 69.9%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -1.4 \cdot 10^{+153}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -1.9 \cdot 10^{-145}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}}\\ \mathbf{elif}\;Ev \leq 1.1 \cdot 10^{-58}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 6: 100.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+
  (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
  (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor 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 - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + 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 - mu) + (vef + ev)) / kbt)))) + (ndchar / (1.0d0 + exp((((vef - ec) + (edonor + 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 - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((((Vef - Ec) + (EDonor + mu)) / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

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

4. Final simplification 100.0%

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

Alternative 7: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -4.7 \cdot 10^{+98} \lor \neg \left(mu \leq 4.4 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= mu -4.7e+98) (not (<= mu 4.4e+25)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
    (/ NdChar (+ 1.0 (exp (/ mu KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
    (/ NdChar (+ 1.0 (exp (/ (+ Vef (- mu Ec)) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -4.7e+98) || !(mu <= 4.4e+25)) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((mu <= (-4.7d+98)) .or. (.not. (mu <= 4.4d+25))) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / (1.0d0 + exp((mu / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp(((vef + (mu - ec)) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -4.7e+98) || !(mu <= 4.4e+25)) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + Math.exp((mu / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp(((Vef + (mu - Ec)) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (mu <= -4.7e+98) or not (mu <= 4.4e+25):
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + math.exp((mu / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp(((Vef + (mu - Ec)) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((mu <= -4.7e+98) || !(mu <= 4.4e+25))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(mu - Ec)) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((mu <= -4.7e+98) || ~((mu <= 4.4e+25)))
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (1.0 + exp((mu / KbT))));
	else
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[mu, -4.7e+98], N[Not[LessEqual[mu, 4.4e+25]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if mu < -4.6999999999999997e98 or 4.4000000000000001e25 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 89.9%

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

   if -4.6999999999999997e98 < mu < 4.4000000000000001e25

   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%

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

   4. Taylor expanded in Vef around inf 79.1%

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

   5. Taylor expanded in EDonor around 0 76.6%

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

      1. +-commutative 22.5%

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

      2. associate--l+ 22.5%

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

   7. Simplified 76.6%

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

4. Final simplification 81.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -4.7 \cdot 10^{+98} \lor \neg \left(mu \leq 4.4 \cdot 10^{+25}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}}\\ \end{array} \]

Alternative 8: 69.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -2.65 \cdot 10^{+132} \lor \neg \left(mu \leq 4.9 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= mu -2.65e+132) (not (<= mu 4.9e+63)))
   (+
    (/ NdChar (+ 1.0 (exp (/ mu KbT))))
    (/ NaChar (+ 1.0 (exp (/ (- mu) KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ Vef KbT))))
    (/ NdChar (+ 1.0 (exp (/ (+ Vef (- mu Ec)) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -2.65e+132) || !(mu <= 4.9e+63)) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((mu <= (-2.65d+132)) .or. (.not. (mu <= 4.9d+63))) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((-mu / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / (1.0d0 + exp(((vef + (mu - ec)) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -2.65e+132) || !(mu <= 4.9e+63)) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((-mu / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / (1.0 + Math.exp(((Vef + (mu - Ec)) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (mu <= -2.65e+132) or not (mu <= 4.9e+63):
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((-mu / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / (1.0 + math.exp(((Vef + (mu - Ec)) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((mu <= -2.65e+132) || !(mu <= 4.9e+63))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(-mu) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(mu - Ec)) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((mu <= -2.65e+132) || ~((mu <= 4.9e+63)))
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((-mu / KbT))));
	else
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[mu, -2.65e+132], N[Not[LessEqual[mu, 4.9e+63]], $MachinePrecision]], 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], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if mu < -2.65e132 or 4.8999999999999997e63 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in mu around inf 90.3%

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

   5. Taylor expanded in mu around inf 83.4%

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

      1. associate-*r/ 42.1%

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

      2. mul-1-neg 42.1%

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

   7. Simplified 83.4%

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

   if -2.65e132 < mu < 4.8999999999999997e63

   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%

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

   4. Taylor expanded in Vef around inf 77.7%

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

   5. Taylor expanded in EDonor around 0 74.8%

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

      1. +-commutative 22.8%

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

      2. associate--l+ 22.8%

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

   7. Simplified 74.8%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -2.65 \cdot 10^{+132} \lor \neg \left(mu \leq 4.9 \cdot 10^{+63}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{-mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}}\\ \end{array} \]

