Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 30.8s

Alternatives: 28

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = -1.547862053217662e-110
  2. Ec = 4.984487111383406e+280
  3. Vef = -5.345479933519347e+250
  4. EDonor = 7.943146725266341e-104
  5. mu = -9.429826895340837e-251
  6. KbT = 4.6312001116193015e-251
  7. NaChar = -9.407916072885582e-111
  8. Ev = -1.2377317342179852e+41
  9. EAccept = -4.8477894696547626e-290

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

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

FPCore

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

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NdChar / (1.0 + exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / 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(((edonor - ((ec - vef) - mu)) / kbt)))) + (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / 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(((EDonor - ((Ec - Vef) - mu)) / KbT)))) + (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 73.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_2 := t\_1 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{if}\;EDonor \leq -3 \cdot 10^{+68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;EDonor \leq -1.5 \cdot 10^{-125}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;EDonor \leq -1.85 \cdot 10^{-224}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 - Vef \cdot \left(\frac{-1}{KbT} + EDonor \cdot \frac{\frac{-1}{KbT} - \frac{mu}{EDonor \cdot KbT}}{Vef}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;EDonor \leq 1.8 \cdot 10^{-5}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_2 (+ t_1 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))))
   (if (<= EDonor -3e+68)
     t_2
     (if (<= EDonor -1.5e-125)
       t_0
       (if (<= EDonor -1.85e-224)
         (+
          t_1
          (/
           NdChar
           (-
            (-
             2.0
             (*
              Vef
              (+
               (/ -1.0 KbT)
               (* EDonor (/ (- (/ -1.0 KbT) (/ mu (* EDonor KbT))) Vef)))))
            (/ Ec KbT))))
         (if (<= EDonor 1.8e-5) t_0 t_2))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -3e+68) {
		tmp = t_2;
	} else if (EDonor <= -1.5e-125) {
		tmp = t_0;
	} else if (EDonor <= -1.85e-224) {
		tmp = t_1 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)));
	} else if (EDonor <= 1.8e-5) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_2 = t_1 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    if (edonor <= (-3d+68)) then
        tmp = t_2
    else if (edonor <= (-1.5d-125)) then
        tmp = t_0
    else if (edonor <= (-1.85d-224)) then
        tmp = t_1 + (ndchar / ((2.0d0 - (vef * (((-1.0d0) / kbt) + (edonor * ((((-1.0d0) / kbt) - (mu / (edonor * kbt))) / vef))))) - (ec / kbt)))
    else if (edonor <= 1.8d-5) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_2 = t_1 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	double tmp;
	if (EDonor <= -3e+68) {
		tmp = t_2;
	} else if (EDonor <= -1.5e-125) {
		tmp = t_0;
	} else if (EDonor <= -1.85e-224) {
		tmp = t_1 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)));
	} else if (EDonor <= 1.8e-5) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_2 = t_1 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	tmp = 0
	if EDonor <= -3e+68:
		tmp = t_2
	elif EDonor <= -1.5e-125:
		tmp = t_0
	elif EDonor <= -1.85e-224:
		tmp = t_1 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)))
	elif EDonor <= 1.8e-5:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_2 = Float64(t_1 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))))
	tmp = 0.0
	if (EDonor <= -3e+68)
		tmp = t_2;
	elseif (EDonor <= -1.5e-125)
		tmp = t_0;
	elseif (EDonor <= -1.85e-224)
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 - Float64(Vef * Float64(Float64(-1.0 / KbT) + Float64(EDonor * Float64(Float64(Float64(-1.0 / KbT) - Float64(mu / Float64(EDonor * KbT))) / Vef))))) - Float64(Ec / KbT))));
	elseif (EDonor <= 1.8e-5)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_2 = t_1 + (NdChar / (1.0 + exp((EDonor / KbT))));
	tmp = 0.0;
	if (EDonor <= -3e+68)
		tmp = t_2;
	elseif (EDonor <= -1.5e-125)
		tmp = t_0;
	elseif (EDonor <= -1.85e-224)
		tmp = t_1 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)));
	elseif (EDonor <= 1.8e-5)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(t$95$1 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[EDonor, -3e+68], t$95$2, If[LessEqual[EDonor, -1.5e-125], t$95$0, If[LessEqual[EDonor, -1.85e-224], N[(t$95$1 + N[(NdChar / N[(N[(2.0 - N[(Vef * N[(N[(-1.0 / KbT), $MachinePrecision] + N[(EDonor * N[(N[(N[(-1.0 / KbT), $MachinePrecision] - N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[EDonor, 1.8e-5], t$95$0, t$95$2]]]]]]]

Derivation

1. Split input into 3 regimes

2. if EDonor < -3.0000000000000002e68 or 1.80000000000000005e-5 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 89.0%

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

   if -3.0000000000000002e68 < EDonor < -1.49999999999999995e-125 or -1.8500000000000001e-224 < EDonor < 1.80000000000000005e-5

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 85.3%

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

   6. Taylor expanded in EAccept around 0 80.6%

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

   if -1.49999999999999995e-125 < EDonor < -1.8500000000000001e-224

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.6%

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

   6. Taylor expanded in EDonor around inf 58.7%

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

      1. associate-/r* 63.0%

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

      2. associate-/r* 67.2%

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

   8. Simplified 67.2%

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

   9. Taylor expanded in Vef around inf 71.5%

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

       1. associate-/l* 75.6%

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

   11. Simplified 75.6%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -3 \cdot 10^{+68}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -1.5 \cdot 10^{-125}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{elif}\;EDonor \leq -1.85 \cdot 10^{-224}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 - Vef \cdot \left(\frac{-1}{KbT} + EDonor \cdot \frac{\frac{-1}{KbT} - \frac{mu}{EDonor \cdot KbT}}{Vef}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;EDonor \leq 1.8 \cdot 10^{-5}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 77.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;EDonor \leq -2.8 \cdot 10^{+113} \lor \neg \left(EDonor \leq 4.2 \cdot 10^{+54}\right):\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (or (<= EDonor -2.8e+113) (not (<= EDonor 4.2e+54)))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))))
     (+ t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if ((EDonor <= -2.8e+113) || !(EDonor <= 4.2e+54)) {
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if ((edonor <= (-2.8d+113)) .or. (.not. (edonor <= 4.2d+54))) then
        tmp = t_0 + (ndchar / (1.0d0 + exp((edonor / kbt))))
    else
        tmp = t_0 + (ndchar / (1.0d0 + exp((vef / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if ((EDonor <= -2.8e+113) || !(EDonor <= 4.2e+54)) {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((EDonor / KbT))));
	} else {
		tmp = t_0 + (NdChar / (1.0 + Math.exp((Vef / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if (EDonor <= -2.8e+113) or not (EDonor <= 4.2e+54):
		tmp = t_0 + (NdChar / (1.0 + math.exp((EDonor / KbT))))
	else:
		tmp = t_0 + (NdChar / (1.0 + math.exp((Vef / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if ((EDonor <= -2.8e+113) || !(EDonor <= 4.2e+54))
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))));
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if ((EDonor <= -2.8e+113) || ~((EDonor <= 4.2e+54)))
		tmp = t_0 + (NdChar / (1.0 + exp((EDonor / KbT))));
	else
		tmp = t_0 + (NdChar / (1.0 + exp((Vef / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[EDonor, -2.8e+113], N[Not[LessEqual[EDonor, 4.2e+54]], $MachinePrecision]], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if EDonor < -2.79999999999999998e113 or 4.19999999999999972e54 < EDonor

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 93.6%

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

   if -2.79999999999999998e113 < EDonor < 4.19999999999999972e54

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 83.9%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq -2.8 \cdot 10^{+113} \lor \neg \left(EDonor \leq 4.2 \cdot 10^{+54}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}\\ t_1 := \frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - t\_0}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -6.2 \cdot 10^{+47}:\\ \;\;\;\;t\_2 - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \left(\left(\frac{2}{Ec} + \frac{\frac{EDonor}{Ec}}{KbT}\right) + \left(\frac{Vef}{Ec \cdot KbT} + \frac{\frac{mu}{Ec}}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq -210000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -4.3 \cdot 10^{-22}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2 \cdot 10^{-29}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} - Ev \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot Ev}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2.6 \cdot 10^{-118}:\\ \;\;\;\;t\_2 + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-91}:\\ \;\;\;\;t\_2 + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 8.8 \cdot 10^{-32}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))
        (t_1 (- (/ NaChar (+ 2.0 (/ Ev KbT))) (/ NdChar (- -1.0 t_0))))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -6.2e+47)
     (-
      t_2
      (/
       NdChar
       (*
        Ec
        (-
         (/ 1.0 KbT)
         (+
          (+ (/ 2.0 Ec) (/ (/ EDonor Ec) KbT))
          (+ (/ Vef (* Ec KbT)) (/ (/ mu Ec) KbT)))))))
     (if (<= NaChar -210000.0)
       t_1
       (if (<= NaChar -4.3e-22)
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
         (if (<= NaChar -2e-29)
           (+
            (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
            (/
             NaChar
             (-
              (+
               2.0
               (- (/ EAccept KbT) (* Ev (- (/ -1.0 KbT) (/ Vef (* KbT Ev))))))
              (/ mu KbT))))
           (if (<= NaChar -2.6e-118)
             (+ t_2 (/ NdChar (+ (/ EDonor KbT) 2.0)))
             (if (<= NaChar 1.8e-193)
               (-
                (/ NdChar (+ 1.0 t_0))
                (/
                 NaChar
                 (-
                  (/ mu KbT)
                  (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))))))
               (if (<= NaChar 8.5e-91)
                 (+ t_2 (/ NdChar (- (+ 2.0 (/ mu KbT)) (/ Ec KbT))))
                 (if (<= NaChar 8.8e-32)
                   t_1
                   (+
                    t_2
                    (/
                     NdChar
                     (-
                      (+
                       2.0
                       (*
                        EDonor
                        (+
                         (/ 1.0 KbT)
                         (+ (/ (/ Vef EDonor) KbT) (/ (/ mu EDonor) KbT)))))
                      (/ Ec KbT))))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	double t_1 = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - t_0));
	double t_2 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -6.2e+47) {
		tmp = t_2 - (NdChar / (Ec * ((1.0 / KbT) - (((2.0 / Ec) + ((EDonor / Ec) / KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))))));
	} else if (NaChar <= -210000.0) {
		tmp = t_1;
	} else if (NaChar <= -4.3e-22) {
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (NaChar <= -2e-29) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) - (Ev * ((-1.0 / KbT) - (Vef / (KbT * Ev)))))) - (mu / KbT)));
	} else if (NaChar <= -2.6e-118) {
		tmp = t_2 + (NdChar / ((EDonor / KbT) + 2.0));
	} else if (NaChar <= 1.8e-193) {
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	} else if (NaChar <= 8.5e-91) {
		tmp = t_2 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	} else if (NaChar <= 8.8e-32) {
		tmp = t_1;
	} else {
		tmp = t_2 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = exp(((edonor - ((ec - vef) - mu)) / kbt))
    t_1 = (nachar / (2.0d0 + (ev / kbt))) - (ndchar / ((-1.0d0) - t_0))
    t_2 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-6.2d+47)) then
        tmp = t_2 - (ndchar / (ec * ((1.0d0 / kbt) - (((2.0d0 / ec) + ((edonor / ec) / kbt)) + ((vef / (ec * kbt)) + ((mu / ec) / kbt))))))
    else if (nachar <= (-210000.0d0)) then
        tmp = t_1
    else if (nachar <= (-4.3d-22)) then
        tmp = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (nachar <= (-2d-29)) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / ((2.0d0 + ((eaccept / kbt) - (ev * (((-1.0d0) / kbt) - (vef / (kbt * ev)))))) - (mu / kbt)))
    else if (nachar <= (-2.6d-118)) then
        tmp = t_2 + (ndchar / ((edonor / kbt) + 2.0d0))
    else if (nachar <= 1.8d-193) then
        tmp = (ndchar / (1.0d0 + t_0)) - (nachar / ((mu / kbt) - (2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt))))))
    else if (nachar <= 8.5d-91) then
        tmp = t_2 + (ndchar / ((2.0d0 + (mu / kbt)) - (ec / kbt)))
    else if (nachar <= 8.8d-32) then
        tmp = t_1
    else
        tmp = t_2 + (ndchar / ((2.0d0 + (edonor * ((1.0d0 / kbt) + (((vef / edonor) / kbt) + ((mu / edonor) / kbt))))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	double t_1 = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - t_0));
	double t_2 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -6.2e+47) {
		tmp = t_2 - (NdChar / (Ec * ((1.0 / KbT) - (((2.0 / Ec) + ((EDonor / Ec) / KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))))));
	} else if (NaChar <= -210000.0) {
		tmp = t_1;
	} else if (NaChar <= -4.3e-22) {
		tmp = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (NaChar <= -2e-29) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) - (Ev * ((-1.0 / KbT) - (Vef / (KbT * Ev)))))) - (mu / KbT)));
	} else if (NaChar <= -2.6e-118) {
		tmp = t_2 + (NdChar / ((EDonor / KbT) + 2.0));
	} else if (NaChar <= 1.8e-193) {
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	} else if (NaChar <= 8.5e-91) {
		tmp = t_2 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	} else if (NaChar <= 8.8e-32) {
		tmp = t_1;
	} else {
		tmp = t_2 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))
	t_1 = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - t_0))
	t_2 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -6.2e+47:
		tmp = t_2 - (NdChar / (Ec * ((1.0 / KbT) - (((2.0 / Ec) + ((EDonor / Ec) / KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))))))
	elif NaChar <= -210000.0:
		tmp = t_1
	elif NaChar <= -4.3e-22:
		tmp = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif NaChar <= -2e-29:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) - (Ev * ((-1.0 / KbT) - (Vef / (KbT * Ev)))))) - (mu / KbT)))
	elif NaChar <= -2.6e-118:
		tmp = t_2 + (NdChar / ((EDonor / KbT) + 2.0))
	elif NaChar <= 1.8e-193:
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))))
	elif NaChar <= 8.5e-91:
		tmp = t_2 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)))
	elif NaChar <= 8.8e-32:
		tmp = t_1
	else:
		tmp = t_2 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))
	t_1 = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - Float64(NdChar / Float64(-1.0 - t_0)))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -6.2e+47)
		tmp = Float64(t_2 - Float64(NdChar / Float64(Ec * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(2.0 / Ec) + Float64(Float64(EDonor / Ec) / KbT)) + Float64(Float64(Vef / Float64(Ec * KbT)) + Float64(Float64(mu / Ec) / KbT)))))));
	elseif (NaChar <= -210000.0)
		tmp = t_1;
	elseif (NaChar <= -4.3e-22)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (NaChar <= -2e-29)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(Float64(2.0 + Float64(Float64(EAccept / KbT) - Float64(Ev * Float64(Float64(-1.0 / KbT) - Float64(Vef / Float64(KbT * Ev)))))) - Float64(mu / KbT))));
	elseif (NaChar <= -2.6e-118)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Float64(EDonor / KbT) + 2.0)));
	elseif (NaChar <= 1.8e-193)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) - Float64(NaChar / Float64(Float64(mu / KbT) - Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))))));
	elseif (NaChar <= 8.5e-91)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Float64(2.0 + Float64(mu / KbT)) - Float64(Ec / KbT))));
	elseif (NaChar <= 8.8e-32)
		tmp = t_1;
	else
		tmp = Float64(t_2 + Float64(NdChar / Float64(Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(Vef / EDonor) / KbT) + Float64(Float64(mu / EDonor) / KbT))))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	t_1 = (NaChar / (2.0 + (Ev / KbT))) - (NdChar / (-1.0 - t_0));
	t_2 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -6.2e+47)
		tmp = t_2 - (NdChar / (Ec * ((1.0 / KbT) - (((2.0 / Ec) + ((EDonor / Ec) / KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))))));
	elseif (NaChar <= -210000.0)
		tmp = t_1;
	elseif (NaChar <= -4.3e-22)
		tmp = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (NaChar <= -2e-29)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / ((2.0 + ((EAccept / KbT) - (Ev * ((-1.0 / KbT) - (Vef / (KbT * Ev)))))) - (mu / KbT)));
	elseif (NaChar <= -2.6e-118)
		tmp = t_2 + (NdChar / ((EDonor / KbT) + 2.0));
	elseif (NaChar <= 1.8e-193)
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	elseif (NaChar <= 8.5e-91)
		tmp = t_2 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	elseif (NaChar <= 8.8e-32)
		tmp = t_1;
	else
		tmp = t_2 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.2e+47], N[(t$95$2 - N[(NdChar / N[(Ec * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(2.0 / Ec), $MachinePrecision] + N[(N[(EDonor / Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(mu / Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -210000.0], t$95$1, If[LessEqual[NaChar, -4.3e-22], N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2e-29], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] - N[(Ev * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(Vef / N[(KbT * Ev), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2.6e-118], N[(t$95$2 + N[(NdChar / N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.8e-193], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(N[(mu / KbT), $MachinePrecision] - N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8.5e-91], N[(t$95$2 + N[(NdChar / N[(N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8.8e-32], t$95$1, N[(t$95$2 + N[(NdChar / N[(N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(Vef / EDonor), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(mu / EDonor), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 8 regimes

