Bulmash initializePoisson

Percentage Accurate: 100.0% → 100.0%

Time: 10.9s

Alternatives: 20

Speedup: 1.0×

• could not determine a ground truth

  1. NdChar = 2.6024204268067304e+257
  2. Ec = -8.58847602892912e+48
  3. Vef = -0.000553011656078688
  4. EDonor = -3.7002861005344728e-103
  5. mu = 4.320427784223913e-55
  6. KbT = -1.3845626399693495e+26
  7. NaChar = -1.7588856261793295e+258
  8. Ev = 2.408628839717056e+252
  9. EAccept = -3.852406310048499e-58

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

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

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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) - 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]

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 78.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\\ t_1 := e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\\ t_2 := \frac{NaChar}{1 + t\_1}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t\_2\\ t_4 := t\_0 + t\_2\\ \mathbf{if}\;t\_4 \leq -5000000000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{-251}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 10^{-167}:\\ \;\;\;\;\frac{NaChar}{t\_1 + 1}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+21} \lor \neg \left(t\_4 \leq 10^{+240}\right):\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;t\_3\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
        (t_1 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
        (t_2 (/ NaChar (+ 1.0 t_1)))
        (t_3 (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_2))
        (t_4 (+ t_0 t_2)))
   (if (<= t_4 -5000000000000.0)
     (+
      (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
      (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= t_4 -1e-251)
       t_3
       (if (<= t_4 1e-167)
         (/ NaChar (+ t_1 1.0))
         (if (or (<= t_4 2e+21) (not (<= t_4 1e+240)))
           (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
           t_3))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = (NdChar / (1.0 + exp((mu / KbT)))) + t_2;
	double t_4 = t_0 + t_2;
	double tmp;
	if (t_4 <= -5000000000000.0) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (t_4 <= -1e-251) {
		tmp = t_3;
	} else if (t_4 <= 1e-167) {
		tmp = NaChar / (t_1 + 1.0);
	} else if ((t_4 <= 2e+21) || !(t_4 <= 1e+240)) {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))
    t_1 = exp(((((ev + vef) + eaccept) - mu) / kbt))
    t_2 = nachar / (1.0d0 + t_1)
    t_3 = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_2
    t_4 = t_0 + t_2
    if (t_4 <= (-5000000000000.0d0)) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (t_4 <= (-1d-251)) then
        tmp = t_3
    else if (t_4 <= 1d-167) then
        tmp = nachar / (t_1 + 1.0d0)
    else if ((t_4 <= 2d+21) .or. (.not. (t_4 <= 1d+240))) then
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_2;
	double t_4 = t_0 + t_2;
	double tmp;
	if (t_4 <= -5000000000000.0) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (t_4 <= -1e-251) {
		tmp = t_3;
	} else if (t_4 <= 1e-167) {
		tmp = NaChar / (t_1 + 1.0);
	} else if ((t_4 <= 2e+21) || !(t_4 <= 1e+240)) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))
	t_1 = math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))
	t_2 = NaChar / (1.0 + t_1)
	t_3 = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_2
	t_4 = t_0 + t_2
	tmp = 0
	if t_4 <= -5000000000000.0:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif t_4 <= -1e-251:
		tmp = t_3
	elif t_4 <= 1e-167:
		tmp = NaChar / (t_1 + 1.0)
	elif (t_4 <= 2e+21) or not (t_4 <= 1e+240):
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	else:
		tmp = t_3
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT))))
	t_1 = exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + t_1))
	t_3 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_2)
	t_4 = Float64(t_0 + t_2)
	tmp = 0.0
	if (t_4 <= -5000000000000.0)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (t_4 <= -1e-251)
		tmp = t_3;
	elseif (t_4 <= 1e-167)
		tmp = Float64(NaChar / Float64(t_1 + 1.0));
	elseif ((t_4 <= 2e+21) || !(t_4 <= 1e+240))
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	t_1 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	t_2 = NaChar / (1.0 + t_1);
	t_3 = (NdChar / (1.0 + exp((mu / KbT)))) + t_2;
	t_4 = t_0 + t_2;
	tmp = 0.0;
	if (t_4 <= -5000000000000.0)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (t_4 <= -1e-251)
		tmp = t_3;
	elseif (t_4 <= 1e-167)
		tmp = NaChar / (t_1 + 1.0);
	elseif ((t_4 <= 2e+21) || ~((t_4 <= 1e+240)))
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$0 + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, -5000000000000.0], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -1e-251], t$95$3, If[LessEqual[t$95$4, 1e-167], N[(NaChar / N[(t$95$1 + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[t$95$4, 2e+21], N[Not[LessEqual[t$95$4, 1e+240]], $MachinePrecision]], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$3]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -5e12

   1. Initial program 100.0%

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

   3. Taylor expanded in Ev around inf

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

      1. lower-/.f64 83.4

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in EDonor around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 79.4

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

   8. Applied rewrites 79.4%

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

   if -5e12 < (+.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 2e21 < (+.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))))) < 1.00000000000000001e240

   1. Initial program 100.0%

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

   3. Taylor expanded in mu around inf

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

      1. lower-/.f64 89.9

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

   5. Applied rewrites 89.9%

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

   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))))) < 1e-167

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 89.3

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

   5. Applied rewrites 89.3%

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

   if 1e-167 < (+.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))))) < 2e21 or 1.00000000000000001e240 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 82.1