Alternative 9: 66.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}}\\ \mathbf{if}\;NaChar \leq -1.4 \cdot 10^{-14}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;NaChar \leq 6.6 \cdot 10^{-162}:\\ \;\;\;\;t_0 + \frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-146} \lor \neg \left(NaChar \leq 1.9 \cdot 10^{-43}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor mu)) KbT)))))
        (t_1
         (+
          (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
          (/ NdChar (- 2.0 (/ (- (- (- Ec EDonor) mu) Vef) KbT))))))
   (if (<= NaChar -1.4e-14)
     t_1
     (if (<= NaChar 6.6e-162)
       (+ t_0 (/ NaChar (+ 2.0 (/ Vef KbT))))
       (if (or (<= NaChar 1.45e-146) (not (<= NaChar 1.9e-43)))
         t_1
         (+ t_0 (/ NaChar (/ (- (+ 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 t_0 = NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)));
	double t_1 = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT)));
	double tmp;
	if (NaChar <= -1.4e-14) {
		tmp = t_1;
	} else if (NaChar <= 6.6e-162) {
		tmp = t_0 + (NaChar / (2.0 + (Vef / KbT)));
	} else if ((NaChar <= 1.45e-146) || !(NaChar <= 1.9e-43)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NaChar / (((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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((((vef - ec) + (edonor + mu)) / kbt)))
    t_1 = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / (2.0d0 - ((((ec - edonor) - mu) - vef) / kbt)))
    if (nachar <= (-1.4d-14)) then
        tmp = t_1
    else if (nachar <= 6.6d-162) then
        tmp = t_0 + (nachar / (2.0d0 + (vef / kbt)))
    else if ((nachar <= 1.45d-146) .or. (.not. (nachar <= 1.9d-43))) then
        tmp = t_1
    else
        tmp = t_0 + (nachar / (((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 t_0 = NdChar / (1.0 + Math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)));
	double t_1 = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT)));
	double tmp;
	if (NaChar <= -1.4e-14) {
		tmp = t_1;
	} else if (NaChar <= 6.6e-162) {
		tmp = t_0 + (NaChar / (2.0 + (Vef / KbT)));
	} else if ((NaChar <= 1.45e-146) || !(NaChar <= 1.9e-43)) {
		tmp = t_1;
	} else {
		tmp = t_0 + (NaChar / (((EAccept + (Vef + Ev)) - mu) / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))
	t_1 = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT)))
	tmp = 0
	if NaChar <= -1.4e-14:
		tmp = t_1
	elif NaChar <= 6.6e-162:
		tmp = t_0 + (NaChar / (2.0 + (Vef / KbT)))
	elif (NaChar <= 1.45e-146) or not (NaChar <= 1.9e-43):
		tmp = t_1
	else:
		tmp = t_0 + (NaChar / (((EAccept + (Vef + Ev)) - mu) / 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(Float64(Vef - Ec) + Float64(EDonor + mu)) / KbT))))
	t_1 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / Float64(2.0 - Float64(Float64(Float64(Float64(Ec - EDonor) - mu) - Vef) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.4e-14)
		tmp = t_1;
	elseif (NaChar <= 6.6e-162)
		tmp = Float64(t_0 + Float64(NaChar / Float64(2.0 + Float64(Vef / KbT))));
	elseif ((NaChar <= 1.45e-146) || !(NaChar <= 1.9e-43))
		tmp = t_1;
	else
		tmp = Float64(t_0 + Float64(NaChar / 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)
	t_0 = NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)));
	t_1 = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.4e-14)
		tmp = t_1;
	elseif (NaChar <= 6.6e-162)
		tmp = t_0 + (NaChar / (2.0 + (Vef / KbT)));
	elseif ((NaChar <= 1.45e-146) || ~((NaChar <= 1.9e-43)))
		tmp = t_1;
	else
		tmp = t_0 + (NaChar / (((EAccept + (Vef + Ev)) - mu) / 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[(N[(Vef - Ec), $MachinePrecision] + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 - N[(N[(N[(N[(Ec - EDonor), $MachinePrecision] - mu), $MachinePrecision] - Vef), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.4e-14], t$95$1, If[LessEqual[NaChar, 6.6e-162], N[(t$95$0 + N[(NaChar / N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, 1.45e-146], N[Not[LessEqual[NaChar, 1.9e-43]], $MachinePrecision]], t$95$1, N[(t$95$0 + N[(NaChar / N[(N[(N[(EAccept + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.4e-14 or 6.60000000000000026e-162 < NaChar < 1.45000000000000005e-146 or 1.89999999999999985e-43 < 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%

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

   4. Taylor expanded in KbT around inf 64.6%

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

      1. associate--l+ 43.3%

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

      2. sub-neg 43.3%

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

      3. mul-1-neg 43.3%

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

      4. +-commutative 43.3%

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

      5. associate-+r+ 43.3%

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

      6. +-commutative 43.3%

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

      7. associate-+r+ 43.3%

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

      8. mul-1-neg 43.3%

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

      9. neg-sub0 43.3%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 43.3%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 44.0%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 44.0%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 45.5%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 45.5%

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

      15. +-commutative 45.5%

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

      16. sub-neg 45.5%

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

      17. div-sub 46.3%

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

   6. Simplified 72.5%

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

   if -1.4e-14 < NaChar < 6.60000000000000026e-162

   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%

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

   4. Taylor expanded in Vef around inf 77.7%

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

   5. Taylor expanded in Vef around 0 72.5%

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

   if 1.45000000000000005e-146 < NaChar < 1.89999999999999985e-43

   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%

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

   4. Taylor expanded in KbT around inf 67.4%

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

   5. Taylor expanded in KbT around 0 73.2%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.4 \cdot 10^{-14}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 6.6 \cdot 10^{-162}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.45 \cdot 10^{-146} \lor \neg \left(NaChar \leq 1.9 \cdot 10^{-43}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{\frac{\left(EAccept + \left(Vef + Ev\right)\right) - mu}{KbT}}\\ \end{array} \]

Alternative 10: 60.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2 \cdot 10^{+30} \lor \neg \left(NaChar \leq 7200\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2e+30) (not (<= NaChar 7200.0)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
    (/ NdChar 2.0))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor mu)) KbT))))
    (/ NaChar (+ 2.0 (/ Vef KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2e+30) || !(NaChar <= 7200.0)) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-2d+30)) .or. (.not. (nachar <= 7200.0d0))) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((((vef - ec) + (edonor + mu)) / kbt)))) + (nachar / (2.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2e+30) || !(NaChar <= 7200.0)) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2e+30) or not (NaChar <= 7200.0):
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -2e+30) || !(NaChar <= 7200.0))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef - Ec) + Float64(EDonor + mu)) / KbT)))) + Float64(NaChar / Float64(2.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -2e+30) || ~((NaChar <= 7200.0)))
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -2e+30], N[Not[LessEqual[NaChar, 7200.0]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef - Ec), $MachinePrecision] + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2e30 or 7200 < 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%

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

   4. Taylor expanded in KbT around inf 61.7%

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

   if -2e30 < NaChar < 7200

   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%

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

   4. Taylor expanded in Vef around inf 77.4%

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

   5. Taylor expanded in Vef around 0 67.7%

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

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2 \cdot 10^{+30} \lor \neg \left(NaChar \leq 7200\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \end{array} \]

Alternative 11: 62.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.55 \cdot 10^{+27} \lor \neg \left(NaChar \leq 26000\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -2.55e+27) (not (<= NaChar 26000.0)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
    (/ NdChar (+ 2.0 (/ mu KbT))))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor mu)) KbT))))
    (/ NaChar (+ 2.0 (/ Vef KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.55e+27) || !(NaChar <= 26000.0)) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 + (mu / KbT)));
	} else {
		tmp = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-2.55d+27)) .or. (.not. (nachar <= 26000.0d0))) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / (2.0d0 + (mu / kbt)))
    else
        tmp = (ndchar / (1.0d0 + exp((((vef - ec) + (edonor + mu)) / kbt)))) + (nachar / (2.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -2.55e+27) || !(NaChar <= 26000.0)) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 + (mu / KbT)));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -2.55e+27) or not (NaChar <= 26000.0):
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 + (mu / KbT)))
	else:
		tmp = (NdChar / (1.0 + math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -2.55e+27) || !(NaChar <= 26000.0))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / Float64(2.0 + Float64(mu / KbT))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef - Ec) + Float64(EDonor + mu)) / KbT)))) + Float64(NaChar / Float64(2.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -2.55e+27) || ~((NaChar <= 26000.0)))
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / (2.0 + (mu / KbT)));
	else
		tmp = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -2.55e+27], N[Not[LessEqual[NaChar, 26000.0]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef - Ec), $MachinePrecision] + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -2.55e27 or 26000 < 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%