2. if NaChar < -6.2000000000000001e47

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 62.1%

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

   6. Taylor expanded in Ec around inf 72.3%

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

      1. sub-neg 72.3%

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

      2. associate-+r+ 72.3%

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

      3. associate-*r/ 72.3%

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

      4. metadata-eval 72.3%

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

      5. associate-/r* 72.3%

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

      6. *-commutative 72.3%

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

      7. associate-/r* 72.3%

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

      8. distribute-neg-frac 72.3%

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

      9. metadata-eval 72.3%

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

   8. Simplified 72.3%

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

   if -6.2000000000000001e47 < NaChar < -2.1e5 or 8.49999999999999985e-91 < NaChar < 8.7999999999999999e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 75.8%

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

   6. Taylor expanded in Ev around 0 76.2%

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

   if -2.1e5 < NaChar < -4.30000000000000037e-22

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 88.1%

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

   6. Taylor expanded in EAccept around inf 67.5%

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

   if -4.30000000000000037e-22 < NaChar < -1.99999999999999989e-29

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 100.0%

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

   6. Taylor expanded in KbT around inf 68.8%

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

   7. Taylor expanded in Ev around inf 100.0%

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

      1. *-commutative 100.0%

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

   9. Simplified 100.0%

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

   if -1.99999999999999989e-29 < NaChar < -2.6e-118

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 82.4%

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

   6. Taylor expanded in EDonor around 0 76.9%

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

   if -2.6e-118 < NaChar < 1.7999999999999999e-193

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.6%

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

   if 1.7999999999999999e-193 < NaChar < 8.49999999999999985e-91

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.2%

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

   6. Taylor expanded in EDonor around inf 53.8%

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

      1. associate-/r* 67.0%

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

      2. associate-/r* 60.3%

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

   8. Simplified 60.3%

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

   9. Taylor expanded in mu around inf 68.6%

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

   if 8.7999999999999999e-32 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.6%

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

   6. Taylor expanded in EDonor around inf 76.7%

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

      1. associate-/r* 79.2%

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

      2. associate-/r* 79.2%

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

   8. Simplified 79.2%

      \[\leadsto \frac{NdChar}{\left(2 + \color{blue}{EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)}\right) - \frac{Ec}{KbT}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 8 regimes into one program.

4. Final simplification 76.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.2 \cdot 10^{+47}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \left(\left(\frac{2}{Ec} + \frac{\frac{EDonor}{Ec}}{KbT}\right) + \left(\frac{Vef}{Ec \cdot KbT} + \frac{\frac{mu}{Ec}}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq -210000:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -4.3 \cdot 10^{-22}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2 \cdot 10^{-29}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{\left(2 + \left(\frac{EAccept}{KbT} - Ev \cdot \left(\frac{-1}{KbT} - \frac{Vef}{KbT \cdot Ev}\right)\right)\right) - \frac{mu}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2.6 \cdot 10^{-118}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \mathbf{elif}\;NaChar \leq 1.8 \cdot 10^{-193}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 8.5 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 8.8 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;mu \leq -6.6 \cdot 10^{+212} \lor \neg \left(mu \leq 8.5 \cdot 10^{+201}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= mu -6.6e+212) (not (<= mu 8.5e+201)))
   (-
    (/ NaChar (+ 1.0 (exp (/ mu (- KbT)))))
    (/ NdChar (- -1.0 (exp (/ mu KbT)))))
   (+
    (/ NdChar (+ 1.0 (exp (/ Vef KbT))))
    (/ NaChar (+ 1.0 (exp (/ (- (+ Vef Ev) mu) KbT)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -6.6e+212) || !(mu <= 8.5e+201)) {
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) - (NdChar / (-1.0 - exp((mu / KbT))));
	} else {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((mu <= (-6.6d+212)) .or. (.not. (mu <= 8.5d+201))) then
        tmp = (nachar / (1.0d0 + exp((mu / -kbt)))) - (ndchar / ((-1.0d0) - exp((mu / kbt))))
    else
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / (1.0d0 + exp((((vef + ev) - mu) / kbt))))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((mu <= -6.6e+212) || !(mu <= 8.5e+201)) {
		tmp = (NaChar / (1.0 + Math.exp((mu / -KbT)))) - (NdChar / (-1.0 - Math.exp((mu / KbT))));
	} else {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / (1.0 + Math.exp((((Vef + Ev) - mu) / KbT))));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (mu <= -6.6e+212) or not (mu <= 8.5e+201):
		tmp = (NaChar / (1.0 + math.exp((mu / -KbT)))) - (NdChar / (-1.0 - math.exp((mu / KbT))))
	else:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / (1.0 + math.exp((((Vef + Ev) - mu) / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((mu <= -6.6e+212) || !(mu <= 8.5e+201))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(mu / Float64(-KbT))))) - Float64(NdChar / Float64(-1.0 - exp(Float64(mu / KbT)))));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + Ev) - mu) / KbT)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((mu <= -6.6e+212) || ~((mu <= 8.5e+201)))
		tmp = (NaChar / (1.0 + exp((mu / -KbT)))) - (NdChar / (-1.0 - exp((mu / KbT))));
	else
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (1.0 + exp((((Vef + Ev) - mu) / KbT))));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[mu, -6.6e+212], N[Not[LessEqual[mu, 8.5e+201]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(mu / (-KbT)), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + Ev), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if mu < -6.6e212 or 8.5e201 < mu

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in mu around inf 85.0%

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

   6. Taylor expanded in mu around inf 78.1%

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

      1. associate-*r/ 78.1%

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

      2. mul-1-neg 78.1%

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

   8. Simplified 78.1%

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

   if -6.6e212 < mu < 8.5e201

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 82.5%

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

   6. Taylor expanded in EAccept around 0 76.0%

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

4. Final simplification 76.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;mu \leq -6.6 \cdot 10^{+212} \lor \neg \left(mu \leq 8.5 \cdot 10^{+201}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{mu}{-KbT}}} - \frac{NdChar}{-1 - e^{\frac{mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(Vef + Ev\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.2% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}\\ t_1 := \frac{NdChar}{-1 - t\_0}\\ t_2 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.9 \cdot 10^{+97}:\\ \;\;\;\;t\_2 - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \left(\left(\frac{2}{Ec} + \frac{\frac{EDonor}{Ec}}{KbT}\right) + \left(\frac{Vef}{Ec \cdot KbT} + \frac{\frac{mu}{Ec}}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq -6 \cdot 10^{+29}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - t\_1\\ \mathbf{elif}\;NaChar \leq -3 \cdot 10^{-123}:\\ \;\;\;\;t\_2 + \frac{NdChar}{\left(2 - Vef \cdot \left(\frac{-1}{KbT} + EDonor \cdot \frac{\frac{-1}{KbT} - \frac{mu}{EDonor \cdot KbT}}{Vef}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{-187}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 2.8 \cdot 10^{-88}:\\ \;\;\;\;t\_2 + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_2 + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))
        (t_1 (/ NdChar (- -1.0 t_0)))
        (t_2 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -2.9e+97)
     (-
      t_2
      (/
       NdChar
       (*
        Ec
        (-
         (/ 1.0 KbT)
         (+
          (+ (/ 2.0 Ec) (/ (/ EDonor Ec) KbT))
          (+ (/ Vef (* Ec KbT)) (/ (/ mu Ec) KbT)))))))
     (if (<= NaChar -6e+29)
       (- (/ NaChar (+ 2.0 (/ EAccept KbT))) t_1)
       (if (<= NaChar -3e-123)
         (+
          t_2
          (/
           NdChar
           (-
            (-
             2.0
             (*
              Vef
              (+
               (/ -1.0 KbT)
               (* EDonor (/ (- (/ -1.0 KbT) (/ mu (* EDonor KbT))) Vef)))))
            (/ Ec KbT))))
         (if (<= NaChar 4.1e-187)
           (-
            (/ NdChar (+ 1.0 t_0))
            (/
             NaChar
             (-
              (/ mu KbT)
              (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))))))
           (if (<= NaChar 2.8e-88)
             (+ t_2 (/ NdChar (- (+ 2.0 (/ mu KbT)) (/ Ec KbT))))
             (if (<= NaChar 1.9e-32)
               (- (/ NaChar (+ 2.0 (/ Ev KbT))) t_1)
               (+
                t_2
                (/
                 NdChar
                 (-
                  (+
                   2.0
                   (*
                    EDonor
                    (+
                     (/ 1.0 KbT)
                     (+ (/ (/ Vef EDonor) KbT) (/ (/ mu EDonor) KbT)))))
                  (/ Ec KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	double t_1 = NdChar / (-1.0 - t_0);
	double t_2 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.9e+97) {
		tmp = t_2 - (NdChar / (Ec * ((1.0 / KbT) - (((2.0 / Ec) + ((EDonor / Ec) / KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))))));
	} else if (NaChar <= -6e+29) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_1;
	} else if (NaChar <= -3e-123) {
		tmp = t_2 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)));
	} else if (NaChar <= 4.1e-187) {
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	} else if (NaChar <= 2.8e-88) {
		tmp = t_2 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	} else if (NaChar <= 1.9e-32) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_1;
	} else {
		tmp = t_2 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = exp(((edonor - ((ec - vef) - mu)) / kbt))
    t_1 = ndchar / ((-1.0d0) - t_0)
    t_2 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-2.9d+97)) then
        tmp = t_2 - (ndchar / (ec * ((1.0d0 / kbt) - (((2.0d0 / ec) + ((edonor / ec) / kbt)) + ((vef / (ec * kbt)) + ((mu / ec) / kbt))))))
    else if (nachar <= (-6d+29)) then
        tmp = (nachar / (2.0d0 + (eaccept / kbt))) - t_1
    else if (nachar <= (-3d-123)) then
        tmp = t_2 + (ndchar / ((2.0d0 - (vef * (((-1.0d0) / kbt) + (edonor * ((((-1.0d0) / kbt) - (mu / (edonor * kbt))) / vef))))) - (ec / kbt)))
    else if (nachar <= 4.1d-187) then
        tmp = (ndchar / (1.0d0 + t_0)) - (nachar / ((mu / kbt) - (2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt))))))
    else if (nachar <= 2.8d-88) then
        tmp = t_2 + (ndchar / ((2.0d0 + (mu / kbt)) - (ec / kbt)))
    else if (nachar <= 1.9d-32) then
        tmp = (nachar / (2.0d0 + (ev / kbt))) - t_1
    else
        tmp = t_2 + (ndchar / ((2.0d0 + (edonor * ((1.0d0 / kbt) + (((vef / edonor) / kbt) + ((mu / edonor) / kbt))))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	double t_1 = NdChar / (-1.0 - t_0);
	double t_2 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.9e+97) {
		tmp = t_2 - (NdChar / (Ec * ((1.0 / KbT) - (((2.0 / Ec) + ((EDonor / Ec) / KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))))));
	} else if (NaChar <= -6e+29) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_1;
	} else if (NaChar <= -3e-123) {
		tmp = t_2 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)));
	} else if (NaChar <= 4.1e-187) {
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	} else if (NaChar <= 2.8e-88) {
		tmp = t_2 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	} else if (NaChar <= 1.9e-32) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_1;
	} else {
		tmp = t_2 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))
	t_1 = NdChar / (-1.0 - t_0)
	t_2 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -2.9e+97:
		tmp = t_2 - (NdChar / (Ec * ((1.0 / KbT) - (((2.0 / Ec) + ((EDonor / Ec) / KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))))))
	elif NaChar <= -6e+29:
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_1
	elif NaChar <= -3e-123:
		tmp = t_2 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)))
	elif NaChar <= 4.1e-187:
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))))
	elif NaChar <= 2.8e-88:
		tmp = t_2 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)))
	elif NaChar <= 1.9e-32:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_1
	else:
		tmp = t_2 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))
	t_1 = Float64(NdChar / Float64(-1.0 - t_0))
	t_2 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.9e+97)
		tmp = Float64(t_2 - Float64(NdChar / Float64(Ec * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(2.0 / Ec) + Float64(Float64(EDonor / Ec) / KbT)) + Float64(Float64(Vef / Float64(Ec * KbT)) + Float64(Float64(mu / Ec) / KbT)))))));
	elseif (NaChar <= -6e+29)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - t_1);
	elseif (NaChar <= -3e-123)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Float64(2.0 - Float64(Vef * Float64(Float64(-1.0 / KbT) + Float64(EDonor * Float64(Float64(Float64(-1.0 / KbT) - Float64(mu / Float64(EDonor * KbT))) / Vef))))) - Float64(Ec / KbT))));
	elseif (NaChar <= 4.1e-187)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) - Float64(NaChar / Float64(Float64(mu / KbT) - Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))))));
	elseif (NaChar <= 2.8e-88)
		tmp = Float64(t_2 + Float64(NdChar / Float64(Float64(2.0 + Float64(mu / KbT)) - Float64(Ec / KbT))));
	elseif (NaChar <= 1.9e-32)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - t_1);
	else
		tmp = Float64(t_2 + Float64(NdChar / Float64(Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(Vef / EDonor) / KbT) + Float64(Float64(mu / EDonor) / KbT))))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	t_1 = NdChar / (-1.0 - t_0);
	t_2 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.9e+97)
		tmp = t_2 - (NdChar / (Ec * ((1.0 / KbT) - (((2.0 / Ec) + ((EDonor / Ec) / KbT)) + ((Vef / (Ec * KbT)) + ((mu / Ec) / KbT))))));
	elseif (NaChar <= -6e+29)
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_1;
	elseif (NaChar <= -3e-123)
		tmp = t_2 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)));
	elseif (NaChar <= 4.1e-187)
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	elseif (NaChar <= 2.8e-88)
		tmp = t_2 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	elseif (NaChar <= 1.9e-32)
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_1;
	else
		tmp = t_2 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.9e+97], N[(t$95$2 - N[(NdChar / N[(Ec * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(2.0 / Ec), $MachinePrecision] + N[(N[(EDonor / Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(Vef / N[(Ec * KbT), $MachinePrecision]), $MachinePrecision] + N[(N[(mu / Ec), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -6e+29], N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], If[LessEqual[NaChar, -3e-123], N[(t$95$2 + N[(NdChar / N[(N[(2.0 - N[(Vef * N[(N[(-1.0 / KbT), $MachinePrecision] + N[(EDonor * N[(N[(N[(-1.0 / KbT), $MachinePrecision] - N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.1e-187], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(N[(mu / KbT), $MachinePrecision] - N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.8e-88], N[(t$95$2 + N[(NdChar / N[(N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.9e-32], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$1), $MachinePrecision], N[(t$95$2 + N[(NdChar / N[(N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(Vef / EDonor), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(mu / EDonor), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if NaChar < -2.89999999999999987e97