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

   5. Applied rewrites 82.1%

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

4. Final simplification 86.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -5000000000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -1 \cdot 10^{-251}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 10^{-167}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 2 \cdot 10^{+21} \lor \neg \left(\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 10^{+240}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 79.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\\ t_1 := t\_0 + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\\ t_3 := \frac{NaChar}{1 + t\_2}\\ t_4 := t\_0 + t\_3\\ t_5 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t\_3\\ \mathbf{if}\;t\_4 \leq -2 \cdot 10^{-6}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{-251}:\\ \;\;\;\;t\_5\\ \mathbf{elif}\;t\_4 \leq 10^{-167}:\\ \;\;\;\;\frac{NaChar}{t\_2 + 1}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+21}:\\ \;\;\;\;t\_0 + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;t\_4 \leq 2 \cdot 10^{+141}:\\ \;\;\;\;t\_5\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
        (t_1 (+ t_0 (/ NaChar (+ 1.0 (exp (/ Ev KbT))))))
        (t_2 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
        (t_3 (/ NaChar (+ 1.0 t_2)))
        (t_4 (+ t_0 t_3))
        (t_5 (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_3)))
   (if (<= t_4 -2e-6)
     t_1
     (if (<= t_4 -1e-251)
       t_5
       (if (<= t_4 1e-167)
         (/ NaChar (+ t_2 1.0))
         (if (<= t_4 2e+21)
           (+ t_0 (/ NaChar (+ 1.0 (exp (/ EAccept KbT)))))
           (if (<= t_4 2e+141) t_5 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 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	double t_2 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_3 = NaChar / (1.0 + t_2);
	double t_4 = t_0 + t_3;
	double t_5 = (NdChar / (1.0 + exp((mu / KbT)))) + t_3;
	double tmp;
	if (t_4 <= -2e-6) {
		tmp = t_1;
	} else if (t_4 <= -1e-251) {
		tmp = t_5;
	} else if (t_4 <= 1e-167) {
		tmp = NaChar / (t_2 + 1.0);
	} else if (t_4 <= 2e+21) {
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	} else if (t_4 <= 2e+141) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: t_5
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))
    t_1 = t_0 + (nachar / (1.0d0 + exp((ev / kbt))))
    t_2 = exp(((((ev + vef) + eaccept) - mu) / kbt))
    t_3 = nachar / (1.0d0 + t_2)
    t_4 = t_0 + t_3
    t_5 = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_3
    if (t_4 <= (-2d-6)) then
        tmp = t_1
    else if (t_4 <= (-1d-251)) then
        tmp = t_5
    else if (t_4 <= 1d-167) then
        tmp = nachar / (t_2 + 1.0d0)
    else if (t_4 <= 2d+21) then
        tmp = t_0 + (nachar / (1.0d0 + exp((eaccept / kbt))))
    else if (t_4 <= 2d+141) then
        tmp = t_5
    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 = NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = t_0 + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double t_2 = Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_3 = NaChar / (1.0 + t_2);
	double t_4 = t_0 + t_3;
	double t_5 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_3;
	double tmp;
	if (t_4 <= -2e-6) {
		tmp = t_1;
	} else if (t_4 <= -1e-251) {
		tmp = t_5;
	} else if (t_4 <= 1e-167) {
		tmp = NaChar / (t_2 + 1.0);
	} else if (t_4 <= 2e+21) {
		tmp = t_0 + (NaChar / (1.0 + Math.exp((EAccept / KbT))));
	} else if (t_4 <= 2e+141) {
		tmp = t_5;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))
	t_1 = t_0 + (NaChar / (1.0 + math.exp((Ev / KbT))))
	t_2 = math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))
	t_3 = NaChar / (1.0 + t_2)
	t_4 = t_0 + t_3
	t_5 = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_3
	tmp = 0
	if t_4 <= -2e-6:
		tmp = t_1
	elif t_4 <= -1e-251:
		tmp = t_5
	elif t_4 <= 1e-167:
		tmp = NaChar / (t_2 + 1.0)
	elif t_4 <= 2e+21:
		tmp = t_0 + (NaChar / (1.0 + math.exp((EAccept / KbT))))
	elif t_4 <= 2e+141:
		tmp = t_5
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT))))
	t_1 = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	t_2 = exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT))
	t_3 = Float64(NaChar / Float64(1.0 + t_2))
	t_4 = Float64(t_0 + t_3)
	t_5 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_3)
	tmp = 0.0
	if (t_4 <= -2e-6)
		tmp = t_1;
	elseif (t_4 <= -1e-251)
		tmp = t_5;
	elseif (t_4 <= 1e-167)
		tmp = Float64(NaChar / Float64(t_2 + 1.0));
	elseif (t_4 <= 2e+21)
		tmp = Float64(t_0 + Float64(NaChar / Float64(1.0 + exp(Float64(EAccept / KbT)))));
	elseif (t_4 <= 2e+141)
		tmp = t_5;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	t_1 = t_0 + (NaChar / (1.0 + exp((Ev / KbT))));
	t_2 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	t_3 = NaChar / (1.0 + t_2);
	t_4 = t_0 + t_3;
	t_5 = (NdChar / (1.0 + exp((mu / KbT)))) + t_3;
	tmp = 0.0;
	if (t_4 <= -2e-6)
		tmp = t_1;
	elseif (t_4 <= -1e-251)
		tmp = t_5;
	elseif (t_4 <= 1e-167)
		tmp = NaChar / (t_2 + 1.0);
	elseif (t_4 <= 2e+21)
		tmp = t_0 + (NaChar / (1.0 + exp((EAccept / KbT))));
	elseif (t_4 <= 2e+141)
		tmp = t_5;
	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[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = N[(NaChar / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$0 + t$95$3), $MachinePrecision]}, Block[{t$95$5 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$3), $MachinePrecision]}, If[LessEqual[t$95$4, -2e-6], t$95$1, If[LessEqual[t$95$4, -1e-251], t$95$5, If[LessEqual[t$95$4, 1e-167], N[(NaChar / N[(t$95$2 + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+21], N[(t$95$0 + N[(NaChar / N[(1.0 + N[Exp[N[(EAccept / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 2e+141], t$95$5, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999991e-6 or 2.00000000000000003e141 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in Ev around inf

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

      1. lower-/.f64 86.0

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

   5. Applied rewrites 86.0%

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

   if -1.99999999999999991e-6 < (+.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 2e21 < (+.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))))) < 2.00000000000000003e141

   1. Initial program 100.0%

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

   3. Taylor expanded in mu around inf

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

      1. lower-/.f64 92.2

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

   5. Applied rewrites 92.2%

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

   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))))) < 1e-167

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 89.3

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

   5. Applied rewrites 89.3%

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

   if 1e-167 < (+.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))))) < 2e21

   1. Initial program 100.0%

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

   3. Taylor expanded in EAccept around inf

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

      1. lower-/.f64 79.5

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

   5. Applied rewrites 79.5%

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

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -2 \cdot 10^{-6}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -1 \cdot 10^{-251}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 10^{-167}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 2 \cdot 10^{+21}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{EAccept}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 2 \cdot 10^{+141}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 78.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\\ t_1 := e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\\ t_2 := \frac{NaChar}{1 + t\_1}\\ t_3 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + t\_2\\ t_4 := t\_0 + t\_2\\ \mathbf{if}\;t\_4 \leq -5000000000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;t\_4 \leq -1 \cdot 10^{-251}:\\ \;\;\;\;t\_3\\ \mathbf{elif}\;t\_4 \leq 10^{-169}:\\ \;\;\;\;\frac{NaChar}{t\_1 + 1}\\ \mathbf{elif}\;t\_4 \leq 10^{+240}:\\ \;\;\;\;t\_3\\ \mathbf{else}:\\ \;\;\;\;t\_0 + 0.5 \cdot NaChar\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
        (t_1 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
        (t_2 (/ NaChar (+ 1.0 t_1)))
        (t_3 (+ (/ NdChar (+ 1.0 (exp (/ mu KbT)))) t_2))
        (t_4 (+ t_0 t_2)))
   (if (<= t_4 -5000000000000.0)
     (+
      (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
      (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (if (<= t_4 -1e-251)
       t_3
       (if (<= t_4 1e-169)
         (/ NaChar (+ t_1 1.0))
         (if (<= t_4 1e+240) t_3 (+ t_0 (* 0.5 NaChar))))))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = (NdChar / (1.0 + exp((mu / KbT)))) + t_2;
	double t_4 = t_0 + t_2;
	double tmp;
	if (t_4 <= -5000000000000.0) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else if (t_4 <= -1e-251) {
		tmp = t_3;
	} else if (t_4 <= 1e-169) {
		tmp = NaChar / (t_1 + 1.0);
	} else if (t_4 <= 1e+240) {
		tmp = t_3;
	} else {
		tmp = t_0 + (0.5 * NaChar);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: t_4
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))
    t_1 = exp(((((ev + vef) + eaccept) - mu) / kbt))
    t_2 = nachar / (1.0d0 + t_1)
    t_3 = (ndchar / (1.0d0 + exp((mu / kbt)))) + t_2
    t_4 = t_0 + t_2
    if (t_4 <= (-5000000000000.0d0)) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else if (t_4 <= (-1d-251)) then
        tmp = t_3
    else if (t_4 <= 1d-169) then
        tmp = nachar / (t_1 + 1.0d0)
    else if (t_4 <= 1d+240) then
        tmp = t_3
    else
        tmp = t_0 + (0.5d0 * nachar)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + t_2;
	double t_4 = t_0 + t_2;
	double tmp;
	if (t_4 <= -5000000000000.0) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else if (t_4 <= -1e-251) {
		tmp = t_3;
	} else if (t_4 <= 1e-169) {
		tmp = NaChar / (t_1 + 1.0);
	} else if (t_4 <= 1e+240) {
		tmp = t_3;
	} else {
		tmp = t_0 + (0.5 * NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))
	t_1 = math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))
	t_2 = NaChar / (1.0 + t_1)
	t_3 = (NdChar / (1.0 + math.exp((mu / KbT)))) + t_2
	t_4 = t_0 + t_2
	tmp = 0
	if t_4 <= -5000000000000.0:
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	elif t_4 <= -1e-251:
		tmp = t_3
	elif t_4 <= 1e-169:
		tmp = NaChar / (t_1 + 1.0)
	elif t_4 <= 1e+240:
		tmp = t_3
	else:
		tmp = t_0 + (0.5 * NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT))))
	t_1 = exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + t_1))
	t_3 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + t_2)
	t_4 = Float64(t_0 + t_2)
	tmp = 0.0
	if (t_4 <= -5000000000000.0)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	elseif (t_4 <= -1e-251)
		tmp = t_3;
	elseif (t_4 <= 1e-169)
		tmp = Float64(NaChar / Float64(t_1 + 1.0));
	elseif (t_4 <= 1e+240)
		tmp = t_3;
	else
		tmp = Float64(t_0 + Float64(0.5 * NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	t_1 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	t_2 = NaChar / (1.0 + t_1);
	t_3 = (NdChar / (1.0 + exp((mu / KbT)))) + t_2;
	t_4 = t_0 + t_2;
	tmp = 0.0;
	if (t_4 <= -5000000000000.0)
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	elseif (t_4 <= -1e-251)
		tmp = t_3;
	elseif (t_4 <= 1e-169)
		tmp = NaChar / (t_1 + 1.0);
	elseif (t_4 <= 1e+240)
		tmp = t_3;
	else
		tmp = t_0 + (0.5 * NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, Block[{t$95$4 = N[(t$95$0 + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$4, -5000000000000.0], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, -1e-251], t$95$3, If[LessEqual[t$95$4, 1e-169], N[(NaChar / N[(t$95$1 + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$4, 1e+240], t$95$3, N[(t$95$0 + N[(0.5 * NaChar), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -5e12