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

   4. Taylor expanded in mu around inf 76.9%

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

   5. Taylor expanded in mu around 0 65.4%

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

   if -2.55e27 < NaChar < 26000

   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%

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

   4. Taylor expanded in Vef around inf 77.4%

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

   5. Taylor expanded in Vef around 0 67.7%

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

4. Final simplification 66.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.55 \cdot 10^{+27} \lor \neg \left(NaChar \leq 26000\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2 + \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \end{array} \]

Alternative 12: 57.7% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -7 \cdot 10^{+28} \lor \neg \left(NaChar \leq 1650\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NaChar -7e+28) (not (<= NaChar 1650.0)))
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
    (/ NdChar 2.0))
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ Vef (- mu Ec)) KbT))))
    (/ NaChar (+ 2.0 (/ Vef KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -7e+28) || !(NaChar <= 1650.0)) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((nachar <= (-7d+28)) .or. (.not. (nachar <= 1650.0d0))) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((vef + (mu - ec)) / kbt)))) + (nachar / (2.0d0 + (vef / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NaChar <= -7e+28) || !(NaChar <= 1650.0)) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((Vef + (mu - Ec)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NaChar <= -7e+28) or not (NaChar <= 1650.0):
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp(((Vef + (mu - Ec)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NaChar <= -7e+28) || !(NaChar <= 1650.0))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(mu - Ec)) / KbT)))) + Float64(NaChar / Float64(2.0 + Float64(Vef / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NaChar <= -7e+28) || ~((NaChar <= 1650.0)))
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT)))) + (NaChar / (2.0 + (Vef / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NaChar, -7e+28], N[Not[LessEqual[NaChar, 1650.0]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(2.0 + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -6.9999999999999999e28 or 1650 < 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%

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

   4. Taylor expanded in KbT around inf 61.7%

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

   if -6.9999999999999999e28 < NaChar < 1650

   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%

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

   4. Taylor expanded in Vef around inf 77.4%

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

   5. Taylor expanded in EDonor around 0 73.8%

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

      1. +-commutative 38.6%

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

      2. associate--l+ 38.6%

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

   7. Simplified 73.8%

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

   8. Taylor expanded in Vef around 0 63.3%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7 \cdot 10^{+28} \lor \neg \left(NaChar \leq 1650\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}} + \frac{NaChar}{2 + \frac{Vef}{KbT}}\\ \end{array} \]

Alternative 13: 50.3% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}}\\ \mathbf{if}\;NdChar \leq -4.8 \cdot 10^{+71}:\\ \;\;\;\;t_0 + \frac{KbT}{\frac{Ev}{NaChar}}\\ \mathbf{elif}\;NdChar \leq 2 \cdot 10^{+184}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{\frac{EAccept}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor mu)) KbT))))))
   (if (<= NdChar -4.8e+71)
     (+ t_0 (/ KbT (/ Ev NaChar)))
     (if (<= NdChar 2e+184)
       (+
        (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
        (/ NdChar 2.0))
       (+ t_0 (/ NaChar (/ EAccept KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)));
	double tmp;
	if (NdChar <= -4.8e+71) {
		tmp = t_0 + (KbT / (Ev / NaChar));
	} else if (NdChar <= 2e+184) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = t_0 + (NaChar / (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((((vef - ec) + (edonor + mu)) / kbt)))
    if (ndchar <= (-4.8d+71)) then
        tmp = t_0 + (kbt / (ev / nachar))
    else if (ndchar <= 2d+184) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = t_0 + (nachar / (eaccept / kbt))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)));
	double tmp;
	if (NdChar <= -4.8e+71) {
		tmp = t_0 + (KbT / (Ev / NaChar));
	} else if (NdChar <= 2e+184) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = t_0 + (NaChar / (EAccept / KbT));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))
	tmp = 0
	if NdChar <= -4.8e+71:
		tmp = t_0 + (KbT / (Ev / NaChar))
	elif NdChar <= 2e+184:
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = t_0 + (NaChar / (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(Float64(Vef - Ec) + Float64(EDonor + mu)) / KbT))))
	tmp = 0.0
	if (NdChar <= -4.8e+71)
		tmp = Float64(t_0 + Float64(KbT / Float64(Ev / NaChar)));
	elseif (NdChar <= 2e+184)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(EAccept / KbT)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)));
	tmp = 0.0;
	if (NdChar <= -4.8e+71)
		tmp = t_0 + (KbT / (Ev / NaChar));
	elseif (NdChar <= 2e+184)
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = t_0 + (NaChar / (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[(N[(Vef - Ec), $MachinePrecision] + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -4.8e+71], N[(t$95$0 + N[(KbT / N[(Ev / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 2e+184], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -4.79999999999999961e71

   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%

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

   4. Taylor expanded in KbT around inf 59.7%

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

   5. Taylor expanded in Ev around inf 53.6%

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

      1. associate-/l* 53.7%

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

   7. Simplified 53.7%

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

   if -4.79999999999999961e71 < NdChar < 2.00000000000000003e184

   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%

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

   4. Taylor expanded in KbT around inf 55.1%

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

   if 2.00000000000000003e184 < 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%

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

   4. Taylor expanded in KbT around inf 70.0%

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

   5. Taylor expanded in EAccept around inf 53.7%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.8 \cdot 10^{+71}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{KbT}{\frac{Ev}{NaChar}}\\ \mathbf{elif}\;NdChar \leq 2 \cdot 10^{+184}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{NaChar}{\frac{EAccept}{KbT}}\\ \end{array} \]