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.5%

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

   6. Taylor expanded in Ec around inf 77.4%

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

      1. sub-neg 77.4%

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

      2. associate-+r+ 77.4%

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

      3. associate-*r/ 77.4%

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

      4. metadata-eval 77.4%

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

      5. associate-/r* 77.4%

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

      6. *-commutative 77.4%

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

      7. associate-/r* 77.4%

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

      8. distribute-neg-frac 77.4%

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

      9. metadata-eval 77.4%

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

   8. Simplified 77.4%

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

   if -2.89999999999999987e97 < NaChar < -5.9999999999999998e29

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 71.7%

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

   6. Taylor expanded in EAccept around 0 69.8%

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

   if -5.9999999999999998e29 < NaChar < -2.99999999999999984e-123

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 62.9%

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

   6. Taylor expanded in EDonor around inf 59.8%

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

      1. associate-/r* 65.8%

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

      2. associate-/r* 65.8%

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

   8. Simplified 65.8%

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

   9. Taylor expanded in Vef around inf 65.9%

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

       1. associate-/l* 68.6%

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

   11. Simplified 68.6%

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

   if -2.99999999999999984e-123 < NaChar < 4.1000000000000002e-187

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.6%

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

   if 4.1000000000000002e-187 < NaChar < 2.79999999999999976e-88

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 54.2%

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

   6. Taylor expanded in EDonor around inf 53.8%

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

      1. associate-/r* 67.0%

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

      2. associate-/r* 60.3%

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

   8. Simplified 60.3%

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

   9. Taylor expanded in mu around inf 68.6%

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

   if 2.79999999999999976e-88 < NaChar < 1.90000000000000004e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 82.5%

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

   6. Taylor expanded in Ev around 0 74.2%

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

   if 1.90000000000000004e-32 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.6%

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

   6. Taylor expanded in EDonor around inf 76.7%

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

      1. associate-/r* 79.2%

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

      2. associate-/r* 79.2%

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

   8. Simplified 79.2%

      \[\leadsto \frac{NdChar}{\left(2 + \color{blue}{EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)}\right) - \frac{Ec}{KbT}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 7 regimes into one program.

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.9 \cdot 10^{+97}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \left(\left(\frac{2}{Ec} + \frac{\frac{EDonor}{Ec}}{KbT}\right) + \left(\frac{Vef}{Ec \cdot KbT} + \frac{\frac{mu}{Ec}}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq -6 \cdot 10^{+29}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -3 \cdot 10^{-123}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 - Vef \cdot \left(\frac{-1}{KbT} + EDonor \cdot \frac{\frac{-1}{KbT} - \frac{mu}{EDonor \cdot KbT}}{Vef}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 4.1 \cdot 10^{-187}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 2.8 \cdot 10^{-88}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 62.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ t_2 := e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}\\ t_3 := \frac{NdChar}{-1 - t\_2}\\ \mathbf{if}\;NaChar \leq -5.4 \cdot 10^{+107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq -5.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - t\_3\\ \mathbf{elif}\;NaChar \leq -2.15 \cdot 10^{-113}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + 2\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 4.4 \cdot 10^{-187}:\\ \;\;\;\;\frac{NdChar}{1 + t\_2} - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 2.4 \cdot 10^{-91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT)))))
        (t_1 (+ t_0 (/ NdChar (- (+ 2.0 (/ mu KbT)) (/ Ec KbT)))))
        (t_2 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))
        (t_3 (/ NdChar (- -1.0 t_2))))
   (if (<= NaChar -5.4e+107)
     t_1
     (if (<= NaChar -5.9e+30)
       (- (/ NaChar (+ 2.0 (/ EAccept KbT))) t_3)
       (if (<= NaChar -2.15e-113)
         (+
          t_0
          (/ NdChar (- (+ (/ Vef KbT) (+ (/ EDonor KbT) 2.0)) (/ Ec KbT))))
         (if (<= NaChar 4.4e-187)
           (-
            (/ NdChar (+ 1.0 t_2))
            (/
             NaChar
             (-
              (/ mu KbT)
              (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))))))
           (if (<= NaChar 2.4e-91)
             t_1
             (if (<= NaChar 1.7e-32)
               (- (/ NaChar (+ 2.0 (/ Ev KbT))) t_3)
               (+
                t_0
                (/
                 NdChar
                 (-
                  (+ 2.0 (* EDonor (+ (/ 1.0 KbT) (/ Vef (* EDonor KbT)))))
                  (/ Ec KbT))))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	double t_2 = exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	double t_3 = NdChar / (-1.0 - t_2);
	double tmp;
	if (NaChar <= -5.4e+107) {
		tmp = t_1;
	} else if (NaChar <= -5.9e+30) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_3;
	} else if (NaChar <= -2.15e-113) {
		tmp = t_0 + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)));
	} else if (NaChar <= 4.4e-187) {
		tmp = (NdChar / (1.0 + t_2)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	} else if (NaChar <= 2.4e-91) {
		tmp = t_1;
	} else if (NaChar <= 1.7e-32) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_3;
	} else {
		tmp = t_0 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    t_1 = t_0 + (ndchar / ((2.0d0 + (mu / kbt)) - (ec / kbt)))
    t_2 = exp(((edonor - ((ec - vef) - mu)) / kbt))
    t_3 = ndchar / ((-1.0d0) - t_2)
    if (nachar <= (-5.4d+107)) then
        tmp = t_1
    else if (nachar <= (-5.9d+30)) then
        tmp = (nachar / (2.0d0 + (eaccept / kbt))) - t_3
    else if (nachar <= (-2.15d-113)) then
        tmp = t_0 + (ndchar / (((vef / kbt) + ((edonor / kbt) + 2.0d0)) - (ec / kbt)))
    else if (nachar <= 4.4d-187) then
        tmp = (ndchar / (1.0d0 + t_2)) - (nachar / ((mu / kbt) - (2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt))))))
    else if (nachar <= 2.4d-91) then
        tmp = t_1
    else if (nachar <= 1.7d-32) then
        tmp = (nachar / (2.0d0 + (ev / kbt))) - t_3
    else
        tmp = t_0 + (ndchar / ((2.0d0 + (edonor * ((1.0d0 / kbt) + (vef / (edonor * kbt))))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double t_1 = t_0 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	double t_2 = Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	double t_3 = NdChar / (-1.0 - t_2);
	double tmp;
	if (NaChar <= -5.4e+107) {
		tmp = t_1;
	} else if (NaChar <= -5.9e+30) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_3;
	} else if (NaChar <= -2.15e-113) {
		tmp = t_0 + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)));
	} else if (NaChar <= 4.4e-187) {
		tmp = (NdChar / (1.0 + t_2)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	} else if (NaChar <= 2.4e-91) {
		tmp = t_1;
	} else if (NaChar <= 1.7e-32) {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_3;
	} else {
		tmp = t_0 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	t_1 = t_0 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)))
	t_2 = math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))
	t_3 = NdChar / (-1.0 - t_2)
	tmp = 0
	if NaChar <= -5.4e+107:
		tmp = t_1
	elif NaChar <= -5.9e+30:
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_3
	elif NaChar <= -2.15e-113:
		tmp = t_0 + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)))
	elif NaChar <= 4.4e-187:
		tmp = (NdChar / (1.0 + t_2)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))))
	elif NaChar <= 2.4e-91:
		tmp = t_1
	elif NaChar <= 1.7e-32:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_3
	else:
		tmp = t_0 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(mu / KbT)) - Float64(Ec / KbT))))
	t_2 = exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))
	t_3 = Float64(NdChar / Float64(-1.0 - t_2))
	tmp = 0.0
	if (NaChar <= -5.4e+107)
		tmp = t_1;
	elseif (NaChar <= -5.9e+30)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - t_3);
	elseif (NaChar <= -2.15e-113)
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(Float64(Vef / KbT) + Float64(Float64(EDonor / KbT) + 2.0)) - Float64(Ec / KbT))));
	elseif (NaChar <= 4.4e-187)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_2)) - Float64(NaChar / Float64(Float64(mu / KbT) - Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))))));
	elseif (NaChar <= 2.4e-91)
		tmp = t_1;
	elseif (NaChar <= 1.7e-32)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - t_3);
	else
		tmp = Float64(t_0 + Float64(NdChar / Float64(Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Vef / Float64(EDonor * KbT))))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	t_1 = t_0 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	t_2 = exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	t_3 = NdChar / (-1.0 - t_2);
	tmp = 0.0;
	if (NaChar <= -5.4e+107)
		tmp = t_1;
	elseif (NaChar <= -5.9e+30)
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_3;
	elseif (NaChar <= -2.15e-113)
		tmp = t_0 + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)));
	elseif (NaChar <= 4.4e-187)
		tmp = (NdChar / (1.0 + t_2)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	elseif (NaChar <= 2.4e-91)
		tmp = t_1;
	elseif (NaChar <= 1.7e-32)
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_3;
	else
		tmp = t_0 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(NdChar / N[(-1.0 - t$95$2), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -5.4e+107], t$95$1, If[LessEqual[NaChar, -5.9e+30], N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], If[LessEqual[NaChar, -2.15e-113], N[(t$95$0 + N[(NdChar / N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.4e-187], N[(N[(NdChar / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(N[(mu / KbT), $MachinePrecision] - N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.4e-91], t$95$1, If[LessEqual[NaChar, 1.7e-32], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$3), $MachinePrecision], N[(t$95$0 + N[(NdChar / N[(N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(Vef / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if NaChar < -5.4000000000000003e107 or 4.40000000000000016e-187 < NaChar < 2.40000000000000011e-91

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 62.1%

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

   6. Taylor expanded in EDonor around inf 58.1%

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

      1. associate-/r* 62.2%

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

      2. associate-/r* 57.8%

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

   8. Simplified 57.8%

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

   9. Taylor expanded in mu around inf 70.6%

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

   if -5.4000000000000003e107 < NaChar < -5.90000000000000015e30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 71.7%

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

   6. Taylor expanded in EAccept around 0 69.8%

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

   if -5.90000000000000015e30 < NaChar < -2.15e-113

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 62.9%

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

   6. Taylor expanded in mu around 0 66.4%

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

      1. associate-+r+ 66.4%

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

   8. Simplified 66.4%

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

   if -2.15e-113 < NaChar < 4.40000000000000016e-187

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 76.6%

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

   if 2.40000000000000011e-91 < NaChar < 1.69999999999999989e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 82.5%

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

   6. Taylor expanded in Ev around 0 74.2%

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

   if 1.69999999999999989e-32 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 71.6%