   1. Initial program 100.0%

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

   3. Taylor expanded in Ev around inf

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

      1. lower-/.f64 83.4

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

   5. Applied rewrites 83.4%

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

   6. Taylor expanded in EDonor around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 79.4

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

   8. Applied rewrites 79.4%

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

   if -5e12 < (+.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 1.00000000000000002e-169 < (+.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))))) < 1.00000000000000001e240

   1. Initial program 100.0%

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

   3. Taylor expanded in mu around inf

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

      1. lower-/.f64 85.0

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

   5. Applied rewrites 85.0%

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

   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))))) < 1.00000000000000002e-169

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 90.4

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

   5. Applied rewrites 90.4%

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

   if 1.00000000000000001e240 < (+.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

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

      1. lower-*.f64 88.4

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

   5. Applied rewrites 88.4%

      \[\leadsto \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \color{blue}{0.5 \cdot NaChar} \]
3. Recombined 4 regimes into one program.

4. Final simplification 85.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -5000000000000:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -1 \cdot 10^{-251}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 10^{-169}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 10^{+240}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + 0.5 \cdot NaChar\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 76.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(EAccept + Vef\right) - mu}{KbT}}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ t_2 := e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\\ t_3 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + t\_2}\\ \mathbf{if}\;t\_3 \leq -4 \cdot 10^{-94}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_3 \leq -1 \cdot 10^{-251}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_3 \leq 10^{-169}:\\ \;\;\;\;\frac{NaChar}{t\_2 + 1}\\ \mathbf{elif}\;t\_3 \leq 2 \cdot 10^{+141}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ mu KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- (+ EAccept Vef) mu) KbT))))))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
          (/ NaChar (+ 1.0 (exp (/ Ev KbT))))))
        (t_2 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
        (t_3
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 t_2)))))
   (if (<= t_3 -4e-94)
     t_1
     (if (<= t_3 -1e-251)
       t_0
       (if (<= t_3 1e-169)
         (/ NaChar (+ t_2 1.0))
         (if (<= t_3 2e+141) t_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 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((((EAccept + Vef) - mu) / KbT))));
	double t_1 = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	double t_2 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_3 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_2));
	double tmp;
	if (t_3 <= -4e-94) {
		tmp = t_1;
	} else if (t_3 <= -1e-251) {
		tmp = t_0;
	} else if (t_3 <= 1e-169) {
		tmp = NaChar / (t_2 + 1.0);
	} else if (t_3 <= 2e+141) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((mu / kbt)))) + (nachar / (1.0d0 + exp((((eaccept + vef) - mu) / kbt))))
    t_1 = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    t_2 = exp(((((ev + vef) + eaccept) - mu) / kbt))
    t_3 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + t_2))
    if (t_3 <= (-4d-94)) then
        tmp = t_1
    else if (t_3 <= (-1d-251)) then
        tmp = t_0
    else if (t_3 <= 1d-169) then
        tmp = nachar / (t_2 + 1.0d0)
    else if (t_3 <= 2d+141) then
        tmp = t_0
    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 = (NdChar / (1.0 + Math.exp((mu / KbT)))) + (NaChar / (1.0 + Math.exp((((EAccept + Vef) - mu) / KbT))));
	double t_1 = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	double t_2 = Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_3 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_2));
	double tmp;
	if (t_3 <= -4e-94) {
		tmp = t_1;
	} else if (t_3 <= -1e-251) {
		tmp = t_0;
	} else if (t_3 <= 1e-169) {
		tmp = NaChar / (t_2 + 1.0);
	} else if (t_3 <= 2e+141) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((mu / KbT)))) + (NaChar / (1.0 + math.exp((((EAccept + Vef) - mu) / KbT))))
	t_1 = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	t_2 = math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))
	t_3 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_2))
	tmp = 0
	if t_3 <= -4e-94:
		tmp = t_1
	elif t_3 <= -1e-251:
		tmp = t_0
	elif t_3 <= 1e-169:
		tmp = NaChar / (t_2 + 1.0)
	elif t_3 <= 2e+141:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(mu / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(EAccept + Vef) - mu) / KbT)))))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))))
	t_2 = exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT))
	t_3 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + t_2)))
	tmp = 0.0
	if (t_3 <= -4e-94)
		tmp = t_1;
	elseif (t_3 <= -1e-251)
		tmp = t_0;
	elseif (t_3 <= 1e-169)
		tmp = Float64(NaChar / Float64(t_2 + 1.0));
	elseif (t_3 <= 2e+141)
		tmp = t_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 = (NdChar / (1.0 + exp((mu / KbT)))) + (NaChar / (1.0 + exp((((EAccept + Vef) - mu) / KbT))));
	t_1 = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	t_2 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	t_3 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_2));
	tmp = 0.0;
	if (t_3 <= -4e-94)
		tmp = t_1;
	elseif (t_3 <= -1e-251)
		tmp = t_0;
	elseif (t_3 <= 1e-169)
		tmp = NaChar / (t_2 + 1.0);
	elseif (t_3 <= 2e+141)
		tmp = t_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[(N[(NdChar / N[(1.0 + N[Exp[N[(mu / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(N[(N[(EAccept + Vef), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$3 = 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 + t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$3, -4e-94], t$95$1, If[LessEqual[t$95$3, -1e-251], t$95$0, If[LessEqual[t$95$3, 1e-169], N[(NaChar / N[(t$95$2 + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 2e+141], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -3.9999999999999998e-94 or 2.00000000000000003e141 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in Ev around inf