Alternative 14: 49.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -1.45 \cdot 10^{+72}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{KbT}{\frac{Ev}{NaChar}}\\ \mathbf{elif}\;NdChar \leq 1.25 \cdot 10^{+100}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}} - \frac{KbT}{\frac{mu}{NaChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar -1.45e+72)
   (+
    (/ NdChar (+ 1.0 (exp (/ (+ (- Vef Ec) (+ EDonor mu)) KbT))))
    (/ KbT (/ Ev NaChar)))
   (if (<= NdChar 1.25e+100)
     (+
      (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
      (/ NdChar 2.0))
     (-
      (/ NdChar (+ 1.0 (exp (/ (+ Vef (- mu Ec)) KbT))))
      (/ KbT (/ mu NaChar))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -1.45e+72) {
		tmp = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (KbT / (Ev / NaChar));
	} else if (NdChar <= 1.25e+100) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT)))) - (KbT / (mu / NaChar));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ndchar <= (-1.45d+72)) then
        tmp = (ndchar / (1.0d0 + exp((((vef - ec) + (edonor + mu)) / kbt)))) + (kbt / (ev / nachar))
    else if (ndchar <= 1.25d+100) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((vef + (mu - ec)) / kbt)))) - (kbt / (mu / nachar))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -1.45e+72) {
		tmp = (NdChar / (1.0 + Math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (KbT / (Ev / NaChar));
	} else if (NdChar <= 1.25e+100) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((Vef + (mu - Ec)) / KbT)))) - (KbT / (mu / NaChar));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= -1.45e+72:
		tmp = (NdChar / (1.0 + math.exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (KbT / (Ev / NaChar))
	elif NdChar <= 1.25e+100:
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp(((Vef + (mu - Ec)) / KbT)))) - (KbT / (mu / NaChar))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= -1.45e+72)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef - Ec) + Float64(EDonor + mu)) / KbT)))) + Float64(KbT / Float64(Ev / NaChar)));
	elseif (NdChar <= 1.25e+100)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(mu - Ec)) / KbT)))) - Float64(KbT / Float64(mu / NaChar)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= -1.45e+72)
		tmp = (NdChar / (1.0 + exp((((Vef - Ec) + (EDonor + mu)) / KbT)))) + (KbT / (Ev / NaChar));
	elseif (NdChar <= 1.25e+100)
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT)))) - (KbT / (mu / NaChar));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, -1.45e+72], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(Vef - Ec), $MachinePrecision] + N[(EDonor + mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT / N[(Ev / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.25e+100], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(KbT / N[(mu / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -1.45000000000000009e72

   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%

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

   4. Taylor expanded in KbT around inf 59.7%

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

   5. Taylor expanded in Ev around inf 53.6%

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

      1. associate-/l* 53.7%

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

   7. Simplified 53.7%

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

   if -1.45000000000000009e72 < NdChar < 1.25e100

   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%

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

   4. Taylor expanded in KbT around inf 57.0%

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

   if 1.25e100 < 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%

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

   4. Taylor expanded in KbT around inf 62.7%

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

   5. Taylor expanded in mu around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-/l* 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in EDonor around 0 51.5%

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

      1. +-commutative 51.5%

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

      2. associate--l+ 51.5%

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

   10. Simplified 51.5%

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

4. Final simplification 55.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -1.45 \cdot 10^{+72}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(Vef - Ec\right) + \left(EDonor + mu\right)}{KbT}}} + \frac{KbT}{\frac{Ev}{NaChar}}\\ \mathbf{elif}\;NdChar \leq 1.25 \cdot 10^{+100}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}} - \frac{KbT}{\frac{mu}{NaChar}}\\ \end{array} \]

Alternative 15: 39.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.35 \cdot 10^{+27}:\\ \;\;\;\;t_0 + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;KbT \leq 5.8 \cdot 10^{-226}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;KbT \leq 3.7 \cdot 10^{-59}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} - \frac{KbT}{\frac{mu}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
   (if (<= KbT -1.35e+27)
     (+ t_0 (/ NdChar (+ 2.0 (/ EDonor KbT))))
     (if (<= KbT 5.8e-226)
       t_0
       (if (<= KbT 3.7e-59)
         (- (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (/ KbT (/ mu NaChar)))
         (+ (/ 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 t_0 = NaChar / (1.0 + exp((EAccept / KbT)));
	double tmp;
	if (KbT <= -1.35e+27) {
		tmp = t_0 + (NdChar / (2.0 + (EDonor / KbT)));
	} else if (KbT <= 5.8e-226) {
		tmp = t_0;
	} else if (KbT <= 3.7e-59) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) - (KbT / (mu / NaChar));
	} 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) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp((eaccept / kbt)))
    if (kbt <= (-1.35d+27)) then
        tmp = t_0 + (ndchar / (2.0d0 + (edonor / kbt)))
    else if (kbt <= 5.8d-226) then
        tmp = t_0
    else if (kbt <= 3.7d-59) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) - (kbt / (mu / nachar))
    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 t_0 = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	double tmp;
	if (KbT <= -1.35e+27) {
		tmp = t_0 + (NdChar / (2.0 + (EDonor / KbT)));
	} else if (KbT <= 5.8e-226) {
		tmp = t_0;
	} else if (KbT <= 3.7e-59) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) - (KbT / (mu / NaChar));
	} 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):
	t_0 = NaChar / (1.0 + math.exp((EAccept / KbT)))
	tmp = 0
	if KbT <= -1.35e+27:
		tmp = t_0 + (NdChar / (2.0 + (EDonor / KbT)))
	elif KbT <= 5.8e-226:
		tmp = t_0
	elif KbT <= 3.7e-59:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) - (KbT / (mu / NaChar))
	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)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))))
	tmp = 0.0
	if (KbT <= -1.35e+27)
		tmp = Float64(t_0 + Float64(NdChar / Float64(2.0 + Float64(EDonor / KbT))));
	elseif (KbT <= 5.8e-226)
		tmp = t_0;
	elseif (KbT <= 3.7e-59)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) - Float64(KbT / Float64(mu / NaChar)));
	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)
	t_0 = NaChar / (1.0 + exp((EAccept / KbT)));
	tmp = 0.0;
	if (KbT <= -1.35e+27)
		tmp = t_0 + (NdChar / (2.0 + (EDonor / KbT)));
	elseif (KbT <= 5.8e-226)
		tmp = t_0;
	elseif (KbT <= 3.7e-59)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) - (KbT / (mu / NaChar));
	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_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -1.35e+27], N[(t$95$0 + N[(NdChar / N[(2.0 + N[(EDonor / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 5.8e-226], t$95$0, If[LessEqual[KbT, 3.7e-59], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(KbT / N[(mu / NaChar), $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 4 regimes

