Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 18.1s

Alternatives: 16

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 44.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := EDonor + \left(Vef + \left(mu - Ec\right)\right)\\ t_1 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ t_2 := \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-150}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;t\_1 \leq -2 \cdot 10^{-285}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t\_1 \leq 2 \cdot 10^{-299}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\mathsf{fma}\left(-0.5, \frac{t\_0 \cdot t\_0}{KbT}, \left(\left(Ec - mu\right) - Vef\right) - EDonor\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_2\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ EDonor (+ Vef (- mu Ec))))
        (t_1
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0))))
        (t_2 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))))
   (if (<= t_1 -5e-150)
     (* 0.5 (+ NdChar NaChar))
     (if (<= t_1 -2e-285)
       t_2
       (if (<= t_1 2e-299)
         (/
          NdChar
          (-
           2.0
           (/
            (fma -0.5 (/ (* t_0 t_0) KbT) (- (- (- Ec mu) Vef) EDonor))
            KbT)))
         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 = EDonor + (Vef + (mu - Ec));
	double t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double t_2 = NdChar / (exp((EDonor / KbT)) + 1.0);
	double tmp;
	if (t_1 <= -5e-150) {
		tmp = 0.5 * (NdChar + NaChar);
	} else if (t_1 <= -2e-285) {
		tmp = t_2;
	} else if (t_1 <= 2e-299) {
		tmp = NdChar / (2.0 - (fma(-0.5, ((t_0 * t_0) / KbT), (((Ec - mu) - Vef) - EDonor)) / KbT));
	} else {
		tmp = t_2;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(EDonor + Float64(Vef + Float64(mu - Ec)))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)))
	t_2 = Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0))
	tmp = 0.0
	if (t_1 <= -5e-150)
		tmp = Float64(0.5 * Float64(NdChar + NaChar));
	elseif (t_1 <= -2e-285)
		tmp = t_2;
	elseif (t_1 <= 2e-299)
		tmp = Float64(NdChar / Float64(2.0 - Float64(fma(-0.5, Float64(Float64(t_0 * t_0) / KbT), Float64(Float64(Float64(Ec - mu) - Vef) - EDonor)) / KbT)));
	else
		tmp = t_2;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(EDonor + N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-150], N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, -2e-285], t$95$2, If[LessEqual[t$95$1, 2e-299], N[(NdChar / N[(2.0 - N[(N[(-0.5 * N[(N[(t$95$0 * t$95$0), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(N[(Ec - mu), $MachinePrecision] - Vef), $MachinePrecision] - EDonor), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$2]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -4.9999999999999999e-150

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 43.1

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

   5. Applied rewrites 43.1%

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

   if -4.9999999999999999e-150 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -2.00000000000000015e-285 or 1.99999999999999998e-299 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 50.6%

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

   6. Taylor expanded in EDonor around inf

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

   8. Applied rewrites 35.5%

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

   if -2.00000000000000015e-285 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 1.99999999999999998e-299

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 95.7%

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

   6. Taylor expanded in KbT around -inf

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

   8. Applied rewrites 94.2%

      \[\leadsto \frac{NdChar}{2 - \color{blue}{\frac{\mathsf{fma}\left(-0.5, \frac{\left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right) \cdot \left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right)}{KbT}, -\left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right)\right)}{KbT}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 52.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -5 \cdot 10^{-150}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -2 \cdot 10^{-285}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 2 \cdot 10^{-299}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\mathsf{fma}\left(-0.5, \frac{\left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right) \cdot \left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right)}{KbT}, \left(\left(Ec - mu\right) - Vef\right) - EDonor\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ t_1 := t\_0 + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ t_2 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + t\_0\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-272}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 5 \cdot 10^{-247}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept - \left(\left(mu - Vef\right) - Ev\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0)))
        (t_1 (+ t_0 (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))))
        (t_2
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          t_0)))
   (if (<= t_2 -2e-272)
     t_1
     (if (<= t_2 5e-247)
       (/ NaChar (+ (exp (/ (- EAccept (- (- mu Vef) Ev)) KbT)) 1.0))
       t_1))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	double t_2 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + t_0;
	double tmp;
	if (t_2 <= -2e-272) {
		tmp = t_1;
	} else if (t_2 <= 5e-247) {
		tmp = NaChar / (exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = nachar / (exp(((((vef + ev) + eaccept) - mu) / kbt)) + 1.0d0)
    t_1 = t_0 + (ndchar / (exp((edonor / kbt)) + 1.0d0))
    t_2 = (ndchar / (exp(((mu + (edonor + (vef - ec))) / kbt)) + 1.0d0)) + t_0
    if (t_2 <= (-2d-272)) then
        tmp = t_1
    else if (t_2 <= 5d-247) then
        tmp = nachar / (exp(((eaccept - ((mu - vef) - ev)) / kbt)) + 1.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0);
	double t_1 = t_0 + (NdChar / (Math.exp((EDonor / KbT)) + 1.0));
	double t_2 = (NdChar / (Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + t_0;
	double tmp;
	if (t_2 <= -2e-272) {
		tmp = t_1;
	} else if (t_2 <= 5e-247) {
		tmp = NaChar / (Math.exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)
	t_1 = t_0 + (NdChar / (math.exp((EDonor / KbT)) + 1.0))
	t_2 = (NdChar / (math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + t_0
	tmp = 0
	if t_2 <= -2e-272:
		tmp = t_1
	elif t_2 <= 5e-247:
		tmp = NaChar / (math.exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0)
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0))
	t_1 = Float64(t_0 + Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0)))
	t_2 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + t_0)
	tmp = 0.0
	if (t_2 <= -2e-272)
		tmp = t_1;
	elseif (t_2 <= 5e-247)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(EAccept - Float64(Float64(mu - Vef) - Ev)) / KbT)) + 1.0));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0);
	t_1 = t_0 + (NdChar / (exp((EDonor / KbT)) + 1.0));
	t_2 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + t_0;
	tmp = 0.0;
	if (t_2 <= -2e-272)
		tmp = t_1;
	elseif (t_2 <= 5e-247)
		tmp = NaChar / (exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]}, If[LessEqual[t$95$2, -2e-272], t$95$1, If[LessEqual[t$95$2, 5e-247], N[(NaChar / N[(N[Exp[N[(N[(EAccept - N[(N[(mu - Vef), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999986e-272 or 4.99999999999999978e-247 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in EDonor around inf