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

      1. lower-/.f64 84.2

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

   5. Applied rewrites 84.2%

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

   6. Taylor expanded in EDonor around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 79.5

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

   8. Applied rewrites 79.5%

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

   if -3.9999999999999998e-94 < (+.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 1.00000000000000002e-169 < (+.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))))) < 2.00000000000000003e141

   1. Initial program 100.0%

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

   3. Taylor expanded in mu around inf

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

      1. lower-/.f64 86.6

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

   5. Applied rewrites 86.6%

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

   6. Taylor expanded in Ev around 0

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

      1. lower-+.f64 80.3

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

   8. Applied rewrites 80.3%

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

   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))))) < 1.00000000000000002e-169

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 90.4

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

   5. Applied rewrites 90.4%

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

4. Final simplification 83.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -4 \cdot 10^{-94}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -1 \cdot 10^{-251}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(EAccept + Vef\right) - mu}{KbT}}}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 10^{-169}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 2 \cdot 10^{+141}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{mu}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(EAccept + Vef\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 66.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + 0.5 \cdot NaChar\\ t_1 := e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\\ t_2 := \frac{NaChar}{1 + t\_1}\\ t_3 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + t\_2\\ \mathbf{if}\;t\_3 \leq -2 \cdot 10^{-49}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_3 \leq 5 \cdot 10^{-165}:\\ \;\;\;\;\frac{NaChar}{t\_1 + 1}\\ \mathbf{elif}\;t\_3 \leq 10^{+275}:\\ \;\;\;\;0.5 \cdot NdChar + t\_2\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (* 0.5 NaChar)))
        (t_1 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
        (t_2 (/ NaChar (+ 1.0 t_1)))
        (t_3
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          t_2)))
   (if (<= t_3 -2e-49)
     t_0
     (if (<= t_3 5e-165)
       (/ NaChar (+ t_1 1.0))
       (if (<= t_3 1e+275) (+ (* 0.5 NdChar) t_2) t_0)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (0.5 * NaChar);
	double t_1 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + t_2;
	double tmp;
	if (t_3 <= -2e-49) {
		tmp = t_0;
	} else if (t_3 <= 5e-165) {
		tmp = NaChar / (t_1 + 1.0);
	} else if (t_3 <= 1e+275) {
		tmp = (0.5 * NdChar) + t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (0.5d0 * nachar)
    t_1 = exp(((((ev + vef) + eaccept) - mu) / kbt))
    t_2 = nachar / (1.0d0 + t_1)
    t_3 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + t_2
    if (t_3 <= (-2d-49)) then
        tmp = t_0
    else if (t_3 <= 5d-165) then
        tmp = nachar / (t_1 + 1.0d0)
    else if (t_3 <= 1d+275) then
        tmp = (0.5d0 * ndchar) + t_2
    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 / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (0.5 * NaChar);
	double t_1 = Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_2 = NaChar / (1.0 + t_1);
	double t_3 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + t_2;
	double tmp;
	if (t_3 <= -2e-49) {
		tmp = t_0;
	} else if (t_3 <= 5e-165) {
		tmp = NaChar / (t_1 + 1.0);
	} else if (t_3 <= 1e+275) {
		tmp = (0.5 * NdChar) + t_2;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (0.5 * NaChar)
	t_1 = math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))
	t_2 = NaChar / (1.0 + t_1)
	t_3 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + t_2
	tmp = 0
	if t_3 <= -2e-49:
		tmp = t_0
	elif t_3 <= 5e-165:
		tmp = NaChar / (t_1 + 1.0)
	elif t_3 <= 1e+275:
		tmp = (0.5 * NdChar) + t_2
	else:
		tmp = t_0
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(0.5 * NaChar))
	t_1 = exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT))
	t_2 = Float64(NaChar / Float64(1.0 + t_1))
	t_3 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + t_2)
	tmp = 0.0
	if (t_3 <= -2e-49)
		tmp = t_0;
	elseif (t_3 <= 5e-165)
		tmp = Float64(NaChar / Float64(t_1 + 1.0));
	elseif (t_3 <= 1e+275)
		tmp = Float64(Float64(0.5 * NdChar) + t_2);
	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 / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (0.5 * NaChar);
	t_1 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	t_2 = NaChar / (1.0 + t_1);
	t_3 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + t_2;
	tmp = 0.0;
	if (t_3 <= -2e-49)
		tmp = t_0;
	elseif (t_3 <= 5e-165)
		tmp = NaChar / (t_1 + 1.0);
	elseif (t_3 <= 1e+275)
		tmp = (0.5 * NdChar) + t_2;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * NaChar), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$2), $MachinePrecision]}, If[LessEqual[t$95$3, -2e-49], t$95$0, If[LessEqual[t$95$3, 5e-165], N[(NaChar / N[(t$95$1 + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$3, 1e+275], N[(N[(0.5 * NdChar), $MachinePrecision] + t$95$2), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -1.99999999999999987e-49 or 9.9999999999999996e274 < (+.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

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

      1. lower-*.f64 72.7

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in EDonor around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 69.5

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

   8. Applied rewrites 69.5%

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

   if -1.99999999999999987e-49 < (+.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))))) < 4.99999999999999981e-165

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 82.1

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

   5. Applied rewrites 82.1%

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

   if 4.99999999999999981e-165 < (+.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))))) < 9.9999999999999996e274

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. lower-*.f64 67.3

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

   5. Applied rewrites 67.3%

      \[\leadsto \color{blue}{0.5 \cdot NdChar} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -2 \cdot 10^{-49}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + 0.5 \cdot NaChar\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 5 \cdot 10^{-165}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 10^{+275}:\\ \;\;\;\;0.5 \cdot NdChar + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + 0.5 \cdot NaChar\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + t\_0}\\ \mathbf{if}\;t\_1 \leq -5 \cdot 10^{-221} \lor \neg \left(t\_1 \leq 2 \cdot 10^{-258}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t\_0 + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 t_0)))))
   (if (or (<= t_1 -5e-221) (not (<= t_1 2e-258)))
     (+
      (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT))))
      (/ NaChar (+ 1.0 (exp (/ Ev KbT)))))
     (/ NaChar (+ t_0 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 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_0));
	double tmp;
	if ((t_1 <= -5e-221) || !(t_1 <= 2e-258)) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	} else {
		tmp = NaChar / (t_0 + 1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 = exp(((((ev + vef) + eaccept) - mu) / kbt))
    t_1 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + t_0))
    if ((t_1 <= (-5d-221)) .or. (.not. (t_1 <= 2d-258))) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (nachar / (1.0d0 + exp((ev / kbt))))
    else
        tmp = nachar / (t_0 + 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 = Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_1 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_0));
	double tmp;
	if ((t_1 <= -5e-221) || !(t_1 <= 2e-258)) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + Math.exp((Ev / KbT))));
	} else {
		tmp = NaChar / (t_0 + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))
	t_1 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_0))
	tmp = 0
	if (t_1 <= -5e-221) or not (t_1 <= 2e-258):
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + math.exp((Ev / KbT))))
	else:
		tmp = NaChar / (t_0 + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + t_0)))
	tmp = 0.0
	if ((t_1 <= -5e-221) || !(t_1 <= 2e-258))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Ev / KbT)))));
	else
		tmp = Float64(NaChar / Float64(t_0 + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_0));
	tmp = 0.0;
	if ((t_1 <= -5e-221) || ~((t_1 <= 2e-258)))
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (NaChar / (1.0 + exp((Ev / KbT))));
	else
		tmp = NaChar / (t_0 + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = 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 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -5e-221], N[Not[LessEqual[t$95$1, 2e-258]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(NaChar / N[(1.0 + N[Exp[N[(Ev / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision]]]]