2. if KbT < -1.3499999999999999e27

   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%

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

   4. Taylor expanded in EAccept around inf 70.7%

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

   5. Taylor expanded in KbT around inf 52.8%

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

      1. associate--l+ 52.8%

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

      2. sub-neg 52.8%

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

      3. mul-1-neg 52.8%

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

      4. +-commutative 52.8%

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

      5. associate-+r+ 52.8%

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

      6. +-commutative 52.8%

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

      7. associate-+r+ 52.8%

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

      8. mul-1-neg 52.8%

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

      9. neg-sub0 52.8%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 52.8%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 52.8%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 52.8%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 52.8%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 52.8%

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

      15. +-commutative 52.8%

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

      16. sub-neg 52.8%

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

      17. div-sub 52.8%

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

   7. Simplified 52.8%

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

   8. Taylor expanded in EDonor around inf 54.9%

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

   if -1.3499999999999999e27 < KbT < 5.80000000000000003e-226

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in EAccept around inf 69.1%

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

   5. Taylor expanded in KbT around inf 30.1%

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

      1. associate--l+ 30.1%

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

      2. sub-neg 30.1%

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

      3. mul-1-neg 30.1%

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

      4. +-commutative 30.1%

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

      5. associate-+r+ 30.1%

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

      6. +-commutative 30.1%

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

      7. associate-+r+ 30.1%

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

      8. mul-1-neg 30.1%

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

      9. neg-sub0 30.1%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 30.1%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 31.1%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 31.1%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 34.3%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 34.3%

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

      15. +-commutative 34.3%

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

      16. sub-neg 34.3%

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

      17. div-sub 35.6%

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

   7. Simplified 35.6%

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

   8. Taylor expanded in EDonor around inf 23.6%

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

      1. associate-/l* 21.5%

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

   10. Simplified 21.5%

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

   11. Taylor expanded in KbT around 0 37.0%

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

   if 5.80000000000000003e-226 < KbT < 3.6999999999999999e-59

   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%

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

   4. Taylor expanded in KbT around inf 60.2%

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

   5. Taylor expanded in mu around inf 60.8%

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

      1. mul-1-neg 60.8%

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

      2. associate-/l* 53.1%

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

   7. Simplified 53.1%

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

   8. Taylor expanded in mu around inf 47.5%

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

   if 3.6999999999999999e-59 < 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%

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

   4. Taylor expanded in KbT around inf 64.9%

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

   5. Taylor expanded in Ev around inf 54.8%

      \[\leadsto \frac{NdChar}{2} + \frac{NaChar}{1 + e^{\color{blue}{\frac{Ev}{KbT}}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 47.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.35 \cdot 10^{+27}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2 + \frac{EDonor}{KbT}}\\ \mathbf{elif}\;KbT \leq 5.8 \cdot 10^{-226}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 3.7 \cdot 10^{-59}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} - \frac{KbT}{\frac{mu}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 16: 45.9% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq 5.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} - \frac{KbT}{\frac{mu}{NaChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar 5.5e+106)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
    (/ NdChar 2.0))
   (- (/ NdChar (+ 1.0 (exp (/ mu KbT)))) (/ KbT (/ mu NaChar)))))

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 <= 5.5e+106) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) - (KbT / (mu / NaChar));
	}
	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 <= 5.5d+106) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) - (kbt / (mu / nachar))
    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 <= 5.5e+106) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) - (KbT / (mu / NaChar));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= 5.5e+106:
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) - (KbT / (mu / NaChar))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= 5.5e+106)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) - Float64(KbT / Float64(mu / NaChar)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= 5.5e+106)
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) - (KbT / (mu / NaChar));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, 5.5e+106], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(KbT / N[(mu / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < 5.5e106

   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%

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

   4. Taylor expanded in KbT around inf 52.2%

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

   if 5.5e106 < 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%

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

   4. Taylor expanded in KbT around inf 62.7%

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

   5. Taylor expanded in mu around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-/l* 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in mu around inf 43.5%

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

4. Final simplification 50.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq 5.5 \cdot 10^{+106}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} - \frac{KbT}{\frac{mu}{NaChar}}\\ \end{array} \]

Alternative 17: 47.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq 1.75 \cdot 10^{+110}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}} - \frac{KbT}{\frac{mu}{NaChar}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar 1.75e+110)
   (+
    (/ NaChar (+ 1.0 (exp (/ (+ (- EAccept mu) (+ Vef Ev)) KbT))))
    (/ NdChar 2.0))
   (-
    (/ NdChar (+ 1.0 (exp (/ (+ Vef (- mu Ec)) KbT))))
    (/ KbT (/ mu NaChar)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= 1.75e+110) {
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT)))) - (KbT / (mu / NaChar));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ndchar <= 1.75d+110) then
        tmp = (nachar / (1.0d0 + exp((((eaccept - mu) + (vef + ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp(((vef + (mu - ec)) / kbt)))) - (kbt / (mu / nachar))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= 1.75e+110) {
		tmp = (NaChar / (1.0 + Math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp(((Vef + (mu - Ec)) / KbT)))) - (KbT / (mu / NaChar));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= 1.75e+110:
		tmp = (NaChar / (1.0 + math.exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NdChar / (1.0 + math.exp(((Vef + (mu - Ec)) / KbT)))) - (KbT / (mu / NaChar))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= 1.75e+110)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept - mu) + Float64(Vef + Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Vef + Float64(mu - Ec)) / KbT)))) - Float64(KbT / Float64(mu / NaChar)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= 1.75e+110)
		tmp = (NaChar / (1.0 + exp((((EAccept - mu) + (Vef + Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NdChar / (1.0 + exp(((Vef + (mu - Ec)) / KbT)))) - (KbT / (mu / NaChar));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, 1.75e+110], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept - mu), $MachinePrecision] + N[(Vef + Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(KbT / N[(mu / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < 1.75e110

   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%

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

   4. Taylor expanded in KbT around inf 52.2%

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

   if 1.75e110 < 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%

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

   4. Taylor expanded in KbT around inf 62.7%

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

   5. Taylor expanded in mu around inf 51.8%

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

      1. mul-1-neg 51.8%

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

      2. associate-/l* 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in EDonor around 0 51.5%