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

      1. lower-/.f64 80.5

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

   5. Applied rewrites 80.5%

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

   if -1.99999999999999986e-272 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 4.99999999999999978e-247

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. associate-+r+ N/A

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

      9. mul-1-neg N/A

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

      10. lower-+.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 95.9

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

   5. Applied rewrites 95.9%

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

4. Final simplification 84.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -2 \cdot 10^{-272}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 5 \cdot 10^{-247}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept - \left(\left(mu - Vef\right) - Ev\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} + \frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ t_1 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + t\_0\\ \mathbf{if}\;t\_1 \leq -40000000:\\ \;\;\;\;t\_0 + NdChar \cdot 0.5\\ \mathbf{elif}\;t\_1 \leq 10^{-60}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept - \left(\left(mu - Vef\right) - Ev\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0)))
        (t_1
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          t_0)))
   (if (<= t_1 -40000000.0)
     (+ t_0 (* NdChar 0.5))
     (if (<= t_1 1e-60)
       (/ NaChar (+ (exp (/ (- EAccept (- (- mu Vef) Ev)) KbT)) 1.0))
       (+
        (/ NdChar (+ (exp (/ Vef KbT)) 1.0))
        (/ NaChar (+ (exp (/ (- (+ Vef EAccept) mu) KbT)) 1.0)))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0);
	double t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + t_0;
	double tmp;
	if (t_1 <= -40000000.0) {
		tmp = t_0 + (NdChar * 0.5);
	} else if (t_1 <= 1e-60) {
		tmp = NaChar / (exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	} else {
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + EAccept) - mu) / KbT)) + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = nachar / (exp(((((vef + ev) + eaccept) - mu) / kbt)) + 1.0d0)
    t_1 = (ndchar / (exp(((mu + (edonor + (vef - ec))) / kbt)) + 1.0d0)) + t_0
    if (t_1 <= (-40000000.0d0)) then
        tmp = t_0 + (ndchar * 0.5d0)
    else if (t_1 <= 1d-60) then
        tmp = nachar / (exp(((eaccept - ((mu - vef) - ev)) / kbt)) + 1.0d0)
    else
        tmp = (ndchar / (exp((vef / kbt)) + 1.0d0)) + (nachar / (exp((((vef + eaccept) - mu) / kbt)) + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NaChar / (Math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0);
	double t_1 = (NdChar / (Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + t_0;
	double tmp;
	if (t_1 <= -40000000.0) {
		tmp = t_0 + (NdChar * 0.5);
	} else if (t_1 <= 1e-60) {
		tmp = NaChar / (Math.exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	} else {
		tmp = (NdChar / (Math.exp((Vef / KbT)) + 1.0)) + (NaChar / (Math.exp((((Vef + EAccept) - mu) / KbT)) + 1.0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NaChar / (math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)
	t_1 = (NdChar / (math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + t_0
	tmp = 0
	if t_1 <= -40000000.0:
		tmp = t_0 + (NdChar * 0.5)
	elif t_1 <= 1e-60:
		tmp = NaChar / (math.exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0)
	else:
		tmp = (NdChar / (math.exp((Vef / KbT)) + 1.0)) + (NaChar / (math.exp((((Vef + EAccept) - mu) / KbT)) + 1.0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + t_0)
	tmp = 0.0
	if (t_1 <= -40000000.0)
		tmp = Float64(t_0 + Float64(NdChar * 0.5));
	elseif (t_1 <= 1e-60)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(EAccept - Float64(Float64(mu - Vef) - Ev)) / KbT)) + 1.0));
	else
		tmp = Float64(Float64(NdChar / Float64(exp(Float64(Vef / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Vef + EAccept) - mu) / KbT)) + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0);
	t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + t_0;
	tmp = 0.0;
	if (t_1 <= -40000000.0)
		tmp = t_0 + (NdChar * 0.5);
	elseif (t_1 <= 1e-60)
		tmp = NaChar / (exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	else
		tmp = (NdChar / (exp((Vef / KbT)) + 1.0)) + (NaChar / (exp((((Vef + EAccept) - mu) / KbT)) + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]}, If[LessEqual[t$95$1, -40000000.0], N[(t$95$0 + N[(NdChar * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, 1e-60], N[(NaChar / N[(N[Exp[N[(N[(EAccept - N[(N[(mu - Vef), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(N[(NdChar / N[(N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(Vef + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -4e7

   1. Initial program 99.9%

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

   3. Taylor expanded in KbT around inf

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

      1. *-commutative N/A

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

      2. lower-*.f64 74.4

         \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   5. Applied rewrites 74.4%

      \[\leadsto \color{blue}{NdChar \cdot 0.5} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]

   if -4e7 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 9.9999999999999997e-61

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. associate-+r+ N/A

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

      9. mul-1-neg N/A

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

      10. lower-+.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 80.8

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

   5. Applied rewrites 80.8%

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

   if 9.9999999999999997e-61 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in Vef around inf