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))))) < -4.99999999999999996e-221 or 1.99999999999999991e-258 < (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT)))))

   1. Initial program 100.0%

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

   3. Taylor expanded in Ev around inf

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

      1. lower-/.f64 80.2

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

   5. Applied rewrites 80.2%

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

   6. Taylor expanded in EDonor around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 74.7

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

   8. Applied rewrites 74.7%

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

   if -4.99999999999999996e-221 < (+.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))))) < 1.99999999999999991e-258

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 95.9

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

   5. Applied rewrites 95.9%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -5 \cdot 10^{-221} \lor \neg \left(\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 2 \cdot 10^{-258}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + \frac{NaChar}{1 + e^{\frac{Ev}{KbT}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 68.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}}\\ t_1 := e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\\ t_2 := t\_0 + \frac{NaChar}{1 + t\_1}\\ \mathbf{if}\;t\_2 \leq -2 \cdot 10^{-49} \lor \neg \left(t\_2 \leq 5 \cdot 10^{-158}\right):\\ \;\;\;\;t\_0 + 0.5 \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t\_1 + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT)))))
        (t_1 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
        (t_2 (+ t_0 (/ NaChar (+ 1.0 t_1)))))
   (if (or (<= t_2 -2e-49) (not (<= t_2 5e-158)))
     (+ t_0 (* 0.5 NaChar))
     (/ NaChar (+ t_1 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 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_2 = t_0 + (NaChar / (1.0 + t_1));
	double tmp;
	if ((t_2 <= -2e-49) || !(t_2 <= 5e-158)) {
		tmp = t_0 + (0.5 * NaChar);
	} else {
		tmp = NaChar / (t_1 + 1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))
    t_1 = exp(((((ev + vef) + eaccept) - mu) / kbt))
    t_2 = t_0 + (nachar / (1.0d0 + t_1))
    if ((t_2 <= (-2d-49)) .or. (.not. (t_2 <= 5d-158))) then
        tmp = t_0 + (0.5d0 * nachar)
    else
        tmp = nachar / (t_1 + 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 = NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	double t_1 = Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_2 = t_0 + (NaChar / (1.0 + t_1));
	double tmp;
	if ((t_2 <= -2e-49) || !(t_2 <= 5e-158)) {
		tmp = t_0 + (0.5 * NaChar);
	} else {
		tmp = NaChar / (t_1 + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))
	t_1 = math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))
	t_2 = t_0 + (NaChar / (1.0 + t_1))
	tmp = 0
	if (t_2 <= -2e-49) or not (t_2 <= 5e-158):
		tmp = t_0 + (0.5 * NaChar)
	else:
		tmp = NaChar / (t_1 + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT))))
	t_1 = exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT))
	t_2 = Float64(t_0 + Float64(NaChar / Float64(1.0 + t_1)))
	tmp = 0.0
	if ((t_2 <= -2e-49) || !(t_2 <= 5e-158))
		tmp = Float64(t_0 + Float64(0.5 * NaChar));
	else
		tmp = Float64(NaChar / Float64(t_1 + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)));
	t_1 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	t_2 = t_0 + (NaChar / (1.0 + t_1));
	tmp = 0.0;
	if ((t_2 <= -2e-49) || ~((t_2 <= 5e-158)))
		tmp = t_0 + (0.5 * NaChar);
	else
		tmp = NaChar / (t_1 + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(NdChar / N[(1.0 + N[Exp[N[((-N[(N[(N[(Ec - Vef), $MachinePrecision] - EDonor), $MachinePrecision] - mu), $MachinePrecision]) / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$2 = N[(t$95$0 + N[(NaChar / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$2, -2e-49], N[Not[LessEqual[t$95$2, 5e-158]], $MachinePrecision]], N[(t$95$0 + N[(0.5 * NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(t$95$1 + 1.0), $MachinePrecision]), $MachinePrecision]]]]]

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))))) < -1.99999999999999987e-49 or 4.99999999999999972e-158 < (+.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

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

      1. lower-*.f64 68.8

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

   5. Applied rewrites 68.8%

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

   if -1.99999999999999987e-49 < (+.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))))) < 4.99999999999999972e-158

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 81.4

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

   5. Applied rewrites 81.4%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -2 \cdot 10^{-49} \lor \neg \left(\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 5 \cdot 10^{-158}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + 0.5 \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 65.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\\ t_1 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + t\_0}\\ \mathbf{if}\;t\_1 \leq -2 \cdot 10^{-49} \lor \neg \left(t\_1 \leq 5 \cdot 10^{-158}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + 0.5 \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{t\_0 + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
        (t_1
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 t_0)))))
   (if (or (<= t_1 -2e-49) (not (<= t_1 5e-158)))
     (+ (/ NdChar (+ 1.0 (exp (/ (- (+ mu Vef) Ec) KbT)))) (* 0.5 NaChar))
     (/ NaChar (+ t_0 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 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_0));
	double tmp;
	if ((t_1 <= -2e-49) || !(t_1 <= 5e-158)) {
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (0.5 * NaChar);
	} else {
		tmp = NaChar / (t_0 + 1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 = exp(((((ev + vef) + eaccept) - mu) / kbt))
    t_1 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + t_0))
    if ((t_1 <= (-2d-49)) .or. (.not. (t_1 <= 5d-158))) then
        tmp = (ndchar / (1.0d0 + exp((((mu + vef) - ec) / kbt)))) + (0.5d0 * nachar)
    else
        tmp = nachar / (t_0 + 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 = Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	double t_1 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_0));
	double tmp;
	if ((t_1 <= -2e-49) || !(t_1 <= 5e-158)) {
		tmp = (NdChar / (1.0 + Math.exp((((mu + Vef) - Ec) / KbT)))) + (0.5 * NaChar);
	} else {
		tmp = NaChar / (t_0 + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))
	t_1 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_0))
	tmp = 0
	if (t_1 <= -2e-49) or not (t_1 <= 5e-158):
		tmp = (NdChar / (1.0 + math.exp((((mu + Vef) - Ec) / KbT)))) + (0.5 * NaChar)
	else:
		tmp = NaChar / (t_0 + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT))
	t_1 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + t_0)))
	tmp = 0.0
	if ((t_1 <= -2e-49) || !(t_1 <= 5e-158))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(Float64(mu + Vef) - Ec) / KbT)))) + Float64(0.5 * NaChar));
	else
		tmp = Float64(NaChar / Float64(t_0 + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = exp(((((Ev + Vef) + EAccept) - mu) / KbT));
	t_1 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + t_0));
	tmp = 0.0;
	if ((t_1 <= -2e-49) || ~((t_1 <= 5e-158)))
		tmp = (NdChar / (1.0 + exp((((mu + Vef) - Ec) / KbT)))) + (0.5 * NaChar);
	else
		tmp = NaChar / (t_0 + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = 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 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$1, -2e-49], N[Not[LessEqual[t$95$1, 5e-158]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(N[(N[(mu + Vef), $MachinePrecision] - Ec), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(t$95$0 + 1.0), $MachinePrecision]), $MachinePrecision]]]]