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

   6. Taylor expanded in EDonor around inf 76.7%

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

      1. associate-/r* 79.2%

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

      2. associate-/r* 79.2%

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

   8. Simplified 79.2%

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

   9. Taylor expanded in mu around 0 78.2%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.4 \cdot 10^{+107}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq -5.9 \cdot 10^{+30}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.15 \cdot 10^{-113}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + 2\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 4.4 \cdot 10^{-187}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NaChar \leq 2.4 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 62.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{+97}:\\ \;\;\;\;t\_1 - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \frac{\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{Ec}\right)}\\ \mathbf{elif}\;NaChar \leq -9.2 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-212}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 - Vef \cdot \left(\frac{-1}{KbT} + EDonor \cdot \frac{\frac{-1}{KbT} - \frac{mu}{EDonor \cdot KbT}}{Vef}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 8.2 \cdot 10^{-27}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ 2.0 (/ EAccept KbT)))
          (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -2.7e+97)
     (-
      t_1
      (/
       NdChar
       (*
        Ec
        (-
         (/ 1.0 KbT)
         (/ (+ (+ (/ EDonor KbT) 2.0) (+ (/ Vef KbT) (/ mu KbT))) Ec)))))
     (if (<= NaChar -9.2e+27)
       t_0
       (if (<= NaChar -2.3e-212)
         (+
          t_1
          (/
           NdChar
           (-
            (-
             2.0
             (*
              Vef
              (+
               (/ -1.0 KbT)
               (* EDonor (/ (- (/ -1.0 KbT) (/ mu (* EDonor KbT))) Vef)))))
            (/ Ec KbT))))
         (if (<= NaChar 8.2e-27)
           t_0
           (+
            t_1
            (/
             NdChar
             (-
              (+
               2.0
               (*
                EDonor
                (+
                 (/ 1.0 KbT)
                 (+ (/ (/ Vef EDonor) KbT) (/ (/ mu EDonor) KbT)))))
              (/ Ec KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.7e+97) {
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))));
	} else if (NaChar <= -9.2e+27) {
		tmp = t_0;
	} else if (NaChar <= -2.3e-212) {
		tmp = t_1 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)));
	} else if (NaChar <= 8.2e-27) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / (2.0d0 + (eaccept / kbt))) - (ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-2.7d+97)) then
        tmp = t_1 - (ndchar / (ec * ((1.0d0 / kbt) - ((((edonor / kbt) + 2.0d0) + ((vef / kbt) + (mu / kbt))) / ec))))
    else if (nachar <= (-9.2d+27)) then
        tmp = t_0
    else if (nachar <= (-2.3d-212)) then
        tmp = t_1 + (ndchar / ((2.0d0 - (vef * (((-1.0d0) / kbt) + (edonor * ((((-1.0d0) / kbt) - (mu / (edonor * kbt))) / vef))))) - (ec / kbt)))
    else if (nachar <= 8.2d-27) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / ((2.0d0 + (edonor * ((1.0d0 / kbt) + (((vef / edonor) / kbt) + ((mu / edonor) / kbt))))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.7e+97) {
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))));
	} else if (NaChar <= -9.2e+27) {
		tmp = t_0;
	} else if (NaChar <= -2.3e-212) {
		tmp = t_1 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)));
	} else if (NaChar <= 8.2e-27) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -2.7e+97:
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))))
	elif NaChar <= -9.2e+27:
		tmp = t_0
	elif NaChar <= -2.3e-212:
		tmp = t_1 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)))
	elif NaChar <= 8.2e-27:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.7e+97)
		tmp = Float64(t_1 - Float64(NdChar / Float64(Ec * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(Float64(EDonor / KbT) + 2.0) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) / Ec)))));
	elseif (NaChar <= -9.2e+27)
		tmp = t_0;
	elseif (NaChar <= -2.3e-212)
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 - Float64(Vef * Float64(Float64(-1.0 / KbT) + Float64(EDonor * Float64(Float64(Float64(-1.0 / KbT) - Float64(mu / Float64(EDonor * KbT))) / Vef))))) - Float64(Ec / KbT))));
	elseif (NaChar <= 8.2e-27)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(Vef / EDonor) / KbT) + Float64(Float64(mu / EDonor) / KbT))))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.7e+97)
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))));
	elseif (NaChar <= -9.2e+27)
		tmp = t_0;
	elseif (NaChar <= -2.3e-212)
		tmp = t_1 + (NdChar / ((2.0 - (Vef * ((-1.0 / KbT) + (EDonor * (((-1.0 / KbT) - (mu / (EDonor * KbT))) / Vef))))) - (Ec / KbT)));
	elseif (NaChar <= 8.2e-27)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.7e+97], N[(t$95$1 - N[(NdChar / N[(Ec * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -9.2e+27], t$95$0, If[LessEqual[NaChar, -2.3e-212], N[(t$95$1 + N[(NdChar / N[(N[(2.0 - N[(Vef * N[(N[(-1.0 / KbT), $MachinePrecision] + N[(EDonor * N[(N[(N[(-1.0 / KbT), $MachinePrecision] - N[(mu / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 8.2e-27], t$95$0, N[(t$95$1 + N[(NdChar / N[(N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(Vef / EDonor), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(mu / EDonor), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.69999999999999993e97

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.5%

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

   6. Taylor expanded in Ec around -inf 74.4%

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

      1. associate-*r* 74.4%

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

      2. mul-1-neg 74.4%

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

      3. +-commutative 74.4%

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

      4. mul-1-neg 74.4%

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

      5. unsub-neg 74.4%

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

      6. associate-+r+ 74.4%

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

      7. +-commutative 74.4%

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

   8. Simplified 74.4%

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

   if -2.69999999999999993e97 < NaChar < -9.2000000000000002e27 or -2.3000000000000001e-212 < NaChar < 8.1999999999999997e-27

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.4%

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

   6. Taylor expanded in EAccept around 0 69.5%

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

   if -9.2000000000000002e27 < NaChar < -2.3000000000000001e-212

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 56.3%

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

   6. Taylor expanded in EDonor around inf 58.1%

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

      1. associate-/r* 62.0%

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

      2. associate-/r* 62.1%

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

   8. Simplified 62.1%

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

   9. Taylor expanded in Vef around inf 63.9%

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

       1. associate-/l* 65.7%

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

   11. Simplified 65.7%

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

   if 8.1999999999999997e-27 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.2%

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

   6. Taylor expanded in EDonor around inf 78.5%

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

      1. associate-/r* 81.1%

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

      2. associate-/r* 81.1%

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

   8. Simplified 81.1%

      \[\leadsto \frac{NdChar}{\left(2 + \color{blue}{EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)}\right) - \frac{Ec}{KbT}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{+97}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \frac{\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{Ec}\right)}\\ \mathbf{elif}\;NaChar \leq -9.2 \cdot 10^{+27}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.3 \cdot 10^{-212}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 - Vef \cdot \left(\frac{-1}{KbT} + EDonor \cdot \frac{\frac{-1}{KbT} - \frac{mu}{EDonor \cdot KbT}}{Vef}\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 8.2 \cdot 10^{-27}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 62.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -5 \cdot 10^{+98}:\\ \;\;\;\;t\_1 - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \frac{\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{Ec}\right)}\\ \mathbf{elif}\;NaChar \leq -4.1 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -6.5 \cdot 10^{-131}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} - Vef \cdot \left(\frac{-1}{KbT} - \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.42 \cdot 10^{-25}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ 2.0 (/ EAccept KbT)))
          (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -5e+98)
     (-
      t_1
      (/
       NdChar
       (*
        Ec
        (-
         (/ 1.0 KbT)
         (/ (+ (+ (/ EDonor KbT) 2.0) (+ (/ Vef KbT) (/ mu KbT))) Ec)))))
     (if (<= NaChar -4.1e+27)
       t_0
       (if (<= NaChar -6.5e-131)
         (+
          t_1
          (/
           NdChar
           (-
            (+
             2.0
             (- (/ EDonor KbT) (* Vef (- (/ -1.0 KbT) (/ mu (* Vef KbT))))))
            (/ Ec KbT))))
         (if (<= NaChar 1.42e-25)
           t_0
           (+
            t_1
            (/
             NdChar
             (-
              (+
               2.0
               (*
                EDonor
                (+
                 (/ 1.0 KbT)
                 (+ (/ (/ Vef EDonor) KbT) (/ (/ mu EDonor) KbT)))))
              (/ Ec KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -5e+98) {
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))));
	} else if (NaChar <= -4.1e+27) {
		tmp = t_0;
	} else if (NaChar <= -6.5e-131) {
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)));
	} else if (NaChar <= 1.42e-25) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / (2.0d0 + (eaccept / kbt))) - (ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-5d+98)) then
        tmp = t_1 - (ndchar / (ec * ((1.0d0 / kbt) - ((((edonor / kbt) + 2.0d0) + ((vef / kbt) + (mu / kbt))) / ec))))
    else if (nachar <= (-4.1d+27)) then
        tmp = t_0
    else if (nachar <= (-6.5d-131)) then
        tmp = t_1 + (ndchar / ((2.0d0 + ((edonor / kbt) - (vef * (((-1.0d0) / kbt) - (mu / (vef * kbt)))))) - (ec / kbt)))
    else if (nachar <= 1.42d-25) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / ((2.0d0 + (edonor * ((1.0d0 / kbt) + (((vef / edonor) / kbt) + ((mu / edonor) / kbt))))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -5e+98) {
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))));
	} else if (NaChar <= -4.1e+27) {
		tmp = t_0;
	} else if (NaChar <= -6.5e-131) {
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)));
	} else if (NaChar <= 1.42e-25) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -5e+98:
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))))
	elif NaChar <= -4.1e+27:
		tmp = t_0
	elif NaChar <= -6.5e-131:
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)))
	elif NaChar <= 1.42e-25:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -5e+98)
		tmp = Float64(t_1 - Float64(NdChar / Float64(Ec * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(Float64(EDonor / KbT) + 2.0) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) / Ec)))));
	elseif (NaChar <= -4.1e+27)
		tmp = t_0;
	elseif (NaChar <= -6.5e-131)
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) - Float64(Vef * Float64(Float64(-1.0 / KbT) - Float64(mu / Float64(Vef * KbT)))))) - Float64(Ec / KbT))));
	elseif (NaChar <= 1.42e-25)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Float64(Float64(Vef / EDonor) / KbT) + Float64(Float64(mu / EDonor) / KbT))))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -5e+98)
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))));
	elseif (NaChar <= -4.1e+27)
		tmp = t_0;
	elseif (NaChar <= -6.5e-131)
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)));
	elseif (NaChar <= 1.42e-25)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (((Vef / EDonor) / KbT) + ((mu / EDonor) / KbT))))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -5e+98], N[(t$95$1 - N[(NdChar / N[(Ec * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -4.1e+27], t$95$0, If[LessEqual[NaChar, -6.5e-131], N[(t$95$1 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] - N[(Vef * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(mu / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.42e-25], t$95$0, N[(t$95$1 + N[(NdChar / N[(N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(N[(N[(Vef / EDonor), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(mu / EDonor), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -4.9999999999999998e98

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.5%

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

   6. Taylor expanded in Ec around -inf 74.4%

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

      1. associate-*r* 74.4%

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

      2. mul-1-neg 74.4%

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

      3. +-commutative 74.4%

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

      4. mul-1-neg 74.4%

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

      5. unsub-neg 74.4%

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

      6. associate-+r+ 74.4%

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

      7. +-commutative 74.4%

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

   8. Simplified 74.4%

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

   if -4.9999999999999998e98 < NaChar < -4.1000000000000002e27 or -6.5000000000000002e-131 < NaChar < 1.4200000000000001e-25

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.4%

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

   6. Taylor expanded in EAccept around 0 68.2%

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

   if -4.1000000000000002e27 < NaChar < -6.5000000000000002e-131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.0%

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

   6. Taylor expanded in Vef around inf 69.5%

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

      1. *-commutative 69.5%

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

   8. Simplified 69.5%

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

   if 1.4200000000000001e-25 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.2%

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

   6. Taylor expanded in EDonor around inf 78.5%

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

      1. associate-/r* 81.1%

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

      2. associate-/r* 81.1%

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

   8. Simplified 81.1%

      \[\leadsto \frac{NdChar}{\left(2 + \color{blue}{EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)}\right) - \frac{Ec}{KbT}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5 \cdot 10^{+98}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \frac{\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{Ec}\right)}\\ \mathbf{elif}\;NaChar \leq -4.1 \cdot 10^{+27}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -6.5 \cdot 10^{-131}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} - Vef \cdot \left(\frac{-1}{KbT} - \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.42 \cdot 10^{-25}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \left(\frac{\frac{Vef}{EDonor}}{KbT} + \frac{\frac{mu}{EDonor}}{KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 63.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;t\_1 - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \frac{\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{Ec}\right)}\\ \mathbf{elif}\;NaChar \leq -1.16 \cdot 10^{+30}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -2.1 \cdot 10^{-131}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} - Vef \cdot \left(\frac{-1}{KbT} - \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ 2.0 (/ EAccept KbT)))
          (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -1.65e+96)
     (-
      t_1
      (/
       NdChar
       (*
        Ec
        (-
         (/ 1.0 KbT)
         (/ (+ (+ (/ EDonor KbT) 2.0) (+ (/ Vef KbT) (/ mu KbT))) Ec)))))
     (if (<= NaChar -1.16e+30)
       t_0
       (if (<= NaChar -2.1e-131)
         (+
          t_1
          (/
           NdChar
           (-
            (+
             2.0
             (- (/ EDonor KbT) (* Vef (- (/ -1.0 KbT) (/ mu (* Vef KbT))))))
            (/ Ec KbT))))
         (if (<= NaChar 1.7e-26)
           t_0
           (+
            t_1
            (/
             NdChar
             (-
              (+ 2.0 (* EDonor (+ (/ 1.0 KbT) (/ Vef (* EDonor KbT)))))
              (/ Ec KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -1.65e+96) {
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))));
	} else if (NaChar <= -1.16e+30) {
		tmp = t_0;
	} else if (NaChar <= -2.1e-131) {
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)));
	} else if (NaChar <= 1.7e-26) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / (2.0d0 + (eaccept / kbt))) - (ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-1.65d+96)) then
        tmp = t_1 - (ndchar / (ec * ((1.0d0 / kbt) - ((((edonor / kbt) + 2.0d0) + ((vef / kbt) + (mu / kbt))) / ec))))
    else if (nachar <= (-1.16d+30)) then
        tmp = t_0
    else if (nachar <= (-2.1d-131)) then
        tmp = t_1 + (ndchar / ((2.0d0 + ((edonor / kbt) - (vef * (((-1.0d0) / kbt) - (mu / (vef * kbt)))))) - (ec / kbt)))
    else if (nachar <= 1.7d-26) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / ((2.0d0 + (edonor * ((1.0d0 / kbt) + (vef / (edonor * kbt))))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -1.65e+96) {
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))));
	} else if (NaChar <= -1.16e+30) {
		tmp = t_0;
	} else if (NaChar <= -2.1e-131) {
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)));
	} else if (NaChar <= 1.7e-26) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -1.65e+96:
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))))
	elif NaChar <= -1.16e+30:
		tmp = t_0
	elif NaChar <= -2.1e-131:
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)))
	elif NaChar <= 1.7e-26:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -1.65e+96)
		tmp = Float64(t_1 - Float64(NdChar / Float64(Ec * Float64(Float64(1.0 / KbT) - Float64(Float64(Float64(Float64(EDonor / KbT) + 2.0) + Float64(Float64(Vef / KbT) + Float64(mu / KbT))) / Ec)))));
	elseif (NaChar <= -1.16e+30)
		tmp = t_0;
	elseif (NaChar <= -2.1e-131)
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) - Float64(Vef * Float64(Float64(-1.0 / KbT) - Float64(mu / Float64(Vef * KbT)))))) - Float64(Ec / KbT))));
	elseif (NaChar <= 1.7e-26)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Vef / Float64(EDonor * KbT))))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -1.65e+96)
		tmp = t_1 - (NdChar / (Ec * ((1.0 / KbT) - ((((EDonor / KbT) + 2.0) + ((Vef / KbT) + (mu / KbT))) / Ec))));
	elseif (NaChar <= -1.16e+30)
		tmp = t_0;
	elseif (NaChar <= -2.1e-131)
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)));
	elseif (NaChar <= 1.7e-26)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -1.65e+96], N[(t$95$1 - N[(NdChar / N[(Ec * N[(N[(1.0 / KbT), $MachinePrecision] - N[(N[(N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(mu / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -1.16e+30], t$95$0, If[LessEqual[NaChar, -2.1e-131], N[(t$95$1 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] - N[(Vef * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(mu / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.7e-26], t$95$0, N[(t$95$1 + N[(NdChar / N[(N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(Vef / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -1.64999999999999992e96

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.5%

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

   6. Taylor expanded in Ec around -inf 74.4%

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

      1. associate-*r* 74.4%

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

      2. mul-1-neg 74.4%

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

      3. +-commutative 74.4%

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

      4. mul-1-neg 74.4%

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

      5. unsub-neg 74.4%

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

      6. associate-+r+ 74.4%

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

      7. +-commutative 74.4%

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

   8. Simplified 74.4%

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

   if -1.64999999999999992e96 < NaChar < -1.16e30 or -2.09999999999999997e-131 < NaChar < 1.70000000000000007e-26

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.4%

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

   6. Taylor expanded in EAccept around 0 68.2%

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

   if -1.16e30 < NaChar < -2.09999999999999997e-131

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.0%

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

   6. Taylor expanded in Vef around inf 69.5%

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

      1. *-commutative 69.5%

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

   8. Simplified 69.5%

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

   if 1.70000000000000007e-26 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.2%

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

   6. Taylor expanded in EDonor around inf 78.5%

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

      1. associate-/r* 81.1%

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

      2. associate-/r* 81.1%

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

   8. Simplified 81.1%

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

   9. Taylor expanded in mu around 0 80.0%

      \[\leadsto \frac{NdChar}{\left(2 + \color{blue}{EDonor \cdot \left(\frac{1}{KbT} + \frac{Vef}{EDonor \cdot KbT}\right)}\right) - \frac{Ec}{KbT}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.65 \cdot 10^{+96}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} - \frac{NdChar}{Ec \cdot \left(\frac{1}{KbT} - \frac{\left(\frac{EDonor}{KbT} + 2\right) + \left(\frac{Vef}{KbT} + \frac{mu}{KbT}\right)}{Ec}\right)}\\ \mathbf{elif}\;NaChar \leq -1.16 \cdot 10^{+30}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.1 \cdot 10^{-131}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} - Vef \cdot \left(\frac{-1}{KbT} - \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 1.7 \cdot 10^{-26}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 63.0% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.35 \cdot 10^{+101}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2.4 \cdot 10^{+22}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq -1.2 \cdot 10^{-133}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} - Vef \cdot \left(\frac{-1}{KbT} - \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.05 \cdot 10^{-23}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1 + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (-
          (/ NaChar (+ 2.0 (/ EAccept KbT)))
          (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))))
   (if (<= NaChar -2.35e+101)
     (+ t_1 (/ NdChar (- (+ 2.0 (/ mu KbT)) (/ Ec KbT))))
     (if (<= NaChar -2.4e+22)
       t_0
       (if (<= NaChar -1.2e-133)
         (+
          t_1
          (/
           NdChar
           (-
            (+
             2.0
             (- (/ EDonor KbT) (* Vef (- (/ -1.0 KbT) (/ mu (* Vef KbT))))))
            (/ Ec KbT))))
         (if (<= NaChar 2.05e-23)
           t_0
           (+
            t_1
            (/
             NdChar
             (-
              (+ 2.0 (* EDonor (+ (/ 1.0 KbT) (/ Vef (* EDonor KbT)))))
              (/ Ec KbT))))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	double t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.35e+101) {
		tmp = t_1 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	} else if (NaChar <= -2.4e+22) {
		tmp = t_0;
	} else if (NaChar <= -1.2e-133) {
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)));
	} else if (NaChar <= 2.05e-23) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (nachar / (2.0d0 + (eaccept / kbt))) - (ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt))))
    t_1 = nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))
    if (nachar <= (-2.35d+101)) then
        tmp = t_1 + (ndchar / ((2.0d0 + (mu / kbt)) - (ec / kbt)))
    else if (nachar <= (-2.4d+22)) then
        tmp = t_0
    else if (nachar <= (-1.2d-133)) then
        tmp = t_1 + (ndchar / ((2.0d0 + ((edonor / kbt) - (vef * (((-1.0d0) / kbt) - (mu / (vef * kbt)))))) - (ec / kbt)))
    else if (nachar <= 2.05d-23) then
        tmp = t_0
    else
        tmp = t_1 + (ndchar / ((2.0d0 + (edonor * ((1.0d0 / kbt) + (vef / (edonor * kbt))))) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	double t_1 = NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	double tmp;
	if (NaChar <= -2.35e+101) {
		tmp = t_1 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	} else if (NaChar <= -2.4e+22) {
		tmp = t_0;
	} else if (NaChar <= -1.2e-133) {
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)));
	} else if (NaChar <= 2.05e-23) {
		tmp = t_0;
	} else {
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))))
	t_1 = NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))
	tmp = 0
	if NaChar <= -2.35e+101:
		tmp = t_1 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)))
	elif NaChar <= -2.4e+22:
		tmp = t_0
	elif NaChar <= -1.2e-133:
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)))
	elif NaChar <= 2.05e-23:
		tmp = t_0
	else:
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.35e+101)
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 + Float64(mu / KbT)) - Float64(Ec / KbT))));
	elseif (NaChar <= -2.4e+22)
		tmp = t_0;
	elseif (NaChar <= -1.2e-133)
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 + Float64(Float64(EDonor / KbT) - Float64(Vef * Float64(Float64(-1.0 / KbT) - Float64(mu / Float64(Vef * KbT)))))) - Float64(Ec / KbT))));
	elseif (NaChar <= 2.05e-23)
		tmp = t_0;
	else
		tmp = Float64(t_1 + Float64(NdChar / Float64(Float64(2.0 + Float64(EDonor * Float64(Float64(1.0 / KbT) + Float64(Vef / Float64(EDonor * KbT))))) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	t_1 = NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.35e+101)
		tmp = t_1 + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	elseif (NaChar <= -2.4e+22)
		tmp = t_0;
	elseif (NaChar <= -1.2e-133)
		tmp = t_1 + (NdChar / ((2.0 + ((EDonor / KbT) - (Vef * ((-1.0 / KbT) - (mu / (Vef * KbT)))))) - (Ec / KbT)));
	elseif (NaChar <= 2.05e-23)
		tmp = t_0;
	else
		tmp = t_1 + (NdChar / ((2.0 + (EDonor * ((1.0 / KbT) + (Vef / (EDonor * KbT))))) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.35e+101], N[(t$95$1 + N[(NdChar / N[(N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -2.4e+22], t$95$0, If[LessEqual[NaChar, -1.2e-133], N[(t$95$1 + N[(NdChar / N[(N[(2.0 + N[(N[(EDonor / KbT), $MachinePrecision] - N[(Vef * N[(N[(-1.0 / KbT), $MachinePrecision] - N[(mu / N[(Vef * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 2.05e-23], t$95$0, N[(t$95$1 + N[(NdChar / N[(N[(2.0 + N[(EDonor * N[(N[(1.0 / KbT), $MachinePrecision] + N[(Vef / N[(EDonor * KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.34999999999999985e101

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 65.5%

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

   6. Taylor expanded in EDonor around inf 60.0%

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

      1. associate-/r* 60.1%

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

      2. associate-/r* 56.7%

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

   8. Simplified 56.7%

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

   9. Taylor expanded in mu around inf 71.5%

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

   if -2.34999999999999985e101 < NaChar < -2.4e22 or -1.2e-133 < NaChar < 2.05000000000000015e-23

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.4%

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

   6. Taylor expanded in EAccept around 0 68.2%

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

   if -2.4e22 < NaChar < -1.2e-133

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.0%

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

   6. Taylor expanded in Vef around inf 69.5%

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

      1. *-commutative 69.5%

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

   8. Simplified 69.5%

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

   if 2.05000000000000015e-23 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 73.2%

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

   6. Taylor expanded in EDonor around inf 78.5%

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

      1. associate-/r* 81.1%

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

      2. associate-/r* 81.1%

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

   8. Simplified 81.1%

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

   9. Taylor expanded in mu around 0 80.0%

      \[\leadsto \frac{NdChar}{\left(2 + \color{blue}{EDonor \cdot \left(\frac{1}{KbT} + \frac{Vef}{EDonor \cdot KbT}\right)}\right) - \frac{Ec}{KbT}} + \frac{NaChar}{1 + e^{\frac{Vef + \left(Ev + \left(EAccept - mu\right)\right)}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.35 \cdot 10^{+101}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq -2.4 \cdot 10^{+22}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.2 \cdot 10^{-133}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \left(\frac{EDonor}{KbT} - Vef \cdot \left(\frac{-1}{KbT} - \frac{mu}{Vef \cdot KbT}\right)\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{elif}\;NaChar \leq 2.05 \cdot 10^{-23}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + EDonor \cdot \left(\frac{1}{KbT} + \frac{Vef}{EDonor \cdot KbT}\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 59.1% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.2 \cdot 10^{+147}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.65 \cdot 10^{+26} \lor \neg \left(NaChar \leq -6.2 \cdot 10^{-132}\right) \land NaChar \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -2.2e+147)
   (+ (/ NdChar 2.0) (/ NaChar (+ 1.0 (exp (/ (- (+ Vef EAccept) mu) KbT)))))
   (if (or (<= NaChar -1.65e+26)
           (and (not (<= NaChar -6.2e-132)) (<= NaChar 2.15e-32)))
     (-
      (/ NaChar (+ 2.0 (/ EAccept KbT)))
      (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
     (+
      (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
      (/ NdChar (+ (/ EDonor KbT) 2.0))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -2.2e+147) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	} else if ((NaChar <= -1.65e+26) || (!(NaChar <= -6.2e-132) && (NaChar <= 2.15e-32))) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-2.2d+147)) then
        tmp = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((((vef + eaccept) - mu) / kbt))))
    else if ((nachar <= (-1.65d+26)) .or. (.not. (nachar <= (-6.2d-132))) .and. (nachar <= 2.15d-32)) then
        tmp = (nachar / (2.0d0 + (eaccept / kbt))) - (ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / ((edonor / kbt) + 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -2.2e+147) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((((Vef + EAccept) - mu) / KbT))));
	} else if ((NaChar <= -1.65e+26) || (!(NaChar <= -6.2e-132) && (NaChar <= 2.15e-32))) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -2.2e+147:
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((((Vef + EAccept) - mu) / KbT))))
	elif (NaChar <= -1.65e+26) or (not (NaChar <= -6.2e-132) and (NaChar <= 2.15e-32)):
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -2.2e+147)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + EAccept) - mu) / KbT)))));
	elseif ((NaChar <= -1.65e+26) || (!(NaChar <= -6.2e-132) && (NaChar <= 2.15e-32)))
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(Float64(EDonor / KbT) + 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -2.2e+147)
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	elseif ((NaChar <= -1.65e+26) || (~((NaChar <= -6.2e-132)) && (NaChar <= 2.15e-32)))
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / ((EDonor / KbT) + 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -2.2e+147], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, -1.65e+26], And[N[Not[LessEqual[NaChar, -6.2e-132]], $MachinePrecision], LessEqual[NaChar, 2.15e-32]]], N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2.2000000000000002e147

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.6%

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

   6. Taylor expanded in Vef around 0 68.8%

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

   7. Taylor expanded in Ev around 0 68.3%

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

   if -2.2000000000000002e147 < NaChar < -1.64999999999999997e26 or -6.20000000000000016e-132 < NaChar < 2.14999999999999995e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.9%

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

   6. Taylor expanded in EAccept around 0 68.8%

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

   if -1.64999999999999997e26 < NaChar < -6.20000000000000016e-132 or 2.14999999999999995e-32 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EDonor around inf 76.6%

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

   6. Taylor expanded in EDonor around 0 68.2%

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

4. Final simplification 68.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.2 \cdot 10^{+147}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.65 \cdot 10^{+26} \lor \neg \left(NaChar \leq -6.2 \cdot 10^{-132}\right) \land NaChar \leq 2.15 \cdot 10^{-32}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\frac{EDonor}{KbT} + 2}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 58.0% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{if}\;NaChar \leq -2.4 \cdot 10^{+145}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -9.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - t\_0\\ \mathbf{elif}\;NaChar \leq -2.7 \cdot 10^{-112} \lor \neg \left(NaChar \leq 6.2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))))
   (if (<= NaChar -2.4e+145)
     (+ (/ NdChar 2.0) (/ NaChar (+ 1.0 (exp (/ (- (+ Vef EAccept) mu) KbT)))))
     (if (<= NaChar -9.5e-64)
       (- (/ NaChar (+ 2.0 (/ EAccept KbT))) t_0)
       (if (or (<= NaChar -2.7e-112) (not (<= NaChar 6.2e-31)))
         (+
          (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
          (/ NdChar 2.0))
         (- (/ NaChar (+ 2.0 (/ Ev 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 = NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double tmp;
	if (NaChar <= -2.4e+145) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	} else if (NaChar <= -9.5e-64) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_0;
	} else if ((NaChar <= -2.7e-112) || !(NaChar <= 6.2e-31)) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - 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 = ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt)))
    if (nachar <= (-2.4d+145)) then
        tmp = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((((vef + eaccept) - mu) / kbt))))
    else if (nachar <= (-9.5d-64)) then
        tmp = (nachar / (2.0d0 + (eaccept / kbt))) - t_0
    else if ((nachar <= (-2.7d-112)) .or. (.not. (nachar <= 6.2d-31))) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    else
        tmp = (nachar / (2.0d0 + (ev / kbt))) - t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	double tmp;
	if (NaChar <= -2.4e+145) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((((Vef + EAccept) - mu) / KbT))));
	} else if (NaChar <= -9.5e-64) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_0;
	} else if ((NaChar <= -2.7e-112) || !(NaChar <= 6.2e-31)) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	} else {
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT)))
	tmp = 0
	if NaChar <= -2.4e+145:
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((((Vef + EAccept) - mu) / KbT))))
	elif NaChar <= -9.5e-64:
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_0
	elif (NaChar <= -2.7e-112) or not (NaChar <= 6.2e-31):
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	else:
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))))
	tmp = 0.0
	if (NaChar <= -2.4e+145)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + EAccept) - mu) / KbT)))));
	elseif (NaChar <= -9.5e-64)
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - t_0);
	elseif ((NaChar <= -2.7e-112) || !(NaChar <= 6.2e-31))
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(Ev / KbT))) - t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT)));
	tmp = 0.0;
	if (NaChar <= -2.4e+145)
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	elseif (NaChar <= -9.5e-64)
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - t_0;
	elseif ((NaChar <= -2.7e-112) || ~((NaChar <= 6.2e-31)))
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	else
		tmp = (NaChar / (2.0 + (Ev / KbT))) - t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -2.4e+145], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, -9.5e-64], N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], If[Or[LessEqual[NaChar, -2.7e-112], N[Not[LessEqual[NaChar, 6.2e-31]], $MachinePrecision]], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(2.0 + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if NaChar < -2.39999999999999992e145

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.6%

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

   6. Taylor expanded in Vef around 0 68.8%

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

   7. Taylor expanded in Ev around 0 68.3%

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

   if -2.39999999999999992e145 < NaChar < -9.50000000000000043e-64

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 70.4%

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

   6. Taylor expanded in EAccept around 0 60.7%

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

   if -9.50000000000000043e-64 < NaChar < -2.7000000000000001e-112 or 6.19999999999999999e-31 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 85.8%

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

   6. Taylor expanded in Vef around 0 64.7%

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

   if -2.7000000000000001e-112 < NaChar < 6.19999999999999999e-31

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 74.6%

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

   6. Taylor expanded in Ev around 0 65.8%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{EDonor + \left(mu + \left(Vef - Ec\right)\right)}{KbT}}} + \frac{NaChar}{\color{blue}{2 + \frac{Ev}{KbT}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -2.4 \cdot 10^{+145}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -9.5 \cdot 10^{-64}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -2.7 \cdot 10^{-112} \lor \neg \left(NaChar \leq 6.2 \cdot 10^{-31}\right):\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{Ev}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 57.5% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -1.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -7.5 \cdot 10^{-61} \lor \neg \left(NaChar \leq -2.3 \cdot 10^{-126}\right) \land NaChar \leq 1.15 \cdot 10^{-30}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -1.5e+145)
   (+ (/ NdChar 2.0) (/ NaChar (+ 1.0 (exp (/ (- (+ Vef EAccept) mu) KbT)))))
   (if (or (<= NaChar -7.5e-61)
           (and (not (<= NaChar -2.3e-126)) (<= NaChar 1.15e-30)))
     (-
      (/ NaChar (+ 2.0 (/ EAccept KbT)))
      (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
     (+
      (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
      (/ NdChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.5e+145) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	} else if ((NaChar <= -7.5e-61) || (!(NaChar <= -2.3e-126) && (NaChar <= 1.15e-30))) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-1.5d+145)) then
        tmp = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((((vef + eaccept) - mu) / kbt))))
    else if ((nachar <= (-7.5d-61)) .or. (.not. (nachar <= (-2.3d-126))) .and. (nachar <= 1.15d-30)) then
        tmp = (nachar / (2.0d0 + (eaccept / kbt))) - (ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -1.5e+145) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((((Vef + EAccept) - mu) / KbT))));
	} else if ((NaChar <= -7.5e-61) || (!(NaChar <= -2.3e-126) && (NaChar <= 1.15e-30))) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -1.5e+145:
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((((Vef + EAccept) - mu) / KbT))))
	elif (NaChar <= -7.5e-61) or (not (NaChar <= -2.3e-126) and (NaChar <= 1.15e-30)):
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -1.5e+145)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + EAccept) - mu) / KbT)))));
	elseif ((NaChar <= -7.5e-61) || (!(NaChar <= -2.3e-126) && (NaChar <= 1.15e-30)))
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -1.5e+145)
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	elseif ((NaChar <= -7.5e-61) || (~((NaChar <= -2.3e-126)) && (NaChar <= 1.15e-30)))
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -1.5e+145], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, -7.5e-61], And[N[Not[LessEqual[NaChar, -2.3e-126]], $MachinePrecision], LessEqual[NaChar, 1.15e-30]]], N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -1.5000000000000001e145

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.6%

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

   6. Taylor expanded in Vef around 0 68.8%

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

   7. Taylor expanded in Ev around 0 68.3%

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

   if -1.5000000000000001e145 < NaChar < -7.50000000000000047e-61 or -2.30000000000000011e-126 < NaChar < 1.14999999999999992e-30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 72.7%

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

   6. Taylor expanded in EAccept around 0 67.1%

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

   if -7.50000000000000047e-61 < NaChar < -2.30000000000000011e-126 or 1.14999999999999992e-30 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 85.8%

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

   6. Taylor expanded in Vef around 0 64.7%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -1.5 \cdot 10^{+145}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -7.5 \cdot 10^{-61} \lor \neg \left(NaChar \leq -2.3 \cdot 10^{-126}\right) \land NaChar \leq 1.15 \cdot 10^{-30}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 62.9% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -7 \cdot 10^{+145} \lor \neg \left(NdChar \leq 3.4 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + 2\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -7e+145) (not (<= NdChar 3.4e-30)))
   (-
    (/ NaChar (+ 2.0 (/ EAccept KbT)))
    (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar (- (+ (/ Vef KbT) (+ (/ EDonor KbT) 2.0)) (/ Ec KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -7e+145) || !(NdChar <= 3.4e-30)) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-7d+145)) .or. (.not. (ndchar <= 3.4d-30))) then
        tmp = (nachar / (2.0d0 + (eaccept / kbt))) - (ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / (((vef / kbt) + ((edonor / kbt) + 2.0d0)) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -7e+145) || !(NdChar <= 3.4e-30)) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -7e+145) or not (NdChar <= 3.4e-30):
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -7e+145) || !(NdChar <= 3.4e-30))
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(Float64(Float64(Vef / KbT) + Float64(Float64(EDonor / KbT) + 2.0)) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -7e+145) || ~((NdChar <= 3.4e-30)))
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -7e+145], N[Not[LessEqual[NdChar, 3.4e-30]], $MachinePrecision]], N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -7.0000000000000002e145 or 3.4000000000000003e-30 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 71.2%

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

   6. Taylor expanded in EAccept around 0 60.3%

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

   if -7.0000000000000002e145 < NdChar < 3.4000000000000003e-30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.2%

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

   6. Taylor expanded in mu around 0 70.5%

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

      1. associate-+r+ 70.5%

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

   8. Simplified 70.5%

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

4. Final simplification 66.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -7 \cdot 10^{+145} \lor \neg \left(NdChar \leq 3.4 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + 2\right)\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 16: 62.3% accurate, 1.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}\\ \mathbf{if}\;NdChar \leq -2.4 \cdot 10^{+162}:\\ \;\;\;\;\frac{NdChar}{1 + t\_0} - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NdChar \leq 1.12 \cdot 10^{-29}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + 2\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT))))
   (if (<= NdChar -2.4e+162)
     (-
      (/ NdChar (+ 1.0 t_0))
      (/
       NaChar
       (- (/ mu KbT) (+ 2.0 (+ (/ EAccept KbT) (+ (/ Vef KbT) (/ Ev KbT)))))))
     (if (<= NdChar 1.12e-29)
       (+
        (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
        (/ NdChar (- (+ (/ Vef KbT) (+ (/ EDonor KbT) 2.0)) (/ Ec KbT))))
       (- (/ NaChar (+ 2.0 (/ EAccept KbT))) (/ NdChar (- -1.0 t_0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	double tmp;
	if (NdChar <= -2.4e+162) {
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	} else if (NdChar <= 1.12e-29) {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)));
	} else {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - t_0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = exp(((edonor - ((ec - vef) - mu)) / kbt))
    if (ndchar <= (-2.4d+162)) then
        tmp = (ndchar / (1.0d0 + t_0)) - (nachar / ((mu / kbt) - (2.0d0 + ((eaccept / kbt) + ((vef / kbt) + (ev / kbt))))))
    else if (ndchar <= 1.12d-29) then
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / (((vef / kbt) + ((edonor / kbt) + 2.0d0)) - (ec / kbt)))
    else
        tmp = (nachar / (2.0d0 + (eaccept / kbt))) - (ndchar / ((-1.0d0) - t_0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	double tmp;
	if (NdChar <= -2.4e+162) {
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	} else if (NdChar <= 1.12e-29) {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)));
	} else {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))
	tmp = 0
	if NdChar <= -2.4e+162:
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))))
	elif NdChar <= 1.12e-29:
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)))
	else:
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT))
	tmp = 0.0
	if (NdChar <= -2.4e+162)
		tmp = Float64(Float64(NdChar / Float64(1.0 + t_0)) - Float64(NaChar / Float64(Float64(mu / KbT) - Float64(2.0 + Float64(Float64(EAccept / KbT) + Float64(Float64(Vef / KbT) + Float64(Ev / KbT)))))));
	elseif (NdChar <= 1.12e-29)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(Float64(Float64(Vef / KbT) + Float64(Float64(EDonor / KbT) + 2.0)) - Float64(Ec / KbT))));
	else
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - Float64(NdChar / Float64(-1.0 - t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((EDonor - ((Ec - Vef) - mu)) / KbT));
	tmp = 0.0;
	if (NdChar <= -2.4e+162)
		tmp = (NdChar / (1.0 + t_0)) - (NaChar / ((mu / KbT) - (2.0 + ((EAccept / KbT) + ((Vef / KbT) + (Ev / KbT))))));
	elseif (NdChar <= 1.12e-29)
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / (((Vef / KbT) + ((EDonor / KbT) + 2.0)) - (Ec / KbT)));
	else
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[NdChar, -2.4e+162], N[(N[(NdChar / N[(1.0 + t$95$0), $MachinePrecision]), $MachinePrecision] - N[(NaChar / N[(N[(mu / KbT), $MachinePrecision] - N[(2.0 + N[(N[(EAccept / KbT), $MachinePrecision] + N[(N[(Vef / KbT), $MachinePrecision] + N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[NdChar, 1.12e-29], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(N[(Vef / KbT), $MachinePrecision] + N[(N[(EDonor / KbT), $MachinePrecision] + 2.0), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if NdChar < -2.40000000000000009e162

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 64.7%

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

   if -2.40000000000000009e162 < NdChar < 1.11999999999999995e-29

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 66.6%

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

   6. Taylor expanded in mu around 0 69.8%

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

      1. associate-+r+ 69.8%

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

   8. Simplified 69.8%

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

   if 1.11999999999999995e-29 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 74.6%

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

   6. Taylor expanded in EAccept around 0 63.2%

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

4. Final simplification 67.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.4 \cdot 10^{+162}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}} - \frac{NaChar}{\frac{mu}{KbT} - \left(2 + \left(\frac{EAccept}{KbT} + \left(\frac{Vef}{KbT} + \frac{Ev}{KbT}\right)\right)\right)}\\ \mathbf{elif}\;NdChar \leq 1.12 \cdot 10^{-29}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(\frac{Vef}{KbT} + \left(\frac{EDonor}{KbT} + 2\right)\right) - \frac{Ec}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 17: 54.2% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -5.8 \cdot 10^{+116}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.1 \cdot 10^{-62} \lor \neg \left(NaChar \leq -9 \cdot 10^{-133}\right) \land NaChar \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -5.8e+116)
   (+ (/ NdChar 2.0) (/ NaChar (+ 1.0 (exp (/ (- (+ Vef EAccept) mu) KbT)))))
   (if (or (<= NaChar -1.1e-62)
           (and (not (<= NaChar -9e-133)) (<= NaChar 4.8e-30)))
     (-
      (/ NaChar 2.0)
      (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
     (+
      (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
      (/ NdChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -5.8e+116) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	} else if ((NaChar <= -1.1e-62) || (!(NaChar <= -9e-133) && (NaChar <= 4.8e-30))) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-5.8d+116)) then
        tmp = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((((vef + eaccept) - mu) / kbt))))
    else if ((nachar <= (-1.1d-62)) .or. (.not. (nachar <= (-9d-133))) .and. (nachar <= 4.8d-30)) then
        tmp = (nachar / 2.0d0) - (ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NaChar <= -5.8e+116) {
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((((Vef + EAccept) - mu) / KbT))));
	} else if ((NaChar <= -1.1e-62) || (!(NaChar <= -9e-133) && (NaChar <= 4.8e-30))) {
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -5.8e+116:
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((((Vef + EAccept) - mu) / KbT))))
	elif (NaChar <= -1.1e-62) or (not (NaChar <= -9e-133) and (NaChar <= 4.8e-30)):
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -5.8e+116)
		tmp = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + EAccept) - mu) / KbT)))));
	elseif ((NaChar <= -1.1e-62) || (!(NaChar <= -9e-133) && (NaChar <= 4.8e-30)))
		tmp = Float64(Float64(NaChar / 2.0) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NaChar <= -5.8e+116)
		tmp = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	elseif ((NaChar <= -1.1e-62) || (~((NaChar <= -9e-133)) && (NaChar <= 4.8e-30)))
		tmp = (NaChar / 2.0) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -5.8e+116], N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[NaChar, -1.1e-62], And[N[Not[LessEqual[NaChar, -9e-133]], $MachinePrecision], LessEqual[NaChar, 4.8e-30]]], N[(N[(NaChar / 2.0), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -5.8000000000000003e116

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.0%

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

   6. Taylor expanded in Vef around 0 67.1%

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

   7. Taylor expanded in Ev around 0 66.6%

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

   if -5.8000000000000003e116 < NaChar < -1.10000000000000009e-62 or -9.00000000000000019e-133 < NaChar < 4.7999999999999997e-30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 55.9%

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

   if -1.10000000000000009e-62 < NaChar < -9.00000000000000019e-133 or 4.7999999999999997e-30 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 84.8%

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

   6. Taylor expanded in Vef around 0 64.0%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -5.8 \cdot 10^{+116}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq -1.1 \cdot 10^{-62} \lor \neg \left(NaChar \leq -9 \cdot 10^{-133}\right) \land NaChar \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;\frac{NaChar}{2} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 18: 62.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -4.4 \cdot 10^{+144} \lor \neg \left(NdChar \leq 7.6 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -4.4e+144) (not (<= NdChar 7.6e-30)))
   (-
    (/ NaChar (+ 2.0 (/ EAccept KbT)))
    (/ NdChar (- -1.0 (exp (/ (- EDonor (- (- Ec Vef) mu)) KbT)))))
   (+
    (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
    (/ NdChar (- (+ 2.0 (/ mu KbT)) (/ Ec KbT))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -4.4e+144) || !(NdChar <= 7.6e-30)) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-4.4d+144)) .or. (.not. (ndchar <= 7.6d-30))) then
        tmp = (nachar / (2.0d0 + (eaccept / kbt))) - (ndchar / ((-1.0d0) - exp(((edonor - ((ec - vef) - mu)) / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / ((2.0d0 + (mu / kbt)) - (ec / kbt)))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -4.4e+144) || !(NdChar <= 7.6e-30)) {
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - Math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -4.4e+144) or not (NdChar <= 7.6e-30):
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - math.exp(((EDonor - ((Ec - Vef) - mu)) / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -4.4e+144) || !(NdChar <= 7.6e-30))
		tmp = Float64(Float64(NaChar / Float64(2.0 + Float64(EAccept / KbT))) - Float64(NdChar / Float64(-1.0 - exp(Float64(Float64(EDonor - Float64(Float64(Ec - Vef) - mu)) / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / Float64(Float64(2.0 + Float64(mu / KbT)) - Float64(Ec / KbT))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -4.4e+144) || ~((NdChar <= 7.6e-30)))
		tmp = (NaChar / (2.0 + (EAccept / KbT))) - (NdChar / (-1.0 - exp(((EDonor - ((Ec - Vef) - mu)) / KbT))));
	else
		tmp = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / ((2.0 + (mu / KbT)) - (Ec / KbT)));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -4.4e+144], N[Not[LessEqual[NdChar, 7.6e-30]], $MachinePrecision]], N[(N[(NaChar / N[(2.0 + N[(EAccept / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(NdChar / N[(-1.0 - N[Exp[N[(N[(EDonor - N[(N[(Ec - Vef), $MachinePrecision] - mu), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / N[(N[(2.0 + N[(mu / KbT), $MachinePrecision]), $MachinePrecision] - N[(Ec / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -4.39999999999999976e144 or 7.6000000000000006e-30 < NdChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in EAccept around inf 71.2%

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

   6. Taylor expanded in EAccept around 0 60.3%

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

   if -4.39999999999999976e144 < NdChar < 7.6000000000000006e-30

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 67.2%

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

   6. Taylor expanded in EDonor around inf 68.2%

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

      1. associate-/r* 70.7%

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

      2. associate-/r* 70.2%

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

   8. Simplified 70.2%

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

   9. Taylor expanded in mu around inf 69.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -4.4 \cdot 10^{+144} \lor \neg \left(NdChar \leq 7.6 \cdot 10^{-30}\right):\\ \;\;\;\;\frac{NaChar}{2 + \frac{EAccept}{KbT}} - \frac{NdChar}{-1 - e^{\frac{EDonor - \left(\left(Ec - Vef\right) - mu\right)}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{\left(2 + \frac{mu}{KbT}\right) - \frac{Ec}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 37.0% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ \mathbf{if}\;KbT \leq -1.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 5.8 \cdot 10^{-295}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq 7 \cdot 10^{-198} \lor \neg \left(KbT \leq 1.36 \cdot 10^{-152}\right):\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_0 + \frac{KbT \cdot NaChar}{Vef}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT))))))
   (if (<= KbT -1.8e-92)
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
     (if (<= KbT 5.8e-295)
       (+ t_0 (/ NaChar (/ Ev KbT)))
       (if (or (<= KbT 7e-198) (not (<= KbT 1.36e-152)))
         (+ (* NdChar 0.5) (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
         (+ t_0 (/ (* KbT NaChar) Vef)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((Vef / KbT)));
	double tmp;
	if (KbT <= -1.8e-92) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 5.8e-295) {
		tmp = t_0 + (NaChar / (Ev / KbT));
	} else if ((KbT <= 7e-198) || !(KbT <= 1.36e-152)) {
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = t_0 + ((KbT * NaChar) / Vef);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((vef / kbt)))
    if (kbt <= (-1.8d-92)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 5.8d-295) then
        tmp = t_0 + (nachar / (ev / kbt))
    else if ((kbt <= 7d-198) .or. (.not. (kbt <= 1.36d-152))) then
        tmp = (ndchar * 0.5d0) + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = t_0 + ((kbt * nachar) / vef)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((Vef / KbT)));
	double tmp;
	if (KbT <= -1.8e-92) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 5.8e-295) {
		tmp = t_0 + (NaChar / (Ev / KbT));
	} else if ((KbT <= 7e-198) || !(KbT <= 1.36e-152)) {
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = t_0 + ((KbT * NaChar) / Vef);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((Vef / KbT)))
	tmp = 0
	if KbT <= -1.8e-92:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= 5.8e-295:
		tmp = t_0 + (NaChar / (Ev / KbT))
	elif (KbT <= 7e-198) or not (KbT <= 1.36e-152):
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = t_0 + ((KbT * NaChar) / Vef)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	tmp = 0.0
	if (KbT <= -1.8e-92)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 5.8e-295)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Ev / KbT)));
	elseif ((KbT <= 7e-198) || !(KbT <= 1.36e-152))
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(t_0 + Float64(Float64(KbT * NaChar) / Vef));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((Vef / KbT)));
	tmp = 0.0;
	if (KbT <= -1.8e-92)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 5.8e-295)
		tmp = t_0 + (NaChar / (Ev / KbT));
	elseif ((KbT <= 7e-198) || ~((KbT <= 1.36e-152)))
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = t_0 + ((KbT * NaChar) / Vef);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -1.8e-92], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 5.8e-295], N[(t$95$0 + N[(NaChar / N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[KbT, 7e-198], N[Not[LessEqual[KbT, 1.36e-152]], $MachinePrecision]], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(N[(KbT * NaChar), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if KbT < -1.80000000000000008e-92

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 88.1%

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

   6. Taylor expanded in Vef around 0 64.0%

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

   7. Taylor expanded in EAccept around inf 48.7%

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

   if -1.80000000000000008e-92 < KbT < 5.8000000000000003e-295

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 70.0%

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

   6. Taylor expanded in KbT around inf 33.8%

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

   7. Taylor expanded in Ev around inf 43.3%

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

   if 5.8000000000000003e-295 < KbT < 7.0000000000000005e-198 or 1.3599999999999999e-152 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 69.5%

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

   6. Taylor expanded in KbT around inf 40.6%

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

   if 7.0000000000000005e-198 < KbT < 1.3599999999999999e-152

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 76.5%

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

   6. Taylor expanded in KbT around inf 40.8%

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

   7. Taylor expanded in Vef around inf 50.7%

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

4. Final simplification 44.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 5.8 \cdot 10^{-295}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq 7 \cdot 10^{-198} \lor \neg \left(KbT \leq 1.36 \cdot 10^{-152}\right):\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{KbT \cdot NaChar}{Vef}\\ \end{array} \]
5. Add Preprocessing

Alternative 20: 37.4% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{Vef}{KbT}}}\\ t_1 := \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{if}\;KbT \leq -3.6 \cdot 10^{-92}:\\ \;\;\;\;t\_1 + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -5.6 \cdot 10^{-303}:\\ \;\;\;\;t\_0 + \frac{NaChar}{\frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq 7 \cdot 10^{-199}:\\ \;\;\;\;t\_1 - \frac{NdChar \cdot KbT}{Ec}\\ \mathbf{elif}\;KbT \leq 6.8 \cdot 10^{-151}:\\ \;\;\;\;t\_0 + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ Vef KbT)))))
        (t_1 (/ NaChar (+ 1.0 (exp (/ EAccept KbT))))))
   (if (<= KbT -3.6e-92)
     (+ t_1 (/ NdChar 2.0))
     (if (<= KbT -5.6e-303)
       (+ t_0 (/ NaChar (/ Ev KbT)))
       (if (<= KbT 7e-199)
         (- t_1 (/ (* NdChar KbT) Ec))
         (if (<= KbT 6.8e-151)
           (+ t_0 (/ (* KbT NaChar) Vef))
           (+ (* NdChar 0.5) (/ 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((Vef / KbT)));
	double t_1 = NaChar / (1.0 + exp((EAccept / KbT)));
	double tmp;
	if (KbT <= -3.6e-92) {
		tmp = t_1 + (NdChar / 2.0);
	} else if (KbT <= -5.6e-303) {
		tmp = t_0 + (NaChar / (Ev / KbT));
	} else if (KbT <= 7e-199) {
		tmp = t_1 - ((NdChar * KbT) / Ec);
	} else if (KbT <= 6.8e-151) {
		tmp = t_0 + ((KbT * NaChar) / Vef);
	} else {
		tmp = (NdChar * 0.5) + (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) :: t_1
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((vef / kbt)))
    t_1 = nachar / (1.0d0 + exp((eaccept / kbt)))
    if (kbt <= (-3.6d-92)) then
        tmp = t_1 + (ndchar / 2.0d0)
    else if (kbt <= (-5.6d-303)) then
        tmp = t_0 + (nachar / (ev / kbt))
    else if (kbt <= 7d-199) then
        tmp = t_1 - ((ndchar * kbt) / ec)
    else if (kbt <= 6.8d-151) then
        tmp = t_0 + ((kbt * nachar) / vef)
    else
        tmp = (ndchar * 0.5d0) + (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((Vef / KbT)));
	double t_1 = NaChar / (1.0 + Math.exp((EAccept / KbT)));
	double tmp;
	if (KbT <= -3.6e-92) {
		tmp = t_1 + (NdChar / 2.0);
	} else if (KbT <= -5.6e-303) {
		tmp = t_0 + (NaChar / (Ev / KbT));
	} else if (KbT <= 7e-199) {
		tmp = t_1 - ((NdChar * KbT) / Ec);
	} else if (KbT <= 6.8e-151) {
		tmp = t_0 + ((KbT * NaChar) / Vef);
	} else {
		tmp = (NdChar * 0.5) + (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((Vef / KbT)))
	t_1 = NaChar / (1.0 + math.exp((EAccept / KbT)))
	tmp = 0
	if KbT <= -3.6e-92:
		tmp = t_1 + (NdChar / 2.0)
	elif KbT <= -5.6e-303:
		tmp = t_0 + (NaChar / (Ev / KbT))
	elif KbT <= 7e-199:
		tmp = t_1 - ((NdChar * KbT) / Ec)
	elif KbT <= 6.8e-151:
		tmp = t_0 + ((KbT * NaChar) / Vef)
	else:
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT))))
	t_1 = Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT))))
	tmp = 0.0
	if (KbT <= -3.6e-92)
		tmp = Float64(t_1 + Float64(NdChar / 2.0));
	elseif (KbT <= -5.6e-303)
		tmp = Float64(t_0 + Float64(NaChar / Float64(Ev / KbT)));
	elseif (KbT <= 7e-199)
		tmp = Float64(t_1 - Float64(Float64(NdChar * KbT) / Ec));
	elseif (KbT <= 6.8e-151)
		tmp = Float64(t_0 + Float64(Float64(KbT * NaChar) / Vef));
	else
		tmp = Float64(Float64(NdChar * 0.5) + 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((Vef / KbT)));
	t_1 = NaChar / (1.0 + exp((EAccept / KbT)));
	tmp = 0.0;
	if (KbT <= -3.6e-92)
		tmp = t_1 + (NdChar / 2.0);
	elseif (KbT <= -5.6e-303)
		tmp = t_0 + (NaChar / (Ev / KbT));
	elseif (KbT <= 7e-199)
		tmp = t_1 - ((NdChar * KbT) / Ec);
	elseif (KbT <= 6.8e-151)
		tmp = t_0 + ((KbT * NaChar) / Vef);
	else
		tmp = (NdChar * 0.5) + (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[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[KbT, -3.6e-92], N[(t$95$1 + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, -5.6e-303], N[(t$95$0 + N[(NaChar / N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 7e-199], N[(t$95$1 - N[(N[(NdChar * KbT), $MachinePrecision] / Ec), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 6.8e-151], N[(t$95$0 + N[(N[(KbT * NaChar), $MachinePrecision] / Vef), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if KbT < -3.60000000000000016e-92

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 88.1%

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

   6. Taylor expanded in Vef around 0 64.0%

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

   7. Taylor expanded in EAccept around inf 48.7%

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

   if -3.60000000000000016e-92 < KbT < -5.6e-303

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 68.5%

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

   6. Taylor expanded in KbT around inf 35.0%

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

   7. Taylor expanded in Ev around inf 45.0%

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

   if -5.6e-303 < KbT < 6.9999999999999998e-199

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 50.5%

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

   6. Taylor expanded in EDonor around inf 50.2%

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

      1. associate-/r* 54.4%

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

      2. associate-/r* 54.4%

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

   8. Simplified 54.4%

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

   9. Taylor expanded in Ec around inf 55.8%

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

       1. associate-*r/ 55.8%

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

       2. mul-1-neg 55.8%

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

       3. *-commutative 55.8%

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

   11. Simplified 55.8%

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

   12. Taylor expanded in EAccept around inf 43.5%

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

   if 6.9999999999999998e-199 < KbT < 6.8000000000000005e-151

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 76.5%

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

   6. Taylor expanded in KbT around inf 40.8%

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

   7. Taylor expanded in Vef around inf 50.7%

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

   if 6.8000000000000005e-151 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 68.4%

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

   6. Taylor expanded in KbT around inf 41.3%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}} \]
3. Recombined 5 regimes into one program.

4. Final simplification 44.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.6 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq -5.6 \cdot 10^{-303}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT}}\\ \mathbf{elif}\;KbT \leq 7 \cdot 10^{-199}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} - \frac{NdChar \cdot KbT}{Ec}\\ \mathbf{elif}\;KbT \leq 6.8 \cdot 10^{-151}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{KbT \cdot NaChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 21: 47.1% accurate, 1.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{if}\;NaChar \leq -3.1 \cdot 10^{-213}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 7.5 \cdot 10^{-302}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 9.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + KbT \cdot \frac{NaChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NaChar (+ 1.0 (exp (/ (- Vef (- (- mu EAccept) Ev)) KbT))))
          (/ NdChar 2.0))))
   (if (<= NaChar -3.1e-213)
     t_0
     (if (<= NaChar 7.5e-302)
       (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
       (if (<= NaChar 9.8e-33)
         (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (* KbT (/ NaChar Vef)))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -3.1e-213) {
		tmp = t_0;
	} else if (NaChar <= 7.5e-302) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (NaChar <= 9.8e-33) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (KbT * (NaChar / Vef));
	} 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 / (1.0d0 + exp(((vef - ((mu - eaccept) - ev)) / kbt)))) + (ndchar / 2.0d0)
    if (nachar <= (-3.1d-213)) then
        tmp = t_0
    else if (nachar <= 7.5d-302) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else if (nachar <= 9.8d-33) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (kbt * (nachar / vef))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NaChar / (1.0 + Math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	double tmp;
	if (NaChar <= -3.1e-213) {
		tmp = t_0;
	} else if (NaChar <= 7.5e-302) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (NaChar <= 9.8e-33) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (KbT * (NaChar / Vef));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NaChar / (1.0 + math.exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0)
	tmp = 0
	if NaChar <= -3.1e-213:
		tmp = t_0
	elif NaChar <= 7.5e-302:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	elif NaChar <= 9.8e-33:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (KbT * (NaChar / Vef))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Vef - Float64(Float64(mu - EAccept) - Ev)) / KbT)))) + Float64(NdChar / 2.0))
	tmp = 0.0
	if (NaChar <= -3.1e-213)
		tmp = t_0;
	elseif (NaChar <= 7.5e-302)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	elseif (NaChar <= 9.8e-33)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(KbT * Float64(NaChar / Vef)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NaChar / (1.0 + exp(((Vef - ((mu - EAccept) - Ev)) / KbT)))) + (NdChar / 2.0);
	tmp = 0.0;
	if (NaChar <= -3.1e-213)
		tmp = t_0;
	elseif (NaChar <= 7.5e-302)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	elseif (NaChar <= 9.8e-33)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (KbT * (NaChar / Vef));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NaChar / N[(1.0 + N[Exp[N[(N[(Vef - N[(N[(mu - EAccept), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -3.1e-213], t$95$0, If[LessEqual[NaChar, 7.5e-302], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 9.8e-33], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NaChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -3.0999999999999998e-213 or 9.7999999999999996e-33 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.7%

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

   6. Taylor expanded in Vef around 0 56.3%

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

   if -3.0999999999999998e-213 < NaChar < 7.49999999999999998e-302

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 74.0%

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

   6. Taylor expanded in EDonor around inf 59.7%

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

   if 7.49999999999999998e-302 < NaChar < 9.7999999999999996e-33

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 71.3%

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

   6. Taylor expanded in KbT around inf 48.9%

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

   7. Taylor expanded in Vef around inf 47.6%

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

      1. associate-/l* 49.5%

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

   9. Simplified 49.5%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -3.1 \cdot 10^{-213}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;NaChar \leq 7.5 \cdot 10^{-302}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 9.8 \cdot 10^{-33}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + KbT \cdot \frac{NaChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{Vef - \left(\left(mu - EAccept\right) - Ev\right)}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 22: 43.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;NaChar \leq -6.6 \cdot 10^{-212}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{-302}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.22 \cdot 10^{-32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + KbT \cdot \frac{NaChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar 2.0)
          (/ NaChar (+ 1.0 (exp (/ (- (+ Vef EAccept) mu) KbT)))))))
   (if (<= NaChar -6.6e-212)
     t_0
     (if (<= NaChar 1.9e-302)
       (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (/ NaChar 2.0))
       (if (<= NaChar 1.22e-32)
         (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (* KbT (/ NaChar Vef)))
         t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	double tmp;
	if (NaChar <= -6.6e-212) {
		tmp = t_0;
	} else if (NaChar <= 1.9e-302) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (NaChar <= 1.22e-32) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (KbT * (NaChar / Vef));
	} 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 = (ndchar / 2.0d0) + (nachar / (1.0d0 + exp((((vef + eaccept) - mu) / kbt))))
    if (nachar <= (-6.6d-212)) then
        tmp = t_0
    else if (nachar <= 1.9d-302) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (nachar / 2.0d0)
    else if (nachar <= 1.22d-32) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (kbt * (nachar / vef))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / 2.0) + (NaChar / (1.0 + Math.exp((((Vef + EAccept) - mu) / KbT))));
	double tmp;
	if (NaChar <= -6.6e-212) {
		tmp = t_0;
	} else if (NaChar <= 1.9e-302) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (NaChar / 2.0);
	} else if (NaChar <= 1.22e-32) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (KbT * (NaChar / Vef));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / 2.0) + (NaChar / (1.0 + math.exp((((Vef + EAccept) - mu) / KbT))))
	tmp = 0
	if NaChar <= -6.6e-212:
		tmp = t_0
	elif NaChar <= 1.9e-302:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (NaChar / 2.0)
	elif NaChar <= 1.22e-32:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (KbT * (NaChar / Vef))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / 2.0) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Vef + EAccept) - mu) / KbT)))))
	tmp = 0.0
	if (NaChar <= -6.6e-212)
		tmp = t_0;
	elseif (NaChar <= 1.9e-302)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(NaChar / 2.0));
	elseif (NaChar <= 1.22e-32)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(KbT * Float64(NaChar / Vef)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / 2.0) + (NaChar / (1.0 + exp((((Vef + EAccept) - mu) / KbT))));
	tmp = 0.0;
	if (NaChar <= -6.6e-212)
		tmp = t_0;
	elseif (NaChar <= 1.9e-302)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (NaChar / 2.0);
	elseif (NaChar <= 1.22e-32)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (KbT * (NaChar / Vef));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / 2.0), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NaChar, -6.6e-212], t$95$0, If[LessEqual[NaChar, 1.9e-302], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 1.22e-32], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NaChar / Vef), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -6.6000000000000004e-212 or 1.22e-32 < NaChar

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 80.7%

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

   6. Taylor expanded in Vef around 0 56.3%

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

   7. Taylor expanded in Ev around 0 50.7%

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

   if -6.6000000000000004e-212 < NaChar < 1.9e-302

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in KbT around inf 74.0%

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

   6. Taylor expanded in EDonor around inf 59.7%

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

   if 1.9e-302 < NaChar < 1.22e-32

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 71.3%

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

   6. Taylor expanded in KbT around inf 48.9%

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

   7. Taylor expanded in Vef around inf 47.6%

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

      1. associate-/l* 49.5%

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

   9. Simplified 49.5%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -6.6 \cdot 10^{-212}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;NaChar \leq 1.9 \cdot 10^{-302}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{elif}\;NaChar \leq 1.22 \cdot 10^{-32}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + KbT \cdot \frac{NaChar}{Vef}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{2} + \frac{NaChar}{1 + e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 23: 36.6% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -3.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 7.1 \cdot 10^{-295}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -3.8e-92)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (if (<= KbT 7.1e-295)
     (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (/ NaChar (/ Ev KbT)))
     (+ (* NdChar 0.5) (/ 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 <= -3.8e-92) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 7.1e-295) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (Ev / KbT));
	} else {
		tmp = (NdChar * 0.5) + (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 <= (-3.8d-92)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 7.1d-295) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / (ev / kbt))
    else
        tmp = (ndchar * 0.5d0) + (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 <= -3.8e-92) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 7.1e-295) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / (Ev / KbT));
	} else {
		tmp = (NdChar * 0.5) + (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 <= -3.8e-92:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= 7.1e-295:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / (Ev / KbT))
	else:
		tmp = (NdChar * 0.5) + (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 <= -3.8e-92)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 7.1e-295)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / Float64(Ev / KbT)));
	else
		tmp = Float64(Float64(NdChar * 0.5) + 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 <= -3.8e-92)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 7.1e-295)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / (Ev / KbT));
	else
		tmp = (NdChar * 0.5) + (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, -3.8e-92], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 7.1e-295], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(Ev / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar * 0.5), $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 < -3.8000000000000001e-92

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 88.1%

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

   6. Taylor expanded in Vef around 0 64.0%

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

   7. Taylor expanded in EAccept around inf 48.7%

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

   if -3.8000000000000001e-92 < KbT < 7.09999999999999958e-295

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 70.0%

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

   6. Taylor expanded in KbT around inf 33.8%

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

   7. Taylor expanded in Ev around inf 43.3%

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

   if 7.09999999999999958e-295 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 69.1%

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

   6. Taylor expanded in KbT around inf 37.9%

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

4. Final simplification 42.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -3.8 \cdot 10^{-92}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 7.1 \cdot 10^{-295}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{\frac{Ev}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 24: 36.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -1.3 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.2 \cdot 10^{-295}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + KbT \cdot \frac{NaChar}{Ev}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -1.3e-91)
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))
   (if (<= KbT 1.2e-295)
     (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (* KbT (/ NaChar Ev)))
     (+ (* NdChar 0.5) (/ 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 <= -1.3e-91) {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.2e-295) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (KbT * (NaChar / Ev));
	} else {
		tmp = (NdChar * 0.5) + (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 <= (-1.3d-91)) then
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    else if (kbt <= 1.2d-295) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (kbt * (nachar / ev))
    else
        tmp = (ndchar * 0.5d0) + (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 <= -1.3e-91) {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	} else if (KbT <= 1.2e-295) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (KbT * (NaChar / Ev));
	} else {
		tmp = (NdChar * 0.5) + (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 <= -1.3e-91:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	elif KbT <= 1.2e-295:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (KbT * (NaChar / Ev))
	else:
		tmp = (NdChar * 0.5) + (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 <= -1.3e-91)
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	elseif (KbT <= 1.2e-295)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(KbT * Float64(NaChar / Ev)));
	else
		tmp = Float64(Float64(NdChar * 0.5) + 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 <= -1.3e-91)
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	elseif (KbT <= 1.2e-295)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (KbT * (NaChar / Ev));
	else
		tmp = (NdChar * 0.5) + (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, -1.3e-91], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[KbT, 1.2e-295], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(KbT * N[(NaChar / Ev), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar * 0.5), $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 < -1.30000000000000007e-91

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 88.1%

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

   6. Taylor expanded in Vef around 0 64.0%

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

   7. Taylor expanded in EAccept around inf 48.7%

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

   if -1.30000000000000007e-91 < KbT < 1.1999999999999999e-295

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 70.0%

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

   6. Taylor expanded in KbT around inf 33.8%

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

   7. Taylor expanded in Ev around inf 43.3%

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

      1. associate-/l* 41.1%

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

   9. Simplified 41.1%

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

   if 1.1999999999999999e-295 < KbT

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 69.1%

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

   6. Taylor expanded in KbT around inf 37.9%

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

4. Final simplification 42.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;KbT \leq -1.3 \cdot 10^{-91}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \mathbf{elif}\;KbT \leq 1.2 \cdot 10^{-295}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + KbT \cdot \frac{NaChar}{Ev}\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 25: 36.8% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -2.4 \cdot 10^{+114}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -3 \cdot 10^{-139}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -2.4e+114)
   (+ (* NdChar 0.5) (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
   (if (<= Ev -3e-139)
     (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (/ NaChar 2.0))
     (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -2.4e+114) {
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (Ev <= -3e-139) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-2.4d+114)) then
        tmp = (ndchar * 0.5d0) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (ev <= (-3d-139)) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (nachar / 2.0d0)
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -2.4e+114) {
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (Ev <= -3e-139) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (NaChar / 2.0);
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -2.4e+114:
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif Ev <= -3e-139:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (NaChar / 2.0)
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -2.4e+114)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (Ev <= -3e-139)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(NaChar / 2.0));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -2.4e+114)
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (Ev <= -3e-139)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (NaChar / 2.0);
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -2.4e+114], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[Ev, -3e-139], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / 2.0), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if Ev < -2.4e114

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 86.5%

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

   6. Taylor expanded in KbT around inf 50.3%

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

   if -2.4e114 < Ev < -2.9999999999999999e-139

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 81.9%

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

   6. Taylor expanded in KbT around inf 36.9%

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

   if -2.9999999999999999e-139 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 75.1%

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

   6. Taylor expanded in Vef around 0 48.1%

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

   7. Taylor expanded in EAccept around inf 37.7%

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

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -2.4 \cdot 10^{+114}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;Ev \leq -3 \cdot 10^{-139}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + \frac{NaChar}{2}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 26: 37.2% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -6.6 \cdot 10^{+64}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -6.6e+64)
   (+ (* NdChar 0.5) (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
   (+ (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))) (/ NdChar 2.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -6.6e+64) {
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-6.6d+64)) then
        tmp = (ndchar * 0.5d0) + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = (nachar / (1.0d0 + exp((eaccept / kbt)))) + (ndchar / 2.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (Ev <= -6.6e+64) {
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = (NaChar / (1.0 + Math.exp((EAccept / KbT)))) + (NdChar / 2.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -6.6e+64:
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = (NaChar / (1.0 + math.exp((EAccept / KbT)))) + (NdChar / 2.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -6.6e+64)
		tmp = Float64(Float64(NdChar * 0.5) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))) + Float64(NdChar / 2.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -6.6e+64)
		tmp = (NdChar * 0.5) + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = (NaChar / (1.0 + exp((EAccept / KbT)))) + (NdChar / 2.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -6.6e+64], N[(N[(NdChar * 0.5), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NdChar / 2.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -6.59999999999999976e64

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Ev around inf 89.5%

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

   6. Taylor expanded in KbT around inf 54.1%

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

   if -6.59999999999999976e64 < Ev

   1. Initial program 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in Vef around inf 75.6%

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

   6. Taylor expanded in Vef around 0 47.0%

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

   7. Taylor expanded in EAccept around inf 36.5%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;Ev \leq -6.6 \cdot 10^{+64}:\\ \;\;\;\;NdChar \cdot 0.5 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}} + \frac{NdChar}{2}\\ \end{array} \]
5. Add Preprocessing

Alternative 27: 35.3% accurate, 2.1× speedup

Math

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

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (* NdChar 0.5) (/ 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) {
	return (NdChar * 0.5) + (NaChar / (1.0 + exp((Ev / 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 * 0.5d0) + (nachar / (1.0d0 + exp((ev / 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 * 0.5) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in Ev around inf 67.3%

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

6. Taylor expanded in KbT around inf 37.6%

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

7. Final simplification 37.6%

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

Alternative 28: 27.3% accurate, 32.7× speedup

Math

\[\begin{array}{l} \\ \frac{NaChar}{2} + NdChar \cdot 0.5 \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (+ (/ NaChar 2.0) (* NdChar 0.5)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / 2.0) + (NdChar * 0.5);
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    code = (nachar / 2.0d0) + (ndchar * 0.5d0)
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	return (NaChar / 2.0) + (NdChar * 0.5);
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	return (NaChar / 2.0) + (NdChar * 0.5)

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	return Float64(Float64(NaChar / 2.0) + Float64(NdChar * 0.5))
end

MATLAB

function tmp = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = (NaChar / 2.0) + (NdChar * 0.5);
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(N[(NaChar / 2.0), $MachinePrecision] + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

3. Simplified 100.0%

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

5. Taylor expanded in KbT around inf 43.3%

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

6. Taylor expanded in KbT around inf 27.8%

   \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{2} \]

7. Final simplification 27.8%

   \[\leadsto \frac{NaChar}{2} + NdChar \cdot 0.5 \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024090 
(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))))))