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

      1. lower-/.f64 82.3

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

   5. Applied rewrites 82.3%

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

   6. Taylor expanded in Ev around 0

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

      1. lower--.f64 N/A

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

      2. lower-+.f64 76.9

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

   8. Applied rewrites 76.9%

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

4. Final simplification 78.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -40000000:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} + NdChar \cdot 0.5\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 10^{-60}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept - \left(\left(mu - Vef\right) - Ev\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{Vef}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(Vef + EAccept\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 44.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := EDonor + \left(Vef + \left(mu - Ec\right)\right)\\ t_1 := 0.5 \cdot \left(NdChar + NaChar\right)\\ t_2 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;t\_2 \leq -1 \cdot 10^{-251}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_2 \leq 10^{-206}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\mathsf{fma}\left(-0.5, \frac{t\_0 \cdot t\_0}{KbT}, \left(\left(Ec - mu\right) - Vef\right) - EDonor\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (+ EDonor (+ Vef (- mu Ec))))
        (t_1 (* 0.5 (+ NdChar NaChar)))
        (t_2
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0)))))
   (if (<= t_2 -1e-251)
     t_1
     (if (<= t_2 1e-206)
       (/
        NdChar
        (-
         2.0
         (/ (fma -0.5 (/ (* t_0 t_0) KbT) (- (- (- Ec mu) Vef) EDonor)) KbT)))
       t_1))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = EDonor + (Vef + (mu - Ec));
	double t_1 = 0.5 * (NdChar + NaChar);
	double t_2 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_2 <= -1e-251) {
		tmp = t_1;
	} else if (t_2 <= 1e-206) {
		tmp = NdChar / (2.0 - (fma(-0.5, ((t_0 * t_0) / KbT), (((Ec - mu) - Vef) - EDonor)) / KbT));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(EDonor + Float64(Vef + Float64(mu - Ec)))
	t_1 = Float64(0.5 * Float64(NdChar + NaChar))
	t_2 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)))
	tmp = 0.0
	if (t_2 <= -1e-251)
		tmp = t_1;
	elseif (t_2 <= 1e-206)
		tmp = Float64(NdChar / Float64(2.0 - Float64(fma(-0.5, Float64(Float64(t_0 * t_0) / KbT), Float64(Float64(Float64(Ec - mu) - Vef) - EDonor)) / KbT)));
	else
		tmp = t_1;
	end
	return tmp
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(EDonor + N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$2, -1e-251], t$95$1, If[LessEqual[t$95$2, 1e-206], N[(NdChar / N[(2.0 - N[(N[(-0.5 * N[(N[(t$95$0 * t$95$0), $MachinePrecision] / KbT), $MachinePrecision] + N[(N[(N[(Ec - mu), $MachinePrecision] - Vef), $MachinePrecision] - EDonor), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.00000000000000002e-251 or 1.00000000000000003e-206 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 36.4

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

   5. Applied rewrites 36.4%

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

   if -1.00000000000000002e-251 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 1.00000000000000003e-206

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 90.0%

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

   6. Taylor expanded in KbT around -inf

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

   8. Applied rewrites 81.0%

      \[\leadsto \frac{NdChar}{2 - \color{blue}{\frac{\mathsf{fma}\left(-0.5, \frac{\left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right) \cdot \left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right)}{KbT}, -\left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right)\right)}{KbT}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 49.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -1 \cdot 10^{-251}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 10^{-206}:\\ \;\;\;\;\frac{NdChar}{2 - \frac{\mathsf{fma}\left(-0.5, \frac{\left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right) \cdot \left(EDonor + \left(Vef + \left(mu - Ec\right)\right)\right)}{KbT}, \left(\left(Ec - mu\right) - Vef\right) - EDonor\right)}{KbT}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 35.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ t_1 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-226}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-247}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{\frac{\frac{NdChar \cdot NdChar}{NaChar} - NdChar}{NaChar} + 1}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar)))
        (t_1
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0)))))
   (if (<= t_1 -2e-226)
     t_0
     (if (<= t_1 5e-247)
       (*
        0.5
        (/
         1.0
         (/
          (+ (/ (- (/ (* NdChar NdChar) NaChar) NdChar) NaChar) 1.0)
          NaChar)))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -2e-226) {
		tmp = t_0;
	} else if (t_1 <= 5e-247) {
		tmp = 0.5 * (1.0 / ((((((NdChar * NdChar) / NaChar) - NdChar) / NaChar) + 1.0) / NaChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    t_1 = (ndchar / (exp(((mu + (edonor + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (exp(((((vef + ev) + eaccept) - mu) / kbt)) + 1.0d0))
    if (t_1 <= (-2d-226)) then
        tmp = t_0
    else if (t_1 <= 5d-247) then
        tmp = 0.5d0 * (1.0d0 / ((((((ndchar * ndchar) / nachar) - ndchar) / nachar) + 1.0d0) / nachar))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (Math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -2e-226) {
		tmp = t_0;
	} else if (t_1 <= 5e-247) {
		tmp = 0.5 * (1.0 / ((((((NdChar * NdChar) / NaChar) - NdChar) / NaChar) + 1.0) / NaChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	t_1 = (NdChar / (math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0))
	tmp = 0
	if t_1 <= -2e-226:
		tmp = t_0
	elif t_1 <= 5e-247:
		tmp = 0.5 * (1.0 / ((((((NdChar * NdChar) / NaChar) - NdChar) / NaChar) + 1.0) / NaChar))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)))
	tmp = 0.0
	if (t_1 <= -2e-226)
		tmp = t_0;
	elseif (t_1 <= 5e-247)
		tmp = Float64(0.5 * Float64(1.0 / Float64(Float64(Float64(Float64(Float64(Float64(NdChar * NdChar) / NaChar) - NdChar) / NaChar) + 1.0) / NaChar)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	tmp = 0.0;
	if (t_1 <= -2e-226)
		tmp = t_0;
	elseif (t_1 <= 5e-247)
		tmp = 0.5 * (1.0 / ((((((NdChar * NdChar) / NaChar) - NdChar) / NaChar) + 1.0) / NaChar));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-226], t$95$0, If[LessEqual[t$95$1, 5e-247], N[(0.5 * N[(1.0 / N[(N[(N[(N[(N[(N[(NdChar * NdChar), $MachinePrecision] / NaChar), $MachinePrecision] - NdChar), $MachinePrecision] / NaChar), $MachinePrecision] + 1.0), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999984e-226 or 4.99999999999999978e-247 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 35.9