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

      1. +-commutative 51.5%

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

      2. associate--l+ 51.5%

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

   10. Simplified 51.5%

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

4. Final simplification 52.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq 1.75 \cdot 10^{+110}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{\left(EAccept - mu\right) + \left(Vef + Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef + \left(mu - Ec\right)}{KbT}}} - \frac{KbT}{\frac{mu}{NaChar}}\\ \end{array} \]

Alternative 18: 39.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -4.4 \cdot 10^{+190}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;KbT \leq 8.2 \cdot 10^{-180}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -4.4e+190)
   (+
    (/ NdChar (- 2.0 (/ (- (- (- Ec EDonor) mu) Vef) KbT)))
    (/
     NaChar
     (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT)))) (/ mu KbT))))
   (if (<= KbT 8.2e-180)
     (/ NaChar (+ 1.0 (exp (/ EAccept 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 <= -4.4e+190) {
		tmp = (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	} else if (KbT <= 8.2e-180) {
		tmp = NaChar / (1.0 + exp((EAccept / 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 <= (-4.4d+190)) then
        tmp = (ndchar / (2.0d0 - ((((ec - edonor) - mu) - vef) / kbt))) + (nachar / ((2.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (mu / kbt)))
    else if (kbt <= 8.2d-180) then
        tmp = nachar / (1.0d0 + exp((eaccept / 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 <= -4.4e+190) {
		tmp = (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	} else if (KbT <= 8.2e-180) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / 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 <= -4.4e+190:
		tmp = (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)))
	elif KbT <= 8.2e-180:
		tmp = NaChar / (1.0 + math.exp((EAccept / 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 <= -4.4e+190)
		tmp = Float64(Float64(NdChar / Float64(2.0 - Float64(Float64(Float64(Float64(Ec - EDonor) - mu) - Vef) / KbT))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT))));
	elseif (KbT <= 8.2e-180)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / 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 <= -4.4e+190)
		tmp = (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT))) + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	elseif (KbT <= 8.2e-180)
		tmp = NaChar / (1.0 + exp((EAccept / 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, -4.4e+190], N[(N[(NdChar / N[(2.0 - N[(N[(N[(N[(Ec - EDonor), $MachinePrecision] - mu), $MachinePrecision] - Vef), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 8.2e-180], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / 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 < -4.4e190

   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%

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

   4. Taylor expanded in KbT around inf 86.3%

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

   5. Taylor expanded in KbT around inf 82.1%

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

      1. associate--l+ 86.4%

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

      2. sub-neg 86.4%

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

      3. mul-1-neg 86.4%

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

      4. +-commutative 86.4%

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

      5. associate-+r+ 86.4%

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

      6. +-commutative 86.4%

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

      7. associate-+r+ 86.4%

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

      8. mul-1-neg 86.4%

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

      9. neg-sub0 86.4%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 86.4%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 86.4%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 86.4%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 86.4%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 86.4%

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

      15. +-commutative 86.4%

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

      16. sub-neg 86.4%

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

      17. div-sub 86.4%

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

   7. Simplified 82.1%

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

   if -4.4e190 < KbT < 8.2e-180

   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%

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

   4. Taylor expanded in EAccept around inf 65.1%

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

   5. Taylor expanded in KbT around inf 29.3%

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

      1. associate--l+ 29.3%

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

      2. sub-neg 29.3%

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

      3. mul-1-neg 29.3%

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

      4. +-commutative 29.3%

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

      5. associate-+r+ 29.3%

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

      6. +-commutative 29.3%

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

      7. associate-+r+ 29.3%

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

      8. mul-1-neg 29.3%

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

      9. neg-sub0 29.3%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 29.3%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 30.0%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 30.0%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 32.4%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 32.4%

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

      15. +-commutative 32.4%

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

      16. sub-neg 32.4%

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

      17. div-sub 33.3%

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

   7. Simplified 33.3%

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

   8. Taylor expanded in EDonor around inf 22.5%

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

      1. associate-/l* 21.0%

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

   10. Simplified 21.0%

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

   11. Taylor expanded in KbT around 0 35.6%

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

   if 8.2e-180 < 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%

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

   4. Taylor expanded in KbT around inf 56.5%

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

   5. Taylor expanded in Ev around inf 44.1%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -4.4 \cdot 10^{+190}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;KbT \leq 8.2 \cdot 10^{-180}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]

Alternative 19: 37.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EAccept \leq -7.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;EAccept \leq 4.1 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EAccept -7.2e-227)
   (+ (/ NaChar (+ 1.0 (exp (/ Ev KbT)))) (/ NdChar 2.0))
   (if (<= EAccept 4.1e+48)
     (+ (/ NaChar (+ 1.0 (exp (/ Vef KbT)))) (/ NdChar 2.0))
     (/ 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 tmp;
	if (EAccept <= -7.2e-227) {
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (EAccept <= 4.1e+48) {
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (eaccept <= (-7.2d-227)) then
        tmp = (nachar / (1.0d0 + exp((ev / kbt)))) + (ndchar / 2.0d0)
    else if (eaccept <= 4.1d+48) then
        tmp = (nachar / (1.0d0 + exp((vef / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EAccept <= -7.2e-227) {
		tmp = (NaChar / (1.0 + Math.exp((Ev / KbT)))) + (NdChar / 2.0);
	} else if (EAccept <= 4.1e+48) {
		tmp = (NaChar / (1.0 + Math.exp((Vef / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EAccept <= -7.2e-227:
		tmp = (NaChar / (1.0 + math.exp((Ev / KbT)))) + (NdChar / 2.0)
	elif EAccept <= 4.1e+48:
		tmp = (NaChar / (1.0 + math.exp((Vef / KbT)))) + (NdChar / 2.0)
	else:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EAccept <= -7.2e-227)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))) + Float64(NdChar / 2.0));
	elseif (EAccept <= 4.1e+48)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EAccept <= -7.2e-227)
		tmp = (NaChar / (1.0 + exp((Ev / KbT)))) + (NdChar / 2.0);
	elseif (EAccept <= 4.1e+48)
		tmp = (NaChar / (1.0 + exp((Vef / KbT)))) + (NdChar / 2.0);
	else
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EAccept, -7.2e-227], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[EAccept, 4.1e+48], N[(N[(NaChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if EAccept < -7.1999999999999999e-227

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 47.2%

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

   5. Taylor expanded in Ev around inf 37.7%

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

   if -7.1999999999999999e-227 < EAccept < 4.1000000000000003e48

   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%

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

   4. Taylor expanded in KbT around inf 50.6%

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

   5. Taylor expanded in Vef around inf 43.4%

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

   if 4.1000000000000003e48 < 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%

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

   4. Taylor expanded in EAccept around inf 81.8%

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

   5. Taylor expanded in KbT around inf 45.3%

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

      1. associate--l+ 45.3%

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

      2. sub-neg 45.3%

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

      3. mul-1-neg 45.3%

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

      4. +-commutative 45.3%

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

      5. associate-+r+ 45.3%

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

      6. +-commutative 45.3%

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

      7. associate-+r+ 45.3%

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

      8. mul-1-neg 45.3%

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

      9. neg-sub0 45.3%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 45.3%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 45.3%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 45.3%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 49.0%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 49.0%

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

      15. +-commutative 49.0%

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

      16. sub-neg 49.0%

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

      17. div-sub 49.1%

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

   7. Simplified 49.1%

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

   8. Taylor expanded in EDonor around inf 33.4%

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

      1. associate-/l* 33.3%

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

   10. Simplified 33.3%

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

   11. Taylor expanded in KbT around 0 46.8%

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

4. Final simplification 41.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EAccept \leq -7.2 \cdot 10^{-227}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;EAccept \leq 4.1 \cdot 10^{+48}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \end{array} \]

Alternative 20: 40.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}}\\ \mathbf{if}\;KbT \leq -7 \cdot 10^{+190}:\\ \;\;\;\;t_0 + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;KbT \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- 2.0 (/ (- (- (- Ec EDonor) mu) Vef) KbT)))))
   (if (<= KbT -7e+190)
     (+
      t_0
      (/
       NaChar
       (- (+ 2.0 (+ (/ EAccept KbT) (+ (/ Ev KbT) (/ Vef KbT)))) (/ mu KbT))))
     (if (<= KbT 4.5e+123)
       (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))
       (+ t_0 (/ NaChar (+ 1.0 (+ 1.0 (/ 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 / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT));
	double tmp;
	if (KbT <= -7e+190) {
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	} else if (KbT <= 4.5e+123) {
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (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 / (2.0d0 - ((((ec - edonor) - mu) - vef) / kbt))
    if (kbt <= (-7d+190)) then
        tmp = t_0 + (nachar / ((2.0d0 + ((eaccept / kbt) + ((ev / kbt) + (vef / kbt)))) - (mu / kbt)))
    else if (kbt <= 4.5d+123) then
        tmp = nachar / (1.0d0 + exp((eaccept / kbt)))
    else
        tmp = t_0 + (nachar / (1.0d0 + (1.0d0 + (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 / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT));
	double tmp;
	if (KbT <= -7e+190) {
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	} else if (KbT <= 4.5e+123) {
		tmp = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	} else {
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT))
	tmp = 0
	if KbT <= -7e+190:
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)))
	elif KbT <= 4.5e+123:
		tmp = NaChar / (1.0 + math.exp((EAccept / KbT)))
	else:
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(2.0 - Float64(Float64(Float64(Float64(Ec - EDonor) - mu) - Vef) / KbT)))
	tmp = 0.0
	if (KbT <= -7e+190)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Ev / KbT) + Float64(Vef / KbT)))) - Float64(mu / KbT))));
	elseif (KbT <= 4.5e+123)
		tmp = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))));
	else
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT));
	tmp = 0.0;
	if (KbT <= -7e+190)
		tmp = t_0 + (NaChar / ((2.0 + ((EAccept / KbT) + ((Ev / KbT) + (Vef / KbT)))) - (mu / KbT)));
	elseif (KbT <= 4.5e+123)
		tmp = NaChar / (1.0 + exp((EAccept / KbT)));
	else
		tmp = t_0 + (NaChar / (1.0 + (1.0 + (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[(2.0 - N[(N[(N[(N[(Ec - EDonor), $MachinePrecision] - mu), $MachinePrecision] - Vef), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -7e+190], N[(t$95$0 + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Ev / KbT), $MachinePrecision] + N[(Vef / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4.5e+123], N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NaChar / N[(1.0 + N[(1.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -6.9999999999999997e190

   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%

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

   4. Taylor expanded in KbT around inf 86.3%

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

   5. Taylor expanded in KbT around inf 82.1%

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

      1. associate--l+ 86.4%

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

      2. sub-neg 86.4%

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

      3. mul-1-neg 86.4%

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

      4. +-commutative 86.4%

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

      5. associate-+r+ 86.4%

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

      6. +-commutative 86.4%

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

      7. associate-+r+ 86.4%

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

      8. mul-1-neg 86.4%

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

      9. neg-sub0 86.4%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 86.4%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 86.4%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 86.4%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 86.4%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 86.4%

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

      15. +-commutative 86.4%

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

      16. sub-neg 86.4%

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

      17. div-sub 86.4%

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

   7. Simplified 82.1%

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

   if -6.9999999999999997e190 < KbT < 4.49999999999999983e123

   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%

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

   4. Taylor expanded in EAccept around inf 65.1%

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

   5. Taylor expanded in KbT around inf 27.3%

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

      1. associate--l+ 27.3%

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

      2. sub-neg 27.3%

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

      3. mul-1-neg 27.3%

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

      4. +-commutative 27.3%

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

      5. associate-+r+ 27.3%

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

      6. +-commutative 27.3%

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

      7. associate-+r+ 27.3%

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

      8. mul-1-neg 27.3%

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

      9. neg-sub0 27.3%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 27.3%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 27.8%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 27.8%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 29.4%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 29.4%

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

      15. +-commutative 29.4%

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

      16. sub-neg 29.4%

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

      17. div-sub 30.1%

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

   7. Simplified 30.1%

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

   8. Taylor expanded in EDonor around inf 21.4%

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

      1. associate-/l* 20.4%

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

   10. Simplified 20.4%

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

   11. Taylor expanded in KbT around 0 32.9%

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

   if 4.49999999999999983e123 < 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%

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

   4. Taylor expanded in EAccept around inf 75.5%

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

   5. Taylor expanded in KbT around inf 66.6%

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

      1. associate--l+ 66.6%

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

      2. sub-neg 66.6%

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

      3. mul-1-neg 66.6%

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

      4. +-commutative 66.6%

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

      5. associate-+r+ 66.6%

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

      6. +-commutative 66.6%

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

      7. associate-+r+ 66.6%

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

      8. mul-1-neg 66.6%

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

      9. neg-sub0 66.6%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 66.6%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 66.6%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 66.6%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 66.6%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 66.6%

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

      15. +-commutative 66.6%

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

      16. sub-neg 66.6%

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

      17. div-sub 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in EAccept around 0 62.0%

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

4. Final simplification 41.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -7 \cdot 10^{+190}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Ev}{KbT} + \frac{Vef}{KbT}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;KbT \leq 4.5 \cdot 10^{+123}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \end{array} \]

Alternative 21: 28.5% accurate, 9.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.26 \cdot 10^{-166}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.26e-166)
   (* 0.5 (+ NdChar NaChar))
   (+
    (/ NdChar (- 2.0 (/ (- (- (- Ec EDonor) mu) Vef) KbT)))
    (/ NaChar (+ 1.0 (+ 1.0 (/ EAccept KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.26e-166) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-1.26d-166)) then
        tmp = 0.5d0 * (ndchar + nachar)
    else
        tmp = (ndchar / (2.0d0 - ((((ec - edonor) - mu) - vef) / kbt))) + (nachar / (1.0d0 + (1.0d0 + (eaccept / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.26e-166) {
		tmp = 0.5 * (NdChar + NaChar);
	} else {
		tmp = (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -1.26e-166:
		tmp = 0.5 * (NdChar + NaChar)
	else:
		tmp = (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -1.26e-166)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	else
		tmp = Float64(Float64(NdChar / Float64(2.0 - Float64(Float64(Float64(Float64(Ec - EDonor) - mu) - Vef) / KbT))) + Float64(NaChar / Float64(1.0 + Float64(1.0 + Float64(EAccept / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -1.26e-166)
		tmp = 0.5 * (NdChar + NaChar);
	else
		tmp = (NdChar / (2.0 - ((((Ec - EDonor) - mu) - Vef) / KbT))) + (NaChar / (1.0 + (1.0 + (EAccept / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -1.26e-166], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(2.0 - N[(N[(N[(N[(Ec - EDonor), $MachinePrecision] - mu), $MachinePrecision] - Vef), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[(1.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -1.26e-166

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in KbT around inf 47.8%

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

   5. Taylor expanded in mu around inf 37.7%

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

      1. associate-*r/ 37.7%

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

      2. mul-1-neg 37.7%

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

   7. Simplified 37.7%

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

   8. Taylor expanded in mu around 0 25.9%

      \[\leadsto \frac{NdChar}{2} + \color{blue}{\left(0.25 \cdot \frac{NaChar \cdot mu}{KbT} + 0.5 \cdot NaChar\right)} \]

   9. Taylor expanded in mu around 0 31.9%

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

       1. distribute-lft-out 31.9%

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

   11. Simplified 31.9%

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

   if -1.26e-166 < 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%

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

   4. Taylor expanded in EAccept around inf 66.8%

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

   5. Taylor expanded in KbT around inf 36.8%

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

      1. associate--l+ 36.8%

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

      2. sub-neg 36.8%

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

      3. mul-1-neg 36.8%

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

      4. +-commutative 36.8%

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

      5. associate-+r+ 36.8%

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

      6. +-commutative 36.8%

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

      7. associate-+r+ 36.8%

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

      8. mul-1-neg 36.8%

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

      9. neg-sub0 36.8%

         \[\leadsto \frac{NdChar}{2 + \left(\left(\left(\color{blue}{\left(0 - \frac{Ec}{KbT}\right)} + \frac{EDonor}{KbT}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      10. associate-+l- 36.8%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\color{blue}{\left(0 - \left(\frac{Ec}{KbT} - \frac{EDonor}{KbT}\right)\right)} + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      11. div-sub 37.5%

          \[\leadsto \frac{NdChar}{2 + \left(\left(\left(0 - \color{blue}{\frac{Ec - EDonor}{KbT}}\right) + \frac{mu}{KbT}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      12. associate--r- 37.5%

          \[\leadsto \frac{NdChar}{2 + \left(\color{blue}{\left(0 - \left(\frac{Ec - EDonor}{KbT} - \frac{mu}{KbT}\right)\right)} + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      13. div-sub 39.4%

          \[\leadsto \frac{NdChar}{2 + \left(\left(0 - \color{blue}{\frac{\left(Ec - EDonor\right) - mu}{KbT}}\right) + \frac{Vef}{KbT}\right)} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} \]

      14. neg-sub0 39.4%

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

      15. +-commutative 39.4%

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

      16. sub-neg 39.4%

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

      17. div-sub 40.2%

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

   7. Simplified 40.2%

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

   8. Taylor expanded in EAccept around 0 29.9%

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

4. Final simplification 30.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.26 \cdot 10^{-166}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\left(\left(Ec - EDonor\right) - mu\right) - Vef}{KbT}} + \frac{NaChar}{1 + \left(1 + \frac{EAccept}{KbT}\right)}\\ \end{array} \]

Alternative 22: 27.5% 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%

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

4. Taylor expanded in KbT around inf 48.0%

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

5. Taylor expanded in mu around inf 36.3%

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

   1. associate-*r/ 36.3%

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

   2. mul-1-neg 36.3%

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

7. Simplified 36.3%

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

8. Taylor expanded in mu around 0 22.7%

   \[\leadsto \frac{NdChar}{2} + \color{blue}{\left(0.25 \cdot \frac{NaChar \cdot mu}{KbT} + 0.5 \cdot NaChar\right)} \]

9. Taylor expanded in mu around 0 28.4%

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

    1. distribute-lft-out 28.4%

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

11. Simplified 28.4%

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

12. Final simplification 28.4%

    \[\leadsto 0.5 \cdot \left(NdChar + NaChar\right) \]

Alternative 23: 18.1% accurate, 76.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in KbT around inf 48.0%

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

5. Taylor expanded in mu around inf 36.3%

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

   1. associate-*r/ 36.3%

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

   2. mul-1-neg 36.3%

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

7. Simplified 36.3%

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

8. Taylor expanded in mu around 0 22.7%

   \[\leadsto \frac{NdChar}{2} + \color{blue}{\left(0.25 \cdot \frac{NaChar \cdot mu}{KbT} + 0.5 \cdot NaChar\right)} \]

9. Taylor expanded in NdChar around inf 16.0%

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

10. Final simplification 16.0%

    \[\leadsto NdChar \cdot 0.5 \]

Reproduce

herbie shell --seed 2023305 
(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))))))