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))))) < -1.99999999999999987e-49 or 4.99999999999999972e-158 < (+.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

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

      1. lower-*.f64 68.8

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

   5. Applied rewrites 68.8%

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

   6. Taylor expanded in EDonor around 0

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

      1. lower--.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-+.f64 64.9

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

   8. Applied rewrites 64.9%

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

   if -1.99999999999999987e-49 < (+.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))))) < 4.99999999999999972e-158

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 81.4

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

   5. Applied rewrites 81.4%

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

4. Final simplification 71.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -2 \cdot 10^{-49} \lor \neg \left(\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 5 \cdot 10^{-158}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{\left(mu + Vef\right) - Ec}{KbT}}} + 0.5 \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 55.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-49} \lor \neg \left(t\_0 \leq 10^{+90}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + 0.5 \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + Vef\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))))))
   (if (or (<= t_0 -2e-49) (not (<= t_0 1e+90)))
     (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (* 0.5 NaChar))
     (/ NaChar (+ (exp (/ (- (+ EAccept Vef) 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 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
	double tmp;
	if ((t_0 <= -2e-49) || !(t_0 <= 1e+90)) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (0.5 * NaChar);
	} else {
		tmp = NaChar / (exp((((EAccept + Vef) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) - mu) / kbt))))
    if ((t_0 <= (-2d-49)) .or. (.not. (t_0 <= 1d+90))) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (0.5d0 * nachar)
    else
        tmp = nachar / (exp((((eaccept + vef) - 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 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
	double tmp;
	if ((t_0 <= -2e-49) || !(t_0 <= 1e+90)) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (0.5 * NaChar);
	} else {
		tmp = NaChar / (Math.exp((((EAccept + Vef) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))))
	tmp = 0
	if (t_0 <= -2e-49) or not (t_0 <= 1e+90):
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (0.5 * NaChar)
	else:
		tmp = NaChar / (math.exp((((EAccept + Vef) - mu) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT)))))
	tmp = 0.0
	if ((t_0 <= -2e-49) || !(t_0 <= 1e+90))
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(0.5 * NaChar));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Vef) - mu) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
	tmp = 0.0;
	if ((t_0 <= -2e-49) || ~((t_0 <= 1e+90)))
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (0.5 * NaChar);
	else
		tmp = NaChar / (exp((((EAccept + Vef) - 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[(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]}, If[Or[LessEqual[t$95$0, -2e-49], N[Not[LessEqual[t$95$0, 1e+90]], $MachinePrecision]], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + Vef), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

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))))) < -1.99999999999999987e-49 or 9.99999999999999966e89 < (+.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

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

      1. lower-*.f64 72.7

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

   5. Applied rewrites 72.7%

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

   6. Taylor expanded in Vef around inf

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

      1. lower-/.f64 56.1

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

   8. Applied rewrites 56.1%

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

   if -1.99999999999999987e-49 < (+.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))))) < 9.99999999999999966e89

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 73.1

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

   5. Applied rewrites 73.1%

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

   6. Taylor expanded in Ev around 0

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

   8. Applied rewrites 62.7%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -2 \cdot 10^{-49} \lor \neg \left(\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 10^{+90}\right):\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + 0.5 \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + Vef\right) - mu}{KbT}} + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 33.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-202} \lor \neg \left(t\_0 \leq 4 \cdot 10^{-286}\right):\\ \;\;\;\;0.5 \cdot \left(NaChar + NdChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(NdChar \cdot NdChar\right) \cdot -0.5}{NaChar - NdChar}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))))))
   (if (or (<= t_0 -2e-202) (not (<= t_0 4e-286)))
     (* 0.5 (+ NaChar NdChar))
     (/ (* (* NdChar NdChar) -0.5) (- NaChar NdChar)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
	double tmp;
	if ((t_0 <= -2e-202) || !(t_0 <= 4e-286)) {
		tmp = 0.5 * (NaChar + NdChar);
	} else {
		tmp = ((NdChar * NdChar) * -0.5) / (NaChar - NdChar);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) - mu) / kbt))))
    if ((t_0 <= (-2d-202)) .or. (.not. (t_0 <= 4d-286))) then
        tmp = 0.5d0 * (nachar + ndchar)
    else
        tmp = ((ndchar * ndchar) * (-0.5d0)) / (nachar - ndchar)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
	double tmp;
	if ((t_0 <= -2e-202) || !(t_0 <= 4e-286)) {
		tmp = 0.5 * (NaChar + NdChar);
	} else {
		tmp = ((NdChar * NdChar) * -0.5) / (NaChar - NdChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))))
	tmp = 0
	if (t_0 <= -2e-202) or not (t_0 <= 4e-286):
		tmp = 0.5 * (NaChar + NdChar)
	else:
		tmp = ((NdChar * NdChar) * -0.5) / (NaChar - NdChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT)))))
	tmp = 0.0
	if ((t_0 <= -2e-202) || !(t_0 <= 4e-286))
		tmp = Float64(0.5 * Float64(NaChar + NdChar));
	else
		tmp = Float64(Float64(Float64(NdChar * NdChar) * -0.5) / Float64(NaChar - NdChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
	tmp = 0.0;
	if ((t_0 <= -2e-202) || ~((t_0 <= 4e-286)))
		tmp = 0.5 * (NaChar + NdChar);
	else
		tmp = ((NdChar * NdChar) * -0.5) / (NaChar - NdChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(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]}, If[Or[LessEqual[t$95$0, -2e-202], N[Not[LessEqual[t$95$0, 4e-286]], $MachinePrecision]], N[(0.5 * N[(NaChar + NdChar), $MachinePrecision]), $MachinePrecision], N[(N[(N[(NdChar * NdChar), $MachinePrecision] * -0.5), $MachinePrecision] / N[(NaChar - NdChar), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -2.0000000000000001e-202 or 4.0000000000000002e-286 < (+.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. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 36.9

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

   5. Applied rewrites 36.9%

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

   if -2.0000000000000001e-202 < (+.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))))) < 4.0000000000000002e-286

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   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. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 2.6