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

   5. Applied rewrites 35.9%

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

   if -1.99999999999999984e-226 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 4.99999999999999978e-247

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 2.8

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

   5. Applied rewrites 2.8%

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

   7. Applied rewrites 4.1%

      \[\leadsto 0.5 \cdot \frac{1}{\color{blue}{\frac{NdChar - NaChar}{\left(NdChar + NaChar\right) \cdot \left(NdChar - NaChar\right)}}} \]

   8. Taylor expanded in NaChar around -inf

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

   10. Applied rewrites 48.1%

       \[\leadsto 0.5 \cdot \frac{1}{\frac{\frac{\frac{NdChar \cdot NdChar}{NaChar} - NdChar}{-NaChar} + -1}{\color{blue}{-NaChar}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 39.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -2 \cdot 10^{-226}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 5 \cdot 10^{-247}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{\frac{\frac{NdChar \cdot NdChar}{NaChar} - NdChar}{NaChar} + 1}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 35.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ t_1 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-251}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 10^{-206}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{\frac{\frac{NaChar \cdot NaChar}{NdChar} - NaChar}{NdChar} + 1}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar)))
        (t_1
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0)))))
   (if (<= t_1 -1e-251)
     t_0
     (if (<= t_1 1e-206)
       (*
        0.5
        (/
         1.0
         (/
          (+ (/ (- (/ (* NaChar NaChar) NdChar) NaChar) NdChar) 1.0)
          NdChar)))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -1e-251) {
		tmp = t_0;
	} else if (t_1 <= 1e-206) {
		tmp = 0.5 * (1.0 / ((((((NaChar * NaChar) / NdChar) - NaChar) / NdChar) + 1.0) / NdChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    t_1 = (ndchar / (exp(((mu + (edonor + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (exp(((((vef + ev) + eaccept) - mu) / kbt)) + 1.0d0))
    if (t_1 <= (-1d-251)) then
        tmp = t_0
    else if (t_1 <= 1d-206) then
        tmp = 0.5d0 * (1.0d0 / ((((((nachar * nachar) / ndchar) - nachar) / ndchar) + 1.0d0) / ndchar))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (Math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -1e-251) {
		tmp = t_0;
	} else if (t_1 <= 1e-206) {
		tmp = 0.5 * (1.0 / ((((((NaChar * NaChar) / NdChar) - NaChar) / NdChar) + 1.0) / NdChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	t_1 = (NdChar / (math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0))
	tmp = 0
	if t_1 <= -1e-251:
		tmp = t_0
	elif t_1 <= 1e-206:
		tmp = 0.5 * (1.0 / ((((((NaChar * NaChar) / NdChar) - NaChar) / NdChar) + 1.0) / NdChar))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)))
	tmp = 0.0
	if (t_1 <= -1e-251)
		tmp = t_0;
	elseif (t_1 <= 1e-206)
		tmp = Float64(0.5 * Float64(1.0 / Float64(Float64(Float64(Float64(Float64(Float64(NaChar * NaChar) / NdChar) - NaChar) / NdChar) + 1.0) / NdChar)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	tmp = 0.0;
	if (t_1 <= -1e-251)
		tmp = t_0;
	elseif (t_1 <= 1e-206)
		tmp = 0.5 * (1.0 / ((((((NaChar * NaChar) / NdChar) - NaChar) / NdChar) + 1.0) / NdChar));
	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[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-251], t$95$0, If[LessEqual[t$95$1, 1e-206], N[(0.5 * N[(1.0 / N[(N[(N[(N[(N[(N[(NaChar * NaChar), $MachinePrecision] / NdChar), $MachinePrecision] - NaChar), $MachinePrecision] / NdChar), $MachinePrecision] + 1.0), $MachinePrecision] / NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.00000000000000002e-251 or 1.00000000000000003e-206 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 36.4

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

   5. Applied rewrites 36.4%

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

   if -1.00000000000000002e-251 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 1.00000000000000003e-206

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 2.8

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

   5. Applied rewrites 2.8%

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

   7. Applied rewrites 3.9%

      \[\leadsto 0.5 \cdot \frac{1}{\color{blue}{\frac{NdChar - NaChar}{\left(NdChar + NaChar\right) \cdot \left(NdChar - NaChar\right)}}} \]

   8. Taylor expanded in NdChar around -inf

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

   10. Applied rewrites 39.3%

       \[\leadsto 0.5 \cdot \frac{1}{-\frac{\frac{\frac{NaChar \cdot NaChar}{NdChar} - NaChar}{-NdChar} + -1}{NdChar}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -1 \cdot 10^{-251}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 10^{-206}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{\frac{\frac{NaChar \cdot NaChar}{NdChar} - NaChar}{NdChar} + 1}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 33.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ t_1 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-251}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-247}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{1}{NaChar} - \frac{NdChar}{NaChar \cdot NaChar}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar)))
        (t_1
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0)))))
   (if (<= t_1 -1e-251)
     t_0
     (if (<= t_1 5e-247)
       (* 0.5 (/ 1.0 (- (/ 1.0 NaChar) (/ NdChar (* NaChar NaChar)))))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -1e-251) {
		tmp = t_0;
	} else if (t_1 <= 5e-247) {
		tmp = 0.5 * (1.0 / ((1.0 / NaChar) - (NdChar / (NaChar * NaChar))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    t_1 = (ndchar / (exp(((mu + (edonor + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (exp(((((vef + ev) + eaccept) - mu) / kbt)) + 1.0d0))
    if (t_1 <= (-1d-251)) then
        tmp = t_0
    else if (t_1 <= 5d-247) then
        tmp = 0.5d0 * (1.0d0 / ((1.0d0 / nachar) - (ndchar / (nachar * nachar))))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (Math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -1e-251) {
		tmp = t_0;
	} else if (t_1 <= 5e-247) {
		tmp = 0.5 * (1.0 / ((1.0 / NaChar) - (NdChar / (NaChar * NaChar))));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	t_1 = (NdChar / (math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0))
	tmp = 0
	if t_1 <= -1e-251:
		tmp = t_0
	elif t_1 <= 5e-247:
		tmp = 0.5 * (1.0 / ((1.0 / NaChar) - (NdChar / (NaChar * NaChar))))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)))
	tmp = 0.0
	if (t_1 <= -1e-251)
		tmp = t_0;
	elseif (t_1 <= 5e-247)
		tmp = Float64(0.5 * Float64(1.0 / Float64(Float64(1.0 / NaChar) - Float64(NdChar / Float64(NaChar * NaChar)))));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	tmp = 0.0;
	if (t_1 <= -1e-251)
		tmp = t_0;
	elseif (t_1 <= 5e-247)
		tmp = 0.5 * (1.0 / ((1.0 / NaChar) - (NdChar / (NaChar * NaChar))));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-251], t$95$0, If[LessEqual[t$95$1, 5e-247], N[(0.5 * N[(1.0 / N[(N[(1.0 / NaChar), $MachinePrecision] - N[(NdChar / N[(NaChar * NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.00000000000000002e-251 or 4.99999999999999978e-247 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 35.6

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

   5. Applied rewrites 35.6%

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

   if -1.00000000000000002e-251 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 4.99999999999999978e-247

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 2.6

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

   5. Applied rewrites 2.6%

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

   7. Applied rewrites 4.0%

      \[\leadsto 0.5 \cdot \frac{1}{\color{blue}{\frac{NdChar - NaChar}{\left(NdChar + NaChar\right) \cdot \left(NdChar - NaChar\right)}}} \]

   8. Taylor expanded in NdChar around 0

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

   10. Applied rewrites 31.1%

       \[\leadsto 0.5 \cdot \frac{1}{\frac{1}{NaChar} - \color{blue}{\frac{NdChar}{NaChar \cdot NaChar}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -1 \cdot 10^{-251}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 5 \cdot 10^{-247}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{1}{NaChar} - \frac{NdChar}{NaChar \cdot NaChar}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 32.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ t_1 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-226}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-247}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{1 - \frac{NdChar}{NaChar}}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar)))
        (t_1
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0)))))
   (if (<= t_1 -2e-226)
     t_0
     (if (<= t_1 5e-247)
       (* 0.5 (/ 1.0 (/ (- 1.0 (/ NdChar NaChar)) NaChar)))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -2e-226) {
		tmp = t_0;
	} else if (t_1 <= 5e-247) {
		tmp = 0.5 * (1.0 / ((1.0 - (NdChar / NaChar)) / NaChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    t_1 = (ndchar / (exp(((mu + (edonor + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (exp(((((vef + ev) + eaccept) - mu) / kbt)) + 1.0d0))
    if (t_1 <= (-2d-226)) then
        tmp = t_0
    else if (t_1 <= 5d-247) then
        tmp = 0.5d0 * (1.0d0 / ((1.0d0 - (ndchar / nachar)) / nachar))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (Math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -2e-226) {
		tmp = t_0;
	} else if (t_1 <= 5e-247) {
		tmp = 0.5 * (1.0 / ((1.0 - (NdChar / NaChar)) / NaChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	t_1 = (NdChar / (math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0))
	tmp = 0
	if t_1 <= -2e-226:
		tmp = t_0
	elif t_1 <= 5e-247:
		tmp = 0.5 * (1.0 / ((1.0 - (NdChar / NaChar)) / NaChar))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)))
	tmp = 0.0
	if (t_1 <= -2e-226)
		tmp = t_0;
	elseif (t_1 <= 5e-247)
		tmp = Float64(0.5 * Float64(1.0 / Float64(Float64(1.0 - Float64(NdChar / NaChar)) / NaChar)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	tmp = 0.0;
	if (t_1 <= -2e-226)
		tmp = t_0;
	elseif (t_1 <= 5e-247)
		tmp = 0.5 * (1.0 / ((1.0 - (NdChar / NaChar)) / NaChar));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -2e-226], t$95$0, If[LessEqual[t$95$1, 5e-247], N[(0.5 * N[(1.0 / N[(N[(1.0 - N[(NdChar / NaChar), $MachinePrecision]), $MachinePrecision] / NaChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999984e-226 or 4.99999999999999978e-247 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 35.9

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

   5. Applied rewrites 35.9%

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

   if -1.99999999999999984e-226 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 4.99999999999999978e-247

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 2.8

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

   5. Applied rewrites 2.8%

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

   7. Applied rewrites 4.1%

      \[\leadsto 0.5 \cdot \frac{1}{\color{blue}{\frac{NdChar - NaChar}{\left(NdChar + NaChar\right) \cdot \left(NdChar - NaChar\right)}}} \]

   8. Taylor expanded in NaChar around inf

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

   10. Applied rewrites 27.8%

       \[\leadsto 0.5 \cdot \frac{1}{\frac{1 - \frac{NdChar}{NaChar}}{\color{blue}{NaChar}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 33.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -2 \cdot 10^{-226}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 5 \cdot 10^{-247}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{1 - \frac{NdChar}{NaChar}}{NaChar}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 32.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ t_1 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;t\_1 \leq -1 \cdot 10^{-251}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 10^{-206}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{1 - \frac{NaChar}{NdChar}}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar)))
        (t_1
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0)))))
   (if (<= t_1 -1e-251)
     t_0
     (if (<= t_1 1e-206)
       (* 0.5 (/ 1.0 (/ (- 1.0 (/ NaChar NdChar)) NdChar)))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -1e-251) {
		tmp = t_0;
	} else if (t_1 <= 1e-206) {
		tmp = 0.5 * (1.0 / ((1.0 - (NaChar / NdChar)) / NdChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    t_1 = (ndchar / (exp(((mu + (edonor + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (exp(((((vef + ev) + eaccept) - mu) / kbt)) + 1.0d0))
    if (t_1 <= (-1d-251)) then
        tmp = t_0
    else if (t_1 <= 1d-206) then
        tmp = 0.5d0 * (1.0d0 / ((1.0d0 - (nachar / ndchar)) / ndchar))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (Math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -1e-251) {
		tmp = t_0;
	} else if (t_1 <= 1e-206) {
		tmp = 0.5 * (1.0 / ((1.0 - (NaChar / NdChar)) / NdChar));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	t_1 = (NdChar / (math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0))
	tmp = 0
	if t_1 <= -1e-251:
		tmp = t_0
	elif t_1 <= 1e-206:
		tmp = 0.5 * (1.0 / ((1.0 - (NaChar / NdChar)) / NdChar))
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)))
	tmp = 0.0
	if (t_1 <= -1e-251)
		tmp = t_0;
	elseif (t_1 <= 1e-206)
		tmp = Float64(0.5 * Float64(1.0 / Float64(Float64(1.0 - Float64(NaChar / NdChar)) / NdChar)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	tmp = 0.0;
	if (t_1 <= -1e-251)
		tmp = t_0;
	elseif (t_1 <= 1e-206)
		tmp = 0.5 * (1.0 / ((1.0 - (NaChar / NdChar)) / NdChar));
	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[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -1e-251], t$95$0, If[LessEqual[t$95$1, 1e-206], N[(0.5 * N[(1.0 / N[(N[(1.0 - N[(NaChar / NdChar), $MachinePrecision]), $MachinePrecision] / NdChar), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.00000000000000002e-251 or 1.00000000000000003e-206 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 36.4

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

   5. Applied rewrites 36.4%

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

   if -1.00000000000000002e-251 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 1.00000000000000003e-206

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 2.8

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

   5. Applied rewrites 2.8%

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

   7. Applied rewrites 3.9%

      \[\leadsto 0.5 \cdot \frac{1}{\color{blue}{\frac{NdChar - NaChar}{\left(NdChar + NaChar\right) \cdot \left(NdChar - NaChar\right)}}} \]

   8. Taylor expanded in NdChar around inf

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

   10. Applied rewrites 21.0%

       \[\leadsto 0.5 \cdot \frac{1}{\frac{1 - \frac{NaChar}{NdChar}}{\color{blue}{NdChar}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 32.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -1 \cdot 10^{-251}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 10^{-206}:\\ \;\;\;\;0.5 \cdot \frac{1}{\frac{1 - \frac{NaChar}{NdChar}}{NdChar}}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 30.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.5 \cdot \left(NdChar + NaChar\right)\\ t_1 := \frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-293}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_1 \leq 5 \cdot 10^{-247}:\\ \;\;\;\;\frac{-0.25 \cdot \left(NaChar \cdot Ev\right)}{KbT}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (* 0.5 (+ NdChar NaChar)))
        (t_1
         (+
          (/ NdChar (+ (exp (/ (+ mu (+ EDonor (- Vef Ec))) KbT)) 1.0))
          (/ NaChar (+ (exp (/ (- (+ (+ Vef Ev) EAccept) mu) KbT)) 1.0)))))
   (if (<= t_1 -5e-293)
     t_0
     (if (<= t_1 5e-247) (/ (* -0.25 (* NaChar 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 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -5e-293) {
		tmp = t_0;
	} else if (t_1 <= 5e-247) {
		tmp = (-0.25 * (NaChar * Ev)) / KbT;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 0.5d0 * (ndchar + nachar)
    t_1 = (ndchar / (exp(((mu + (edonor + (vef - ec))) / kbt)) + 1.0d0)) + (nachar / (exp(((((vef + ev) + eaccept) - mu) / kbt)) + 1.0d0))
    if (t_1 <= (-5d-293)) then
        tmp = t_0
    else if (t_1 <= 5d-247) then
        tmp = ((-0.25d0) * (nachar * ev)) / kbt
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = 0.5 * (NdChar + NaChar);
	double t_1 = (NdChar / (Math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (Math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	double tmp;
	if (t_1 <= -5e-293) {
		tmp = t_0;
	} else if (t_1 <= 5e-247) {
		tmp = (-0.25 * (NaChar * Ev)) / KbT;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = 0.5 * (NdChar + NaChar)
	t_1 = (NdChar / (math.exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (math.exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0))
	tmp = 0
	if t_1 <= -5e-293:
		tmp = t_0
	elif t_1 <= 5e-247:
		tmp = (-0.25 * (NaChar * Ev)) / KbT
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(0.5 * Float64(NdChar + NaChar))
	t_1 = Float64(Float64(NdChar / Float64(exp(Float64(Float64(mu + Float64(EDonor + Float64(Vef - Ec))) / KbT)) + 1.0)) + Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Vef + Ev) + EAccept) - mu) / KbT)) + 1.0)))
	tmp = 0.0
	if (t_1 <= -5e-293)
		tmp = t_0;
	elseif (t_1 <= 5e-247)
		tmp = Float64(Float64(-0.25 * Float64(NaChar * Ev)) / KbT);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = 0.5 * (NdChar + NaChar);
	t_1 = (NdChar / (exp(((mu + (EDonor + (Vef - Ec))) / KbT)) + 1.0)) + (NaChar / (exp(((((Vef + Ev) + EAccept) - mu) / KbT)) + 1.0));
	tmp = 0.0;
	if (t_1 <= -5e-293)
		tmp = t_0;
	elseif (t_1 <= 5e-247)
		tmp = (-0.25 * (NaChar * Ev)) / KbT;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(0.5 * N[(NdChar + NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(N[Exp[N[(N[(mu + N[(EDonor + N[(Vef - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Vef + Ev), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$1, -5e-293], t$95$0, If[LessEqual[t$95$1, 5e-247], N[(N[(-0.25 * N[(NaChar * Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -5.0000000000000003e-293 or 4.99999999999999978e-247 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 35.0

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

   5. Applied rewrites 35.0%

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

   if -5.0000000000000003e-293 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < 4.99999999999999978e-247

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around -inf

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

   5. Applied rewrites 1.4%

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

   6. Taylor expanded in EAccept around inf

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

   8. Applied rewrites 2.3%

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

   9. Taylor expanded in Ev around inf

      \[\leadsto \frac{-1}{4} \cdot \color{blue}{\frac{Ev \cdot NaChar}{KbT}} \]
   10. Step-by-step derivation

   11. Applied rewrites 13.9%

       \[\leadsto \frac{-0.25 \cdot \left(Ev \cdot NaChar\right)}{\color{blue}{KbT}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 29.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq -5 \cdot 10^{-293}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \mathbf{elif}\;\frac{NdChar}{e^{\frac{mu + \left(EDonor + \left(Vef - Ec\right)\right)}{KbT}} + 1} + \frac{NaChar}{e^{\frac{\left(\left(Vef + Ev\right) + EAccept\right) - mu}{KbT}} + 1} \leq 5 \cdot 10^{-247}:\\ \;\;\;\;\frac{-0.25 \cdot \left(NaChar \cdot Ev\right)}{KbT}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(NdChar + NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 69.1% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{e^{\frac{EDonor + \left(Vef + \left(mu - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{if}\;NdChar \leq -2.2 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;NdChar \leq 2.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept - \left(\left(mu - Vef\right) - Ev\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ (exp (/ (+ EDonor (+ Vef (- mu Ec))) KbT)) 1.0))))
   (if (<= NdChar -2.2e+125)
     t_0
     (if (<= NdChar 2.1e+32)
       (/ NaChar (+ (exp (/ (- EAccept (- (- mu Vef) Ev)) KbT)) 1.0))
       t_0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (exp(((EDonor + (Vef + (mu - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -2.2e+125) {
		tmp = t_0;
	} else if (NdChar <= 2.1e+32) {
		tmp = NaChar / (exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ndchar / (exp(((edonor + (vef + (mu - ec))) / kbt)) + 1.0d0)
    if (ndchar <= (-2.2d+125)) then
        tmp = t_0
    else if (ndchar <= 2.1d+32) then
        tmp = nachar / (exp(((eaccept - ((mu - vef) - ev)) / kbt)) + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (Math.exp(((EDonor + (Vef + (mu - Ec))) / KbT)) + 1.0);
	double tmp;
	if (NdChar <= -2.2e+125) {
		tmp = t_0;
	} else if (NdChar <= 2.1e+32) {
		tmp = NaChar / (Math.exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (math.exp(((EDonor + (Vef + (mu - Ec))) / KbT)) + 1.0)
	tmp = 0
	if NdChar <= -2.2e+125:
		tmp = t_0
	elif NdChar <= 2.1e+32:
		tmp = NaChar / (math.exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(exp(Float64(Float64(EDonor + Float64(Vef + Float64(mu - Ec))) / KbT)) + 1.0))
	tmp = 0.0
	if (NdChar <= -2.2e+125)
		tmp = t_0;
	elseif (NdChar <= 2.1e+32)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(EAccept - Float64(Float64(mu - Vef) - Ev)) / KbT)) + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (exp(((EDonor + (Vef + (mu - Ec))) / KbT)) + 1.0);
	tmp = 0.0;
	if (NdChar <= -2.2e+125)
		tmp = t_0;
	elseif (NdChar <= 2.1e+32)
		tmp = NaChar / (exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(N[Exp[N[(N[(EDonor + N[(Vef + N[(mu - Ec), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[NdChar, -2.2e+125], t$95$0, If[LessEqual[NdChar, 2.1e+32], N[(NaChar / N[(N[Exp[N[(N[(EAccept - N[(N[(mu - Vef), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -2.19999999999999991e125 or 2.1000000000000001e32 < NdChar

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 77.6%

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

   if -2.19999999999999991e125 < NdChar < 2.1000000000000001e32

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. associate-+r+ N/A

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

      9. mul-1-neg N/A

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

      10. lower-+.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 75.7

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

   5. Applied rewrites 75.7%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -2.2 \cdot 10^{+125}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(Vef + \left(mu - Ec\right)\right)}{KbT}} + 1}\\ \mathbf{elif}\;NdChar \leq 2.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept - \left(\left(mu - Vef\right) - Ev\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor + \left(Vef + \left(mu - Ec\right)\right)}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 59.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;EDonor \leq 4.6 \cdot 10^{+228}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept - \left(\left(mu - Vef\right) - Ev\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= EDonor 4.6e+228)
   (/ NaChar (+ (exp (/ (- EAccept (- (- mu Vef) Ev)) KbT)) 1.0))
   (/ NdChar (+ (exp (/ EDonor KbT)) 1.0))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EDonor <= 4.6e+228) {
		tmp = NaChar / (exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (exp((EDonor / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (edonor <= 4.6d+228) then
        tmp = nachar / (exp(((eaccept - ((mu - vef) - ev)) / kbt)) + 1.0d0)
    else
        tmp = ndchar / (exp((edonor / kbt)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (EDonor <= 4.6e+228) {
		tmp = NaChar / (Math.exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	} else {
		tmp = NdChar / (Math.exp((EDonor / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if EDonor <= 4.6e+228:
		tmp = NaChar / (math.exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0)
	else:
		tmp = NdChar / (math.exp((EDonor / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (EDonor <= 4.6e+228)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(EAccept - Float64(Float64(mu - Vef) - Ev)) / KbT)) + 1.0));
	else
		tmp = Float64(NdChar / Float64(exp(Float64(EDonor / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (EDonor <= 4.6e+228)
		tmp = NaChar / (exp(((EAccept - ((mu - Vef) - Ev)) / KbT)) + 1.0);
	else
		tmp = NdChar / (exp((EDonor / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[EDonor, 4.6e+228], N[(NaChar / N[(N[Exp[N[(N[(EAccept - N[(N[(mu - Vef), $MachinePrecision] - Ev), $MachinePrecision]), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NdChar / N[(N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if EDonor < 4.60000000000000026e228

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around 0

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. associate--l+ N/A

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

      6. lower-+.f64 N/A

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

      7. sub-neg N/A

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

      8. associate-+r+ N/A

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

      9. mul-1-neg N/A

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

      10. lower-+.f64 N/A

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

      11. mul-1-neg N/A

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

      12. sub-neg N/A

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

      13. lower--.f64 68.3

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

   5. Applied rewrites 68.3%

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

   if 4.60000000000000026e228 < EDonor

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 93.5%

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

   6. Taylor expanded in EDonor around inf

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

   8. Applied rewrites 93.5%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;EDonor \leq 4.6 \cdot 10^{+228}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{EAccept - \left(\left(mu - Vef\right) - Ev\right)}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{e^{\frac{EDonor}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 22.4% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -2.15 \cdot 10^{+125}:\\ \;\;\;\;NdChar \cdot 0.5\\ \mathbf{elif}\;NdChar \leq 1.55 \cdot 10^{-30}:\\ \;\;\;\;NaChar \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;NdChar \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NdChar -2.15e+125)
   (* NdChar 0.5)
   (if (<= NdChar 1.55e-30) (* NaChar 0.5) (* NdChar 0.5))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -2.15e+125) {
		tmp = NdChar * 0.5;
	} else if (NdChar <= 1.55e-30) {
		tmp = NaChar * 0.5;
	} else {
		tmp = NdChar * 0.5;
	}
	return tmp;
}

Fortran

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ndchar <= (-2.15d+125)) then
        tmp = ndchar * 0.5d0
    else if (ndchar <= 1.55d-30) then
        tmp = nachar * 0.5d0
    else
        tmp = ndchar * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if (NdChar <= -2.15e+125) {
		tmp = NdChar * 0.5;
	} else if (NdChar <= 1.55e-30) {
		tmp = NaChar * 0.5;
	} else {
		tmp = NdChar * 0.5;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NdChar <= -2.15e+125:
		tmp = NdChar * 0.5
	elif NdChar <= 1.55e-30:
		tmp = NaChar * 0.5
	else:
		tmp = NdChar * 0.5
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NdChar <= -2.15e+125)
		tmp = Float64(NdChar * 0.5);
	elseif (NdChar <= 1.55e-30)
		tmp = Float64(NaChar * 0.5);
	else
		tmp = Float64(NdChar * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (NdChar <= -2.15e+125)
		tmp = NdChar * 0.5;
	elseif (NdChar <= 1.55e-30)
		tmp = NaChar * 0.5;
	else
		tmp = NdChar * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NdChar, -2.15e+125], N[(NdChar * 0.5), $MachinePrecision], If[LessEqual[NdChar, 1.55e-30], N[(NaChar * 0.5), $MachinePrecision], N[(NdChar * 0.5), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -2.15000000000000018e125 or 1.54999999999999995e-30 < NdChar

   1. Initial program 100.0%

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

   3. Taylor expanded in NdChar around inf

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

      1. lower-/.f64 N/A

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

      2. lower-+.f64 N/A

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

      3. lower-exp.f64 N/A

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

      4. lower-/.f64 N/A

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

   5. Applied rewrites 73.5%

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

   6. Taylor expanded in KbT around inf

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

   8. Applied rewrites 22.8%

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

   if -2.15000000000000018e125 < NdChar < 1.54999999999999995e-30

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. +-commutative N/A

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

      2. distribute-lft-out N/A

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

      3. lower-*.f64 N/A

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

      4. lower-+.f64 27.0

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

   5. Applied rewrites 27.0%

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

   6. Taylor expanded in NdChar around 0

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

   8. Applied rewrites 26.0%

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

Alternative 15: 27.4% accurate, 30.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in KbT around inf

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

   1. +-commutative N/A

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

   2. distribute-lft-out N/A

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

   3. lower-*.f64 N/A

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

   4. lower-+.f64 26.8

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

5. Applied rewrites 26.8%

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

Alternative 16: 17.9% accurate, 46.0× speedup

Math

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

FPCore

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in KbT around inf

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

   1. +-commutative N/A

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

   2. distribute-lft-out N/A

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

   3. lower-*.f64 N/A

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

   4. lower-+.f64 26.8

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

5. Applied rewrites 26.8%

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

6. Taylor expanded in NdChar around 0

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

8. Applied rewrites 18.3%

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

Reproduce

herbie shell --seed 2024233 
(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))))))