Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 16.7s

Alternatives: 16

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = 1.0600117370744733e-66
  2. Ec = 1.2221267053937364e+120
  3. Vef = 6.475726394464914e+201
  4. EDonor = -1.3669808714342108e-157
  5. mu = -1.5963624969052865e+144
  6. KbT = -1.29565652534141e-183
  7. NaChar = 2.0280272442670723e-66
  8. Ev = -3.7417911714815245e-70
  9. EAccept = -1.1459435481911714e-74

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 45.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;t\_0 \leq -4 \cdot 10^{+166}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{-259}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;t\_0 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{-mu}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NdChar (+ 1.0 (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT))))
          (/ NaChar (- -1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)))))))
   (if (<= t_0 -4e+166)
     (- (* 0.5 NdChar) (/ NaChar (- -1.0 (exp (/ EAccept KbT)))))
     (if (<= t_0 5e-259)
       (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
       (if (<= t_0 5e+102)
         (/ NaChar (- (exp (/ (- mu) KbT)) -1.0))
         (- (* 0.5 NdChar) (/ NaChar (- -1.0 (exp (/ Ev KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_0 <= -4e+166) {
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	} else if (t_0 <= 5e-259) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if (t_0 <= 5e+102) {
		tmp = NaChar / (exp((-mu / KbT)) - -1.0);
	} else {
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - exp((Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp(((mu - ((ec - vef) - edonor)) / kbt)))) - (nachar / ((-1.0d0) - exp((((eaccept + (ev + vef)) - mu) / kbt))))
    if (t_0 <= (-4d+166)) then
        tmp = (0.5d0 * ndchar) - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    else if (t_0 <= 5d-259) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if (t_0 <= 5d+102) then
        tmp = nachar / (exp((-mu / kbt)) - (-1.0d0))
    else
        tmp = (0.5d0 * ndchar) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_0 <= -4e+166) {
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	} else if (t_0 <= 5e-259) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if (t_0 <= 5e+102) {
		tmp = NaChar / (Math.exp((-mu / KbT)) - -1.0);
	} else {
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))))
	tmp = 0
	if t_0 <= -4e+166:
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	elif t_0 <= 5e-259:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif t_0 <= 5e+102:
		tmp = NaChar / (math.exp((-mu / KbT)) - -1.0)
	else:
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu - Float64(Float64(Ec - Vef) - EDonor)) / KbT)))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT)))))
	tmp = 0.0
	if (t_0 <= -4e+166)
		tmp = Float64(Float64(0.5 * NdChar) - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))));
	elseif (t_0 <= 5e-259)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif (t_0 <= 5e+102)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(-mu) / KbT)) - -1.0));
	else
		tmp = Float64(Float64(0.5 * NdChar) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	tmp = 0.0;
	if (t_0 <= -4e+166)
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	elseif (t_0 <= 5e-259)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif (t_0 <= 5e+102)
		tmp = NaChar / (exp((-mu / KbT)) - -1.0);
	else
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - exp((Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu - N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -4e+166], N[(N[(0.5 * NdChar), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e-259], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+102], N[(NaChar / N[(N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * NdChar), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -3.99999999999999976e166

   1. Initial program 100.0%

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

   3. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 95.0

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

   5. Applied rewrites 95.0%

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

   6. Taylor expanded in KbT around inf

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

      1. lower-*.f64 62.9

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

   8. Applied rewrites 62.9%

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

   if -3.99999999999999976e166 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 4.99999999999999977e-259

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 75.7

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in Vef around inf

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

   8. Applied rewrites 58.8%

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

   if 4.99999999999999977e-259 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 5e102

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 61.3

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

   5. Applied rewrites 61.3%

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

   6. Taylor expanded in mu around inf

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

   8. Applied rewrites 52.7%

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

   if 5e102 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in Ev around inf

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

      1. lower-/.f64 79.6

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

   5. Applied rewrites 79.6%

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

   6. Taylor expanded in KbT around inf

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

      1. lower-*.f64 56.3

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

   8. Applied rewrites 56.3%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 57.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq -4 \cdot 10^{+166}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq 5 \cdot 10^{-259}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq 5 \cdot 10^{+102}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{-mu}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 45.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -4 \cdot 10^{+166}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-259}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{+102}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{-mu}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (- (* 0.5 NdChar) (/ NaChar (- -1.0 (exp (/ EAccept KbT))))))
        (t_1
         (-
          (/ NdChar (+ 1.0 (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT))))
          (/ NaChar (- -1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)))))))
   (if (<= t_1 -4e+166)
     t_0
     (if (<= t_1 5e-259)
       (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
       (if (<= t_1 5e+102) (/ NaChar (- (exp (/ (- mu) KbT)) -1.0)) t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (0.5 * NdChar) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	double t_1 = (NdChar / (1.0 + exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_1 <= -4e+166) {
		tmp = t_0;
	} else if (t_1 <= 5e-259) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if (t_1 <= 5e+102) {
		tmp = NaChar / (exp((-mu / KbT)) - -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (0.5d0 * ndchar) - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    t_1 = (ndchar / (1.0d0 + exp(((mu - ((ec - vef) - edonor)) / kbt)))) - (nachar / ((-1.0d0) - exp((((eaccept + (ev + vef)) - mu) / kbt))))
    if (t_1 <= (-4d+166)) then
        tmp = t_0
    else if (t_1 <= 5d-259) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if (t_1 <= 5d+102) then
        tmp = nachar / (exp((-mu / kbt)) - (-1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (0.5 * NdChar) - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	double t_1 = (NdChar / (1.0 + Math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_1 <= -4e+166) {
		tmp = t_0;
	} else if (t_1 <= 5e-259) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if (t_1 <= 5e+102) {
		tmp = NaChar / (Math.exp((-mu / KbT)) - -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (0.5 * NdChar) - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	t_1 = (NdChar / (1.0 + math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))))
	tmp = 0
	if t_1 <= -4e+166:
		tmp = t_0
	elif t_1 <= 5e-259:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif t_1 <= 5e+102:
		tmp = NaChar / (math.exp((-mu / KbT)) - -1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(0.5 * NdChar) - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu - Float64(Float64(Ec - Vef) - EDonor)) / KbT)))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT)))))
	tmp = 0.0
	if (t_1 <= -4e+166)
		tmp = t_0;
	elseif (t_1 <= 5e-259)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif (t_1 <= 5e+102)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(-mu) / KbT)) - -1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (0.5 * NdChar) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	t_1 = (NdChar / (1.0 + exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	tmp = 0.0;
	if (t_1 <= -4e+166)
		tmp = t_0;
	elseif (t_1 <= 5e-259)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif (t_1 <= 5e+102)
		tmp = NaChar / (exp((-mu / KbT)) - -1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(0.5 * NdChar), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu - N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -4e+166], t$95$0, If[LessEqual[t$95$1, 5e-259], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 5e+102], N[(NaChar / N[(N[Exp[N[((-mu) / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -3.99999999999999976e166 or 5e102 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 88.5

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

   5. Applied rewrites 88.5%

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

   6. Taylor expanded in KbT around inf

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

      1. lower-*.f64 61.5

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

   8. Applied rewrites 61.5%

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

   if -3.99999999999999976e166 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 4.99999999999999977e-259

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 75.7

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

   5. Applied rewrites 75.7%

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

   6. Taylor expanded in Vef around inf

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

   8. Applied rewrites 58.8%

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

   if 4.99999999999999977e-259 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 5e102

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 61.3

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

   5. Applied rewrites 61.3%

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

   6. Taylor expanded in mu around inf

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

   8. Applied rewrites 52.7%

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

4. Final simplification 58.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq -4 \cdot 10^{+166}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq 5 \cdot 10^{-259}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq 5 \cdot 10^{+102}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{-mu}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 79.2% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}\\ t_1 := \frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1} - \frac{NdChar}{-1 - t\_0}\\ t_2 := \frac{NdChar}{1 + t\_0} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;t\_2 \leq -4 \cdot 10^{-237}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 2 \cdot 10^{-226}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(\left(mu + Vef\right) + EDonor\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT)))
        (t_1
         (- (/ NaChar (- (exp (/ EAccept KbT)) -1.0)) (/ NdChar (- -1.0 t_0))))
        (t_2
         (-
          (/ NdChar (+ 1.0 t_0))
          (/ NaChar (- -1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)))))))
   (if (<= t_2 -4e-237)
     t_1
     (if (<= t_2 2e-226)
       (/ NdChar (+ 1.0 (exp (/ (- (+ (+ mu Vef) EDonor) Ec) KbT))))
       t_1))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((mu - ((Ec - Vef) - EDonor)) / KbT));
	double t_1 = (NaChar / (exp((EAccept / KbT)) - -1.0)) - (NdChar / (-1.0 - t_0));
	double t_2 = (NdChar / (1.0 + t_0)) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_2 <= -4e-237) {
		tmp = t_1;
	} else if (t_2 <= 2e-226) {
		tmp = NdChar / (1.0 + exp(((((mu + Vef) + EDonor) - Ec) / KbT)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = exp(((mu - ((ec - vef) - edonor)) / kbt))
    t_1 = (nachar / (exp((eaccept / kbt)) - (-1.0d0))) - (ndchar / ((-1.0d0) - t_0))
    t_2 = (ndchar / (1.0d0 + t_0)) - (nachar / ((-1.0d0) - exp((((eaccept + (ev + vef)) - mu) / kbt))))
    if (t_2 <= (-4d-237)) then
        tmp = t_1
    else if (t_2 <= 2d-226) then
        tmp = ndchar / (1.0d0 + exp(((((mu + vef) + edonor) - ec) / kbt)))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT));
	double t_1 = (NaChar / (Math.exp((EAccept / KbT)) - -1.0)) - (NdChar / (-1.0 - t_0));
	double t_2 = (NdChar / (1.0 + t_0)) - (NaChar / (-1.0 - Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_2 <= -4e-237) {
		tmp = t_1;
	} else if (t_2 <= 2e-226) {
		tmp = NdChar / (1.0 + Math.exp(((((mu + Vef) + EDonor) - Ec) / KbT)));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT))
	t_1 = (NaChar / (math.exp((EAccept / KbT)) - -1.0)) - (NdChar / (-1.0 - t_0))
	t_2 = (NdChar / (1.0 + t_0)) - (NaChar / (-1.0 - math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))))
	tmp = 0
	if t_2 <= -4e-237:
		tmp = t_1
	elif t_2 <= 2e-226:
		tmp = NdChar / (1.0 + math.exp(((((mu + Vef) + EDonor) - Ec) / KbT)))
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(mu - Float64(Float64(Ec - Vef) - EDonor)) / KbT))
	t_1 = Float64(Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) - -1.0)) - Float64(NdChar / Float64(-1.0 - t_0)))
	t_2 = Float64(Float64(NdChar / Float64(1.0 + t_0)) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT)))))
	tmp = 0.0
	if (t_2 <= -4e-237)
		tmp = t_1;
	elseif (t_2 <= 2e-226)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(mu + Vef) + EDonor) - Ec) / KbT))));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((mu - ((Ec - Vef) - EDonor)) / KbT));
	t_1 = (NaChar / (exp((EAccept / KbT)) - -1.0)) - (NdChar / (-1.0 - t_0));
	t_2 = (NdChar / (1.0 + t_0)) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	tmp = 0.0;
	if (t_2 <= -4e-237)
		tmp = t_1;
	elseif (t_2 <= 2e-226)
		tmp = NdChar / (1.0 + exp(((((mu + Vef) + EDonor) - Ec) / KbT)));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(mu - N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -4e-237], t$95$1, If[LessEqual[t$95$2, 2e-226], N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(N[(mu + Vef), $MachinePrecision] + EDonor), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -4e-237 or 1.99999999999999984e-226 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 81.5

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

   5. Applied rewrites 81.5%

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

   if -4e-237 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 1.99999999999999984e-226

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 91.6

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

   5. Applied rewrites 91.6%

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

4. Final simplification 83.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq -4 \cdot 10^{-237}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1} - \frac{NdChar}{-1 - e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq 2 \cdot 10^{-226}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(\left(mu + Vef\right) + EDonor\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1} - \frac{NdChar}{-1 - e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 35.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(NaChar + NdChar\right) \cdot 0.5\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-120}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-230}:\\ \;\;\;\;\frac{NaChar}{\left(\left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right) + \left(2 + \frac{EAccept}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* (+ NaChar NdChar) 0.5))
        (t_1
         (-
          (/ NdChar (+ 1.0 (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT))))
          (/ NaChar (- -1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)))))))
   (if (<= t_1 -2e-120)
     t_0
     (if (<= t_1 2e-230)
       (/
        NaChar
        (- (+ (+ (/ Vef KbT) (/ Ev KbT)) (+ 2.0 (/ EAccept KbT))) (/ mu KbT)))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar + NdChar) * 0.5;
	double t_1 = (NdChar / (1.0 + exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_1 <= -2e-120) {
		tmp = t_0;
	} else if (t_1 <= 2e-230) {
		tmp = NaChar / ((((Vef / KbT) + (Ev / KbT)) + (2.0 + (EAccept / KbT))) - (mu / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar + ndchar) * 0.5d0
    t_1 = (ndchar / (1.0d0 + exp(((mu - ((ec - vef) - edonor)) / kbt)))) - (nachar / ((-1.0d0) - exp((((eaccept + (ev + vef)) - mu) / kbt))))
    if (t_1 <= (-2d-120)) then
        tmp = t_0
    else if (t_1 <= 2d-230) then
        tmp = nachar / ((((vef / kbt) + (ev / kbt)) + (2.0d0 + (eaccept / kbt))) - (mu / kbt))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar + NdChar) * 0.5;
	double t_1 = (NdChar / (1.0 + Math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_1 <= -2e-120) {
		tmp = t_0;
	} else if (t_1 <= 2e-230) {
		tmp = NaChar / ((((Vef / KbT) + (Ev / KbT)) + (2.0 + (EAccept / KbT))) - (mu / KbT));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar + NdChar) * 0.5
	t_1 = (NdChar / (1.0 + math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))))
	tmp = 0
	if t_1 <= -2e-120:
		tmp = t_0
	elif t_1 <= 2e-230:
		tmp = NaChar / ((((Vef / KbT) + (Ev / KbT)) + (2.0 + (EAccept / KbT))) - (mu / KbT))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar + NdChar) * 0.5)
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu - Float64(Float64(Ec - Vef) - EDonor)) / KbT)))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT)))))
	tmp = 0.0
	if (t_1 <= -2e-120)
		tmp = t_0;
	elseif (t_1 <= 2e-230)
		tmp = Float64(NaChar / Float64(Float64(Float64(Float64(Vef / KbT) + Float64(Ev / KbT)) + Float64(2.0 + Float64(EAccept / KbT))) - Float64(mu / KbT)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar + NdChar) * 0.5;
	t_1 = (NdChar / (1.0 + exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	tmp = 0.0;
	if (t_1 <= -2e-120)
		tmp = t_0;
	elseif (t_1 <= 2e-230)
		tmp = NaChar / ((((Vef / KbT) + (Ev / KbT)) + (2.0 + (EAccept / KbT))) - (mu / KbT));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar + NdChar), $MachinePrecision] * 0.5), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu - N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-120], t$95$0, If[LessEqual[t$95$1, 2e-230], N[(NaChar / N[(N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision] + N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999996e-120 or 2.00000000000000009e-230 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      4. lower-+.f64 39.2

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

   5. Applied rewrites 39.2%

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

   if -1.99999999999999996e-120 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 2.00000000000000009e-230

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 77.9

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

   5. Applied rewrites 77.9%

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

   6. Taylor expanded in KbT around inf

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

   8. Applied rewrites 43.5%

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

4. Final simplification 40.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq -2 \cdot 10^{-120}:\\ \;\;\;\;\left(NaChar + NdChar\right) \cdot 0.5\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq 2 \cdot 10^{-230}:\\ \;\;\;\;\frac{NaChar}{\left(\left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right) + \left(2 + \frac{EAccept}{KbT}\right)\right) - \frac{mu}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\left(NaChar + NdChar\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 33.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(NaChar + NdChar\right) \cdot 0.5\\ t_1 := \frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-301}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 10^{-248}:\\ \;\;\;\;\frac{-0.5 \cdot \left(NaChar \cdot NaChar\right)}{NdChar - NaChar}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* (+ NaChar NdChar) 0.5))
        (t_1
         (-
          (/ NdChar (+ 1.0 (exp (/ (- mu (- (- Ec Vef) EDonor)) KbT))))
          (/ NaChar (- -1.0 (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)))))))
   (if (<= t_1 -2e-301)
     t_0
     (if (<= t_1 1e-248)
       (/ (* -0.5 (* NaChar NaChar)) (- NdChar NaChar))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar + NdChar) * 0.5;
	double t_1 = (NdChar / (1.0 + exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_1 <= -2e-301) {
		tmp = t_0;
	} else if (t_1 <= 1e-248) {
		tmp = (-0.5 * (NaChar * NaChar)) / (NdChar - NaChar);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar + ndchar) * 0.5d0
    t_1 = (ndchar / (1.0d0 + exp(((mu - ((ec - vef) - edonor)) / kbt)))) - (nachar / ((-1.0d0) - exp((((eaccept + (ev + vef)) - mu) / kbt))))
    if (t_1 <= (-2d-301)) then
        tmp = t_0
    else if (t_1 <= 1d-248) then
        tmp = ((-0.5d0) * (nachar * nachar)) / (ndchar - nachar)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar + NdChar) * 0.5;
	double t_1 = (NdChar / (1.0 + Math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	double tmp;
	if (t_1 <= -2e-301) {
		tmp = t_0;
	} else if (t_1 <= 1e-248) {
		tmp = (-0.5 * (NaChar * NaChar)) / (NdChar - NaChar);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar + NdChar) * 0.5
	t_1 = (NdChar / (1.0 + math.exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - math.exp((((EAccept + (Ev + Vef)) - mu) / KbT))))
	tmp = 0
	if t_1 <= -2e-301:
		tmp = t_0
	elif t_1 <= 1e-248:
		tmp = (-0.5 * (NaChar * NaChar)) / (NdChar - NaChar)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar + NdChar) * 0.5)
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(mu - Float64(Float64(Ec - Vef) - EDonor)) / KbT)))) - Float64(NaChar / Float64(-1.0 - exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT)))))
	tmp = 0.0
	if (t_1 <= -2e-301)
		tmp = t_0;
	elseif (t_1 <= 1e-248)
		tmp = Float64(Float64(-0.5 * Float64(NaChar * NaChar)) / Float64(NdChar - NaChar));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar + NdChar) * 0.5;
	t_1 = (NdChar / (1.0 + exp(((mu - ((Ec - Vef) - EDonor)) / KbT)))) - (NaChar / (-1.0 - exp((((EAccept + (Ev + Vef)) - mu) / KbT))));
	tmp = 0.0;
	if (t_1 <= -2e-301)
		tmp = t_0;
	elseif (t_1 <= 1e-248)
		tmp = (-0.5 * (NaChar * NaChar)) / (NdChar - NaChar);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar + NdChar), $MachinePrecision] * 0.5), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(mu - N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-301], t$95$0, If[LessEqual[t$95$1, 1e-248], N[(N[(-0.5 * N[(NaChar * NaChar), $MachinePrecision]), $MachinePrecision] / N[(NdChar - NaChar), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -2.00000000000000013e-301 or 9.9999999999999998e-249 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      4. lower-+.f64 35.9

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

   5. Applied rewrites 35.9%

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

   if -2.00000000000000013e-301 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 9.9999999999999998e-249

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      4. lower-+.f64 3.0

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

   5. Applied rewrites 3.0%

      \[\leadsto \color{blue}{0.5 \cdot \left(NdChar + NaChar\right)} \]
   6. Step-by-step derivation

   7. Applied rewrites 11.1%

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

   8. Taylor expanded in NaChar around inf

      \[\leadsto \frac{\frac{-1}{2} \cdot {NaChar}^{2}}{\color{blue}{NdChar} - NaChar} \]
   9. Step-by-step derivation

   10. Applied rewrites 39.1%

       \[\leadsto \frac{\left(NaChar \cdot NaChar\right) \cdot -0.5}{\color{blue}{NdChar} - NaChar} \]
3. Recombined 2 regimes into one program.

4. Final simplification 36.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq -2 \cdot 10^{-301}:\\ \;\;\;\;\left(NaChar + NdChar\right) \cdot 0.5\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{mu - \left(\left(Ec - Vef\right) - EDonor\right)}{KbT}}} - \frac{NaChar}{-1 - e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}}} \leq 10^{-248}:\\ \;\;\;\;\frac{-0.5 \cdot \left(NaChar \cdot NaChar\right)}{NdChar - NaChar}\\ \mathbf{else}:\\ \;\;\;\;\left(NaChar + NdChar\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 69.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}} - -1}\\ \mathbf{if}\;NaChar \leq -6.5 \cdot 10^{+112}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.35 \cdot 10^{+46}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(\left(mu + Vef\right) + EDonor\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (- (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)) -1.0))))
   (if (<= NaChar -6.5e+112)
     t_0
     (if (<= NaChar 1.35e+46)
       (/ NdChar (+ 1.0 (exp (/ (- (+ (+ mu Vef) EDonor) Ec) KbT))))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp((((EAccept + (Ev + Vef)) - mu) / KbT)) - -1.0);
	double tmp;
	if (NaChar <= -6.5e+112) {
		tmp = t_0;
	} else if (NaChar <= 1.35e+46) {
		tmp = NdChar / (1.0 + exp(((((mu + Vef) + EDonor) - Ec) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (exp((((eaccept + (ev + vef)) - mu) / kbt)) - (-1.0d0))
    if (nachar <= (-6.5d+112)) then
        tmp = t_0
    else if (nachar <= 1.35d+46) then
        tmp = ndchar / (1.0d0 + exp(((((mu + vef) + edonor) - ec) / kbt)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)) - -1.0);
	double tmp;
	if (NaChar <= -6.5e+112) {
		tmp = t_0;
	} else if (NaChar <= 1.35e+46) {
		tmp = NdChar / (1.0 + Math.exp(((((mu + Vef) + EDonor) - Ec) / KbT)));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)) - -1.0)
	tmp = 0
	if NaChar <= -6.5e+112:
		tmp = t_0
	elif NaChar <= 1.35e+46:
		tmp = NdChar / (1.0 + math.exp(((((mu + Vef) + EDonor) - Ec) / KbT)))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT)) - -1.0))
	tmp = 0.0
	if (NaChar <= -6.5e+112)
		tmp = t_0;
	elseif (NaChar <= 1.35e+46)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(mu + Vef) + EDonor) - Ec) / KbT))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp((((EAccept + (Ev + Vef)) - mu) / KbT)) - -1.0);
	tmp = 0.0;
	if (NaChar <= -6.5e+112)
		tmp = t_0;
	elseif (NaChar <= 1.35e+46)
		tmp = NdChar / (1.0 + exp(((((mu + Vef) + EDonor) - Ec) / KbT)));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.5e+112], t$95$0, If[LessEqual[NaChar, 1.35e+46], N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(N[(mu + Vef), $MachinePrecision] + EDonor), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -6.4999999999999998e112 or 1.3500000000000001e46 < NaChar

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 79.9

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

   5. Applied rewrites 79.9%

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

   if -6.4999999999999998e112 < NaChar < 1.3500000000000001e46

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 73.3

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

   5. Applied rewrites 73.3%

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

4. Final simplification 75.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.5 \cdot 10^{+112}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}} - -1}\\ \mathbf{elif}\;NaChar \leq 1.35 \cdot 10^{+46}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(\left(mu + Vef\right) + EDonor\right) - Ec}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}} - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 63.2% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.7 \cdot 10^{+171}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 4.8 \cdot 10^{+159}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.7e+171)
   (- (* 0.5 NdChar) (/ NaChar (- -1.0 (exp (/ EAccept KbT)))))
   (if (<= KbT 4.8e+159)
     (/ NaChar (- (exp (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)) -1.0))
     (- (* 0.5 NdChar) (/ NaChar (- -1.0 (exp (/ Ev KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.7e+171) {
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	} else if (KbT <= 4.8e+159) {
		tmp = NaChar / (exp((((EAccept + (Ev + Vef)) - mu) / KbT)) - -1.0);
	} else {
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - exp((Ev / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-1.7d+171)) then
        tmp = (0.5d0 * ndchar) - (nachar / ((-1.0d0) - exp((eaccept / kbt))))
    else if (kbt <= 4.8d+159) then
        tmp = nachar / (exp((((eaccept + (ev + vef)) - mu) / kbt)) - (-1.0d0))
    else
        tmp = (0.5d0 * ndchar) - (nachar / ((-1.0d0) - exp((ev / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (KbT <= -1.7e+171) {
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - Math.exp((EAccept / KbT))));
	} else if (KbT <= 4.8e+159) {
		tmp = NaChar / (Math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)) - -1.0);
	} else {
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - Math.exp((Ev / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -1.7e+171:
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - math.exp((EAccept / KbT))))
	elif KbT <= 4.8e+159:
		tmp = NaChar / (math.exp((((EAccept + (Ev + Vef)) - mu) / KbT)) - -1.0)
	else:
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -1.7e+171)
		tmp = Float64(Float64(0.5 * NdChar) - Float64(NaChar / Float64(-1.0 - exp(Float64(EAccept / KbT)))));
	elseif (KbT <= 4.8e+159)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT)) - -1.0));
	else
		tmp = Float64(Float64(0.5 * NdChar) - Float64(NaChar / Float64(-1.0 - exp(Float64(Ev / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (KbT <= -1.7e+171)
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - exp((EAccept / KbT))));
	elseif (KbT <= 4.8e+159)
		tmp = NaChar / (exp((((EAccept + (Ev + Vef)) - mu) / KbT)) - -1.0);
	else
		tmp = (0.5 * NdChar) - (NaChar / (-1.0 - exp((Ev / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -1.7e+171], N[(N[(0.5 * NdChar), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 4.8e+159], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * NdChar), $MachinePrecision] - N[(NaChar / N[(-1.0 - N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -1.7000000000000001e171

   1. Initial program 100.0%

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

   3. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 89.0

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

   5. Applied rewrites 89.0%

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

   6. Taylor expanded in KbT around inf

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

      1. lower-*.f64 74.7

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

   8. Applied rewrites 74.7%

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

   if -1.7000000000000001e171 < KbT < 4.8e159

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 61.8

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

   5. Applied rewrites 61.8%

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

   if 4.8e159 < KbT

   1. Initial program 100.0%

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

   3. Taylor expanded in Ev around inf

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

      1. lower-/.f64 88.7

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

   5. Applied rewrites 88.7%

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

   6. Taylor expanded in KbT around inf

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

      1. lower-*.f64 76.1

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

   8. Applied rewrites 76.1%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.7 \cdot 10^{+171}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;KbT \leq 4.8 \cdot 10^{+159}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NdChar - \frac{NaChar}{-1 - e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 43.5% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{if}\;NaChar \leq -7.8 \cdot 10^{+65}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 2.7 \cdot 10^{+30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{+220}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (- (exp (/ EAccept KbT)) -1.0))))
   (if (<= NaChar -7.8e+65)
     t_0
     (if (<= NaChar 2.7e+30)
       (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
       (if (<= NaChar 4.1e+220) t_0 (/ NaChar (- (exp (/ Ev KbT)) -1.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp((EAccept / KbT)) - -1.0);
	double tmp;
	if (NaChar <= -7.8e+65) {
		tmp = t_0;
	} else if (NaChar <= 2.7e+30) {
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	} else if (NaChar <= 4.1e+220) {
		tmp = t_0;
	} else {
		tmp = NaChar / (exp((Ev / KbT)) - -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (exp((eaccept / kbt)) - (-1.0d0))
    if (nachar <= (-7.8d+65)) then
        tmp = t_0
    else if (nachar <= 2.7d+30) then
        tmp = ndchar / (1.0d0 + exp((vef / kbt)))
    else if (nachar <= 4.1d+220) then
        tmp = t_0
    else
        tmp = nachar / (exp((ev / kbt)) - (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp((EAccept / KbT)) - -1.0);
	double tmp;
	if (NaChar <= -7.8e+65) {
		tmp = t_0;
	} else if (NaChar <= 2.7e+30) {
		tmp = NdChar / (1.0 + Math.exp((Vef / KbT)));
	} else if (NaChar <= 4.1e+220) {
		tmp = t_0;
	} else {
		tmp = NaChar / (Math.exp((Ev / KbT)) - -1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp((EAccept / KbT)) - -1.0)
	tmp = 0
	if NaChar <= -7.8e+65:
		tmp = t_0
	elif NaChar <= 2.7e+30:
		tmp = NdChar / (1.0 + math.exp((Vef / KbT)))
	elif NaChar <= 4.1e+220:
		tmp = t_0
	else:
		tmp = NaChar / (math.exp((Ev / KbT)) - -1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) - -1.0))
	tmp = 0.0
	if (NaChar <= -7.8e+65)
		tmp = t_0;
	elseif (NaChar <= 2.7e+30)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))));
	elseif (NaChar <= 4.1e+220)
		tmp = t_0;
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp((EAccept / KbT)) - -1.0);
	tmp = 0.0;
	if (NaChar <= -7.8e+65)
		tmp = t_0;
	elseif (NaChar <= 2.7e+30)
		tmp = NdChar / (1.0 + exp((Vef / KbT)));
	elseif (NaChar <= 4.1e+220)
		tmp = t_0;
	else
		tmp = NaChar / (exp((Ev / KbT)) - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -7.8e+65], t$95$0, If[LessEqual[NaChar, 2.7e+30], N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.1e+220], t$95$0, N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -7.7999999999999996e65 or 2.6999999999999999e30 < NaChar < 4.09999999999999981e220

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 74.0

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

   5. Applied rewrites 74.0%

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

   6. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} \]
   7. Step-by-step derivation

   8. Applied rewrites 53.4%

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

   if -7.7999999999999996e65 < NaChar < 2.6999999999999999e30

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 74.9

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

   5. Applied rewrites 74.9%

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

   6. Taylor expanded in Vef around inf

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

   8. Applied rewrites 55.5%

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

   if 4.09999999999999981e220 < NaChar

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 83.2

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

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in Ev around inf

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

   8. Applied rewrites 49.1%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -7.8 \cdot 10^{+65}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{elif}\;NaChar \leq 2.7 \cdot 10^{+30}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{+220}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 42.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{if}\;NaChar \leq -2.5 \cdot 10^{+118}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.05 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{+220}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (- (exp (/ EAccept KbT)) -1.0))))
   (if (<= NaChar -2.5e+118)
     t_0
     (if (<= NaChar 1.05e+21)
       (/ NdChar (+ 1.0 (exp (/ EDonor KbT))))
       (if (<= NaChar 4.1e+220) t_0 (/ NaChar (- (exp (/ Ev KbT)) -1.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp((EAccept / KbT)) - -1.0);
	double tmp;
	if (NaChar <= -2.5e+118) {
		tmp = t_0;
	} else if (NaChar <= 1.05e+21) {
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	} else if (NaChar <= 4.1e+220) {
		tmp = t_0;
	} else {
		tmp = NaChar / (exp((Ev / KbT)) - -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (exp((eaccept / kbt)) - (-1.0d0))
    if (nachar <= (-2.5d+118)) then
        tmp = t_0
    else if (nachar <= 1.05d+21) then
        tmp = ndchar / (1.0d0 + exp((edonor / kbt)))
    else if (nachar <= 4.1d+220) then
        tmp = t_0
    else
        tmp = nachar / (exp((ev / kbt)) - (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp((EAccept / KbT)) - -1.0);
	double tmp;
	if (NaChar <= -2.5e+118) {
		tmp = t_0;
	} else if (NaChar <= 1.05e+21) {
		tmp = NdChar / (1.0 + Math.exp((EDonor / KbT)));
	} else if (NaChar <= 4.1e+220) {
		tmp = t_0;
	} else {
		tmp = NaChar / (Math.exp((Ev / KbT)) - -1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp((EAccept / KbT)) - -1.0)
	tmp = 0
	if NaChar <= -2.5e+118:
		tmp = t_0
	elif NaChar <= 1.05e+21:
		tmp = NdChar / (1.0 + math.exp((EDonor / KbT)))
	elif NaChar <= 4.1e+220:
		tmp = t_0
	else:
		tmp = NaChar / (math.exp((Ev / KbT)) - -1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) - -1.0))
	tmp = 0.0
	if (NaChar <= -2.5e+118)
		tmp = t_0;
	elseif (NaChar <= 1.05e+21)
		tmp = Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT))));
	elseif (NaChar <= 4.1e+220)
		tmp = t_0;
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp((EAccept / KbT)) - -1.0);
	tmp = 0.0;
	if (NaChar <= -2.5e+118)
		tmp = t_0;
	elseif (NaChar <= 1.05e+21)
		tmp = NdChar / (1.0 + exp((EDonor / KbT)));
	elseif (NaChar <= 4.1e+220)
		tmp = t_0;
	else
		tmp = NaChar / (exp((Ev / KbT)) - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.5e+118], t$95$0, If[LessEqual[NaChar, 1.05e+21], N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.1e+220], t$95$0, N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2.49999999999999986e118 or 1.05e21 < NaChar < 4.09999999999999981e220

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 76.9

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

   5. Applied rewrites 76.9%

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

   6. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} \]
   7. Step-by-step derivation

   8. Applied rewrites 57.2%

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

   if -2.49999999999999986e118 < NaChar < 1.05e21

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 73.5

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

   5. Applied rewrites 73.5%

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

   6. Taylor expanded in EDonor around inf

      \[\leadsto \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1} \]
   7. Step-by-step derivation

   8. Applied rewrites 46.2%

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

   if 4.09999999999999981e220 < NaChar

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 83.2

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

   5. Applied rewrites 83.2%

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

   6. Taylor expanded in Ev around inf

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

   8. Applied rewrites 49.1%

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

4. Final simplification 49.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.5 \cdot 10^{+118}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{elif}\;NaChar \leq 1.05 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{+220}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 40.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(NaChar + NdChar\right) \cdot 0.5\\ \mathbf{if}\;KbT \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, \mathsf{fma}\left(NaChar, \frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}, \frac{\left(\left(mu + Vef\right) + EDonor\right) - Ec}{KbT} \cdot NdChar\right), t\_0\right)\\ \mathbf{elif}\;KbT \leq -1.3 \cdot 10^{-297}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{elif}\;KbT \leq 1.95 \cdot 10^{+183}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, \frac{NaChar}{KbT} \cdot Ev, t\_0\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* (+ NaChar NdChar) 0.5)))
   (if (<= KbT -3.7e+191)
     (fma
      -0.25
      (fma
       NaChar
       (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)
       (* (/ (- (+ (+ mu Vef) EDonor) Ec) KbT) NdChar))
      t_0)
     (if (<= KbT -1.3e-297)
       (/ NaChar (- (exp (/ EAccept KbT)) -1.0))
       (if (<= KbT 1.95e+183)
         (/ NaChar (- (exp (/ Ev KbT)) -1.0))
         (fma -0.25 (* (/ NaChar KbT) Ev) t_0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar + NdChar) * 0.5;
	double tmp;
	if (KbT <= -3.7e+191) {
		tmp = fma(-0.25, fma(NaChar, (((EAccept + (Ev + Vef)) - mu) / KbT), (((((mu + Vef) + EDonor) - Ec) / KbT) * NdChar)), t_0);
	} else if (KbT <= -1.3e-297) {
		tmp = NaChar / (exp((EAccept / KbT)) - -1.0);
	} else if (KbT <= 1.95e+183) {
		tmp = NaChar / (exp((Ev / KbT)) - -1.0);
	} else {
		tmp = fma(-0.25, ((NaChar / KbT) * Ev), t_0);
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar + NdChar) * 0.5)
	tmp = 0.0
	if (KbT <= -3.7e+191)
		tmp = fma(-0.25, fma(NaChar, Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT), Float64(Float64(Float64(Float64(Float64(mu + Vef) + EDonor) - Ec) / KbT) * NdChar)), t_0);
	elseif (KbT <= -1.3e-297)
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) - -1.0));
	elseif (KbT <= 1.95e+183)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) - -1.0));
	else
		tmp = fma(-0.25, Float64(Float64(NaChar / KbT) * Ev), t_0);
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar + NdChar), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[KbT, -3.7e+191], N[(-0.25 * N[(NaChar * N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(N[(N[(N[(mu + Vef), $MachinePrecision] + EDonor), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision] * NdChar), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[KbT, -1.3e-297], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.95e+183], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], N[(-0.25 * N[(N[(NaChar / KbT), $MachinePrecision] * Ev), $MachinePrecision] + t$95$0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -3.70000000000000019e191

   1. Initial program 99.9%

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

   3. Taylor expanded in KbT around -inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \left(\frac{-1}{4} \cdot \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT} + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\frac{-1}{4} \cdot \frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \frac{-1}{4} \cdot \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT}\right) + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)} \]

      2. distribute-lft-out N/A

         \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(\frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT}\right)} + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{4}, \frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT}, \frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)} \]

   5. Applied rewrites 75.0%

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

   if -3.70000000000000019e191 < KbT < -1.3e-297

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 66.6

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

   5. Applied rewrites 66.6%

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

   6. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} \]
   7. Step-by-step derivation

   8. Applied rewrites 39.2%

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

   if -1.3e-297 < KbT < 1.9499999999999999e183

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 56.0

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

   5. Applied rewrites 56.0%

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

   6. Taylor expanded in Ev around inf

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

   8. Applied rewrites 34.0%

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

   if 1.9499999999999999e183 < KbT

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around -inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \left(\frac{-1}{4} \cdot \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT} + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\frac{-1}{4} \cdot \frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \frac{-1}{4} \cdot \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT}\right) + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)} \]

      2. distribute-lft-out N/A

         \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(\frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT}\right)} + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{4}, \frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT}, \frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)} \]

   5. Applied rewrites 77.5%

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

   6. Taylor expanded in Ev around inf

      \[\leadsto \mathsf{fma}\left(\frac{-1}{4}, \frac{Ev \cdot NaChar}{\color{blue}{KbT}}, \frac{1}{2} \cdot \left(NdChar + NaChar\right)\right) \]
   7. Step-by-step derivation

   8. Applied rewrites 78.8%

      \[\leadsto \mathsf{fma}\left(-0.25, Ev \cdot \color{blue}{\frac{NaChar}{KbT}}, 0.5 \cdot \left(NdChar + NaChar\right)\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 45.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, \mathsf{fma}\left(NaChar, \frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}, \frac{\left(\left(mu + Vef\right) + EDonor\right) - Ec}{KbT} \cdot NdChar\right), \left(NaChar + NdChar\right) \cdot 0.5\right)\\ \mathbf{elif}\;KbT \leq -1.3 \cdot 10^{-297}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{elif}\;KbT \leq 1.95 \cdot 10^{+183}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, \frac{NaChar}{KbT} \cdot Ev, \left(NaChar + NdChar\right) \cdot 0.5\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.8% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -6.4 \cdot 10^{+174}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} - -1}\\ \mathbf{elif}\;Ev \leq -6.7 \cdot 10^{-295}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -6.4e+174)
   (/ NaChar (- (exp (/ Ev KbT)) -1.0))
   (if (<= Ev -6.7e-295)
     (/ NaChar (- (exp (/ Vef KbT)) -1.0))
     (/ NaChar (- (exp (/ EAccept KbT)) -1.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -6.4e+174) {
		tmp = NaChar / (exp((Ev / KbT)) - -1.0);
	} else if (Ev <= -6.7e-295) {
		tmp = NaChar / (exp((Vef / KbT)) - -1.0);
	} else {
		tmp = NaChar / (exp((EAccept / KbT)) - -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-6.4d+174)) then
        tmp = nachar / (exp((ev / kbt)) - (-1.0d0))
    else if (ev <= (-6.7d-295)) then
        tmp = nachar / (exp((vef / kbt)) - (-1.0d0))
    else
        tmp = nachar / (exp((eaccept / kbt)) - (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -6.4e+174) {
		tmp = NaChar / (Math.exp((Ev / KbT)) - -1.0);
	} else if (Ev <= -6.7e-295) {
		tmp = NaChar / (Math.exp((Vef / KbT)) - -1.0);
	} else {
		tmp = NaChar / (Math.exp((EAccept / KbT)) - -1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -6.4e+174:
		tmp = NaChar / (math.exp((Ev / KbT)) - -1.0)
	elif Ev <= -6.7e-295:
		tmp = NaChar / (math.exp((Vef / KbT)) - -1.0)
	else:
		tmp = NaChar / (math.exp((EAccept / KbT)) - -1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -6.4e+174)
		tmp = Float64(NaChar / Float64(exp(Float64(Ev / KbT)) - -1.0));
	elseif (Ev <= -6.7e-295)
		tmp = Float64(NaChar / Float64(exp(Float64(Vef / KbT)) - -1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) - -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -6.4e+174)
		tmp = NaChar / (exp((Ev / KbT)) - -1.0);
	elseif (Ev <= -6.7e-295)
		tmp = NaChar / (exp((Vef / KbT)) - -1.0);
	else
		tmp = NaChar / (exp((EAccept / KbT)) - -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -6.4e+174], N[(NaChar / N[(N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -6.7e-295], N[(NaChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -6.4000000000000001e174

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in Ev around inf

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

   8. Applied rewrites 56.8%

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

   if -6.4000000000000001e174 < Ev < -6.70000000000000034e-295

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in Vef around inf

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

   8. Applied rewrites 41.8%

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

   if -6.70000000000000034e-295 < Ev

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 59.1

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

   5. Applied rewrites 59.1%

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

   6. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} \]
   7. Step-by-step derivation

   8. Applied rewrites 39.3%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -6.4 \cdot 10^{+174}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Ev}{KbT}} - -1}\\ \mathbf{elif}\;Ev \leq -6.7 \cdot 10^{-295}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{Vef}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 40.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(NaChar + NdChar\right) \cdot 0.5\\ \mathbf{if}\;KbT \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, \mathsf{fma}\left(NaChar, \frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}, \frac{\left(\left(mu + Vef\right) + EDonor\right) - Ec}{KbT} \cdot NdChar\right), t\_0\right)\\ \mathbf{elif}\;KbT \leq 4.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* (+ NaChar NdChar) 0.5)))
   (if (<= KbT -3.7e+191)
     (fma
      -0.25
      (fma
       NaChar
       (/ (- (+ EAccept (+ Ev Vef)) mu) KbT)
       (* (/ (- (+ (+ mu Vef) EDonor) Ec) KbT) NdChar))
      t_0)
     (if (<= KbT 4.5e+58) (/ NaChar (- (exp (/ EAccept KbT)) -1.0)) t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar + NdChar) * 0.5;
	double tmp;
	if (KbT <= -3.7e+191) {
		tmp = fma(-0.25, fma(NaChar, (((EAccept + (Ev + Vef)) - mu) / KbT), (((((mu + Vef) + EDonor) - Ec) / KbT) * NdChar)), t_0);
	} else if (KbT <= 4.5e+58) {
		tmp = NaChar / (exp((EAccept / KbT)) - -1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar + NdChar) * 0.5)
	tmp = 0.0
	if (KbT <= -3.7e+191)
		tmp = fma(-0.25, fma(NaChar, Float64(Float64(Float64(EAccept + Float64(Ev + Vef)) - mu) / KbT), Float64(Float64(Float64(Float64(Float64(mu + Vef) + EDonor) - Ec) / KbT) * NdChar)), t_0);
	elseif (KbT <= 4.5e+58)
		tmp = Float64(NaChar / Float64(exp(Float64(EAccept / KbT)) - -1.0));
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar + NdChar), $MachinePrecision] * 0.5), $MachinePrecision]}, If[LessEqual[KbT, -3.7e+191], N[(-0.25 * N[(NaChar * N[(N[(N[(EAccept + N[(Ev + Vef), $MachinePrecision]), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(N[(N[(N[(mu + Vef), $MachinePrecision] + EDonor), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision] * NdChar), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[KbT, 4.5e+58], N[(NaChar / N[(N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 3 regimes

2. if KbT < -3.70000000000000019e191

   1. Initial program 99.9%

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

   3. Taylor expanded in KbT around -inf

      \[\leadsto \color{blue}{\frac{-1}{4} \cdot \frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \left(\frac{-1}{4} \cdot \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT} + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)\right)} \]
   4. Step-by-step derivation

      1. associate-+r+ N/A

         \[\leadsto \color{blue}{\left(\frac{-1}{4} \cdot \frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \frac{-1}{4} \cdot \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT}\right) + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)} \]

      2. distribute-lft-out N/A

         \[\leadsto \color{blue}{\frac{-1}{4} \cdot \left(\frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT}\right)} + \left(\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right) \]

      3. lower-fma.f64 N/A

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{-1}{4}, \frac{NaChar \cdot \left(\left(EAccept + \left(Ev + Vef\right)\right) - mu\right)}{KbT} + \frac{NdChar \cdot \left(\left(EDonor + \left(Vef + mu\right)\right) - Ec\right)}{KbT}, \frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar\right)} \]

   5. Applied rewrites 75.0%

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

   if -3.70000000000000019e191 < KbT < 4.4999999999999998e58

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around inf

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. lower-+.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 63.0

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

   5. Applied rewrites 63.0%

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

   6. Taylor expanded in EAccept around inf

      \[\leadsto \frac{NaChar}{e^{\frac{EAccept}{KbT}} + 1} \]
   7. Step-by-step derivation

   8. Applied rewrites 37.5%

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

   if 4.4999999999999998e58 < KbT

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      4. lower-+.f64 53.6

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

   5. Applied rewrites 53.6%

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

4. Final simplification 45.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.7 \cdot 10^{+191}:\\ \;\;\;\;\mathsf{fma}\left(-0.25, \mathsf{fma}\left(NaChar, \frac{\left(EAccept + \left(Ev + Vef\right)\right) - mu}{KbT}, \frac{\left(\left(mu + Vef\right) + EDonor\right) - Ec}{KbT} \cdot NdChar\right), \left(NaChar + NdChar\right) \cdot 0.5\right)\\ \mathbf{elif}\;KbT \leq 4.5 \cdot 10^{+58}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept}{KbT}} - -1}\\ \mathbf{else}:\\ \;\;\;\;\left(NaChar + NdChar\right) \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 23.0% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -3.5 \cdot 10^{+118}:\\ \;\;\;\;0.5 \cdot NaChar\\ \mathbf{elif}\;NaChar \leq 1.02 \cdot 10^{-57}:\\ \;\;\;\;0.5 \cdot NdChar\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NaChar\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -3.5e+118)
   (* 0.5 NaChar)
   (if (<= NaChar 1.02e-57) (* 0.5 NdChar) (* 0.5 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 (NaChar <= -3.5e+118) {
		tmp = 0.5 * NaChar;
	} else if (NaChar <= 1.02e-57) {
		tmp = 0.5 * NdChar;
	} else {
		tmp = 0.5 * 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 (nachar <= (-3.5d+118)) then
        tmp = 0.5d0 * nachar
    else if (nachar <= 1.02d-57) then
        tmp = 0.5d0 * ndchar
    else
        tmp = 0.5d0 * 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 (NaChar <= -3.5e+118) {
		tmp = 0.5 * NaChar;
	} else if (NaChar <= 1.02e-57) {
		tmp = 0.5 * NdChar;
	} else {
		tmp = 0.5 * NaChar;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -3.5e+118:
		tmp = 0.5 * NaChar
	elif NaChar <= 1.02e-57:
		tmp = 0.5 * NdChar
	else:
		tmp = 0.5 * NaChar
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -3.5e+118)
		tmp = Float64(0.5 * NaChar);
	elseif (NaChar <= 1.02e-57)
		tmp = Float64(0.5 * NdChar);
	else
		tmp = Float64(0.5 * NaChar);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -3.5e+118)
		tmp = 0.5 * NaChar;
	elseif (NaChar <= 1.02e-57)
		tmp = 0.5 * NdChar;
	else
		tmp = 0.5 * NaChar;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -3.5e+118], N[(0.5 * NaChar), $MachinePrecision], If[LessEqual[NaChar, 1.02e-57], N[(0.5 * NdChar), $MachinePrecision], N[(0.5 * NaChar), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -3.50000000000000016e118 or 1.02e-57 < NaChar

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

      \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
   4. Step-by-step derivation

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      3. lower-*.f64 N/A

         \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

      4. lower-+.f64 30.4

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

   5. Applied rewrites 30.4%

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

   6. Taylor expanded in NaChar around inf

      \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
   7. Step-by-step derivation

   8. Applied rewrites 27.7%

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

   if -3.50000000000000016e118 < NaChar < 1.02e-57

   1. Initial program 100.0%

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

   3. Taylor expanded in NaChar around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. +-commutative N/A

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

      10. lower-+.f64 74.7

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

   5. Applied rewrites 74.7%

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

   6. Taylor expanded in KbT around inf

      \[\leadsto \frac{1}{2} \cdot \color{blue}{NdChar} \]
   7. Step-by-step derivation

   8. Applied rewrites 25.4%

      \[\leadsto 0.5 \cdot \color{blue}{NdChar} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 15: 27.5% accurate, 30.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in KbT around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. distribute-lft-out N/A

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

   3. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

   4. lower-+.f64 30.0

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

5. Applied rewrites 30.0%

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

6. Final simplification 30.0%

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

Alternative 16: 17.9% accurate, 46.0× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in KbT around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot NaChar + \frac{1}{2} \cdot NdChar} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. distribute-lft-out N/A

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

   3. lower-*.f64 N/A

      \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(NdChar + NaChar\right)} \]

   4. lower-+.f64 30.0

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

5. Applied rewrites 30.0%

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

6. Taylor expanded in NaChar around inf

   \[\leadsto \frac{1}{2} \cdot \color{blue}{NaChar} \]
7. Step-by-step derivation

8. Applied rewrites 18.9%

   \[\leadsto 0.5 \cdot \color{blue}{NaChar} \]
9. Add Preprocessing

Reproduce

herbie shell --seed 2024267 
(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))))))