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

   5. Applied rewrites 2.6%

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

   7. Applied rewrites 7.1%

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

   8. Taylor expanded in NdChar around inf

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

   10. Applied rewrites 26.5%

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

4. Final simplification 34.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -2 \cdot 10^{-202} \lor \neg \left(\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 4 \cdot 10^{-286}\right):\\ \;\;\;\;0.5 \cdot \left(NaChar + NdChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(NdChar \cdot NdChar\right) \cdot -0.5}{NaChar - NdChar}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}}\\ \mathbf{if}\;t\_0 \leq -2 \cdot 10^{-202} \lor \neg \left(t\_0 \leq 5 \cdot 10^{-281}\right):\\ \;\;\;\;0.5 \cdot \left(NaChar + NdChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{NaChar - NdChar} \cdot \left(NaChar \cdot NaChar\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0
         (+
          (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
          (/ NaChar (+ 1.0 (exp (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))))))
   (if (or (<= t_0 -2e-202) (not (<= t_0 5e-281)))
     (* 0.5 (+ NaChar NdChar))
     (* (/ 0.5 (- NaChar NdChar)) (* NaChar NaChar)))))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
	double tmp;
	if ((t_0 <= -2e-202) || !(t_0 <= 5e-281)) {
		tmp = 0.5 * (NaChar + NdChar);
	} else {
		tmp = (0.5 / (NaChar - NdChar)) * (NaChar * NaChar);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (1.0d0 + exp(((((ev + vef) + eaccept) - mu) / kbt))))
    if ((t_0 <= (-2d-202)) .or. (.not. (t_0 <= 5d-281))) then
        tmp = 0.5d0 * (nachar + ndchar)
    else
        tmp = (0.5d0 / (nachar - ndchar)) * (nachar * nachar)
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
	double tmp;
	if ((t_0 <= -2e-202) || !(t_0 <= 5e-281)) {
		tmp = 0.5 * (NaChar + NdChar);
	} else {
		tmp = (0.5 / (NaChar - NdChar)) * (NaChar * NaChar);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + math.exp(((((Ev + Vef) + EAccept) - mu) / KbT))))
	tmp = 0
	if (t_0 <= -2e-202) or not (t_0 <= 5e-281):
		tmp = 0.5 * (NaChar + NdChar)
	else:
		tmp = (0.5 / (NaChar - NdChar)) * (NaChar * NaChar)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(1.0 + exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT)))))
	tmp = 0.0
	if ((t_0 <= -2e-202) || !(t_0 <= 5e-281))
		tmp = Float64(0.5 * Float64(NaChar + NdChar));
	else
		tmp = Float64(Float64(0.5 / Float64(NaChar - NdChar)) * Float64(NaChar * NaChar));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (1.0 + exp(((((Ev + Vef) + EAccept) - mu) / KbT))));
	tmp = 0.0;
	if ((t_0 <= -2e-202) || ~((t_0 <= 5e-281)))
		tmp = 0.5 * (NaChar + NdChar);
	else
		tmp = (0.5 / (NaChar - NdChar)) * (NaChar * NaChar);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(NdChar / N[(1.0 + N[Exp[N[((-N[(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]}, If[Or[LessEqual[t$95$0, -2e-202], N[Not[LessEqual[t$95$0, 5e-281]], $MachinePrecision]], N[(0.5 * N[(NaChar + NdChar), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 / N[(NaChar - NdChar), $MachinePrecision]), $MachinePrecision] * N[(NaChar * NaChar), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (/.f64 NdChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (neg.f64 (-.f64 (-.f64 (-.f64 Ec Vef) EDonor) mu)) KbT)))) (/.f64 NaChar (+.f64 #s(literal 1 binary64) (exp.f64 (/.f64 (+.f64 (+.f64 (+.f64 Ev Vef) EAccept) (neg.f64 mu)) KbT))))) < -2.0000000000000001e-202 or 4.9999999999999998e-281 < (+.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. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 37.3

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

   5. Applied rewrites 37.3%

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

   if -2.0000000000000001e-202 < (+.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))))) < 4.9999999999999998e-281

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   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. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 2.6

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

   5. Applied rewrites 2.6%

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

   7. Applied rewrites 7.0%

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

   9. Applied rewrites 7.0%

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

   10. Taylor expanded in NdChar around 0

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

   12. Applied rewrites 25.4%

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

4. Final simplification 34.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq -2 \cdot 10^{-202} \lor \neg \left(\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}} \leq 5 \cdot 10^{-281}\right):\\ \;\;\;\;0.5 \cdot \left(NaChar + NdChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{NaChar - NdChar} \cdot \left(NaChar \cdot NaChar\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 68.6% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}\\ \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{+26} \lor \neg \left(NaChar \leq 1.45 \cdot 10^{-177}\right):\\ \;\;\;\;\frac{NaChar}{e^{t\_0} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{2 + t\_0}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (let* ((t_0 (/ (- (+ (+ Ev Vef) EAccept) mu) KbT)))
   (if (or (<= NaChar -4.5e+26) (not (<= NaChar 1.45e-177)))
     (/ NaChar (+ (exp t_0) 1.0))
     (+
      (/ NdChar (+ 1.0 (exp (/ (- (- (- (- Ec Vef) EDonor) mu)) KbT))))
      (/ NaChar (+ 2.0 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 = (((Ev + Vef) + EAccept) - mu) / KbT;
	double tmp;
	if ((NaChar <= -4.5e+26) || !(NaChar <= 1.45e-177)) {
		tmp = NaChar / (exp(t_0) + 1.0);
	} else {
		tmp = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (2.0 + t_0));
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    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 = (((ev + vef) + eaccept) - mu) / kbt
    if ((nachar <= (-4.5d+26)) .or. (.not. (nachar <= 1.45d-177))) then
        tmp = nachar / (exp(t_0) + 1.0d0)
    else
        tmp = (ndchar / (1.0d0 + exp((-(((ec - vef) - edonor) - mu) / kbt)))) + (nachar / (2.0d0 + t_0))
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double t_0 = (((Ev + Vef) + EAccept) - mu) / KbT;
	double tmp;
	if ((NaChar <= -4.5e+26) || !(NaChar <= 1.45e-177)) {
		tmp = NaChar / (Math.exp(t_0) + 1.0);
	} else {
		tmp = (NdChar / (1.0 + Math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (2.0 + t_0));
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	t_0 = (((Ev + Vef) + EAccept) - mu) / KbT
	tmp = 0
	if (NaChar <= -4.5e+26) or not (NaChar <= 1.45e-177):
		tmp = NaChar / (math.exp(t_0) + 1.0)
	else:
		tmp = (NdChar / (1.0 + math.exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (2.0 + t_0))
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / KbT)
	tmp = 0.0
	if ((NaChar <= -4.5e+26) || !(NaChar <= 1.45e-177))
		tmp = Float64(NaChar / Float64(exp(t_0) + 1.0));
	else
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Float64(-Float64(Float64(Float64(Ec - Vef) - EDonor) - mu)) / KbT)))) + Float64(NaChar / Float64(2.0 + t_0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	t_0 = (((Ev + Vef) + EAccept) - mu) / KbT;
	tmp = 0.0;
	if ((NaChar <= -4.5e+26) || ~((NaChar <= 1.45e-177)))
		tmp = NaChar / (exp(t_0) + 1.0);
	else
		tmp = (NdChar / (1.0 + exp((-(((Ec - Vef) - EDonor) - mu) / KbT)))) + (NaChar / (2.0 + t_0));
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := Block[{t$95$0 = N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]}, If[Or[LessEqual[NaChar, -4.5e+26], N[Not[LessEqual[NaChar, 1.45e-177]], $MachinePrecision]], N[(NaChar / N[(N[Exp[t$95$0], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], 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[(2.0 + t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if NaChar < -4.49999999999999978e26 or 1.44999999999999999e-177 < NaChar

   1. Initial program 100.0%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 72.9

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

   5. Applied rewrites 72.9%

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

   if -4.49999999999999978e26 < NaChar < 1.44999999999999999e-177

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. associate--l+ N/A

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

      2. div-add-rev N/A

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

      3. div-add N/A

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

      4. div-sub N/A

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

      5. lower-+.f64 N/A

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

      6. lower-/.f64 N/A

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

      7. lower--.f64 N/A

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

      8. +-commutative N/A

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

      9. lower-+.f64 N/A

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

      10. lower-+.f64 78.8

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

   5. Applied rewrites 78.8%

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

4. Final simplification 75.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NaChar \leq -4.5 \cdot 10^{+26} \lor \neg \left(NaChar \leq 1.45 \cdot 10^{-177}\right):\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{2 + \frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}}\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 53.0% accurate, 1.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NaChar \leq -2.7 \cdot 10^{-45}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Ev + Vef\right) - mu}{KbT}} + 1}\\ \mathbf{elif}\;NaChar \leq 4.6 \cdot 10^{-284}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{EDonor}{KbT}}} + 0.5 \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + Vef\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= NaChar -2.7e-45)
   (/ NaChar (+ (exp (/ (- (+ Ev Vef) mu) KbT)) 1.0))
   (if (<= NaChar 4.6e-284)
     (+ (/ NdChar (+ 1.0 (exp (/ EDonor KbT)))) (* 0.5 NaChar))
     (/ NaChar (+ (exp (/ (- (+ EAccept Vef) 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 tmp;
	if (NaChar <= -2.7e-45) {
		tmp = NaChar / (exp((((Ev + Vef) - mu) / KbT)) + 1.0);
	} else if (NaChar <= 4.6e-284) {
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (0.5 * NaChar);
	} else {
		tmp = NaChar / (exp((((EAccept + Vef) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (nachar <= (-2.7d-45)) then
        tmp = nachar / (exp((((ev + vef) - mu) / kbt)) + 1.0d0)
    else if (nachar <= 4.6d-284) then
        tmp = (ndchar / (1.0d0 + exp((edonor / kbt)))) + (0.5d0 * nachar)
    else
        tmp = nachar / (exp((((eaccept + vef) - 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 tmp;
	if (NaChar <= -2.7e-45) {
		tmp = NaChar / (Math.exp((((Ev + Vef) - mu) / KbT)) + 1.0);
	} else if (NaChar <= 4.6e-284) {
		tmp = (NdChar / (1.0 + Math.exp((EDonor / KbT)))) + (0.5 * NaChar);
	} else {
		tmp = NaChar / (Math.exp((((EAccept + Vef) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if NaChar <= -2.7e-45:
		tmp = NaChar / (math.exp((((Ev + Vef) - mu) / KbT)) + 1.0)
	elif NaChar <= 4.6e-284:
		tmp = (NdChar / (1.0 + math.exp((EDonor / KbT)))) + (0.5 * NaChar)
	else:
		tmp = NaChar / (math.exp((((EAccept + Vef) - mu) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (NaChar <= -2.7e-45)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Ev + Vef) - mu) / KbT)) + 1.0));
	elseif (NaChar <= 4.6e-284)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(EDonor / KbT)))) + Float64(0.5 * NaChar));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Vef) - mu) / 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 (NaChar <= -2.7e-45)
		tmp = NaChar / (exp((((Ev + Vef) - mu) / KbT)) + 1.0);
	elseif (NaChar <= 4.6e-284)
		tmp = (NdChar / (1.0 + exp((EDonor / KbT)))) + (0.5 * NaChar);
	else
		tmp = NaChar / (exp((((EAccept + Vef) - mu) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[NaChar, -2.7e-45], N[(NaChar / N[(N[Exp[N[(N[(N[(Ev + Vef), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[NaChar, 4.6e-284], N[(N[(NdChar / N[(1.0 + N[Exp[N[(EDonor / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + Vef), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if NaChar < -2.69999999999999985e-45

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 67.5

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

   5. Applied rewrites 67.5%

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

   6. Taylor expanded in EAccept around 0

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

   8. Applied rewrites 58.5%

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

   if -2.69999999999999985e-45 < NaChar < 4.6e-284

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. lower-*.f64 75.3

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

   5. Applied rewrites 75.3%

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

   6. Taylor expanded in EDonor around inf

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

      1. lower-/.f64 56.3

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

   8. Applied rewrites 56.3%

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

   if 4.6e-284 < NaChar

   1. Initial program 100.0%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 68.8

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

   5. Applied rewrites 68.8%

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

   6. Taylor expanded in Ev around 0

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

   8. Applied rewrites 60.7%

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

Alternative 15: 61.9% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -4.5 \cdot 10^{+179}:\\ \;\;\;\;\frac{NdChar}{1 + e^{\frac{Vef}{KbT}}} + 0.5 \cdot NaChar\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -4.5e+179)
   (+ (/ NdChar (+ 1.0 (exp (/ Vef KbT)))) (* 0.5 NaChar))
   (/ NaChar (+ (exp (/ (- (+ (+ Ev 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 tmp;
	if (KbT <= -4.5e+179) {
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (0.5 * NaChar);
	} else {
		tmp = NaChar / (exp(((((Ev + Vef) + EAccept) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-4.5d+179)) then
        tmp = (ndchar / (1.0d0 + exp((vef / kbt)))) + (0.5d0 * nachar)
    else
        tmp = nachar / (exp(((((ev + 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 tmp;
	if (KbT <= -4.5e+179) {
		tmp = (NdChar / (1.0 + Math.exp((Vef / KbT)))) + (0.5 * NaChar);
	} else {
		tmp = NaChar / (Math.exp(((((Ev + Vef) + EAccept) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -4.5e+179:
		tmp = (NdChar / (1.0 + math.exp((Vef / KbT)))) + (0.5 * NaChar)
	else:
		tmp = NaChar / (math.exp(((((Ev + Vef) + EAccept) - mu) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -4.5e+179)
		tmp = Float64(Float64(NdChar / Float64(1.0 + exp(Float64(Vef / KbT)))) + Float64(0.5 * NaChar));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Float64(Ev + Vef) + EAccept) - mu) / 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 (KbT <= -4.5e+179)
		tmp = (NdChar / (1.0 + exp((Vef / KbT)))) + (0.5 * NaChar);
	else
		tmp = NaChar / (exp(((((Ev + Vef) + EAccept) - mu) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -4.5e+179], N[(N[(NdChar / N[(1.0 + N[Exp[N[(Vef / KbT), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(0.5 * NaChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(N[(N[(N[(Ev + Vef), $MachinePrecision] + EAccept), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -4.5000000000000003e179

   1. Initial program 100.0%

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

   3. Taylor expanded in KbT around inf

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

      1. lower-*.f64 91.9

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

   5. Applied rewrites 91.9%

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

   6. Taylor expanded in Vef around inf

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

      1. lower-/.f64 88.6

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

   8. Applied rewrites 88.6%

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

   if -4.5000000000000003e179 < 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 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. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 64.2

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

   5. Applied rewrites 64.2%

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

Alternative 16: 56.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;Ev \leq -1.35 \cdot 10^{+109}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Ev + Vef\right) - mu}{KbT}} + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(EAccept + Vef\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= Ev -1.35e+109)
   (/ NaChar (+ (exp (/ (- (+ Ev Vef) mu) KbT)) 1.0))
   (/ NaChar (+ (exp (/ (- (+ EAccept Vef) 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 tmp;
	if (Ev <= -1.35e+109) {
		tmp = NaChar / (exp((((Ev + Vef) - mu) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (exp((((EAccept + Vef) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (ev <= (-1.35d+109)) then
        tmp = nachar / (exp((((ev + vef) - mu) / kbt)) + 1.0d0)
    else
        tmp = nachar / (exp((((eaccept + vef) - 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 tmp;
	if (Ev <= -1.35e+109) {
		tmp = NaChar / (Math.exp((((Ev + Vef) - mu) / KbT)) + 1.0);
	} else {
		tmp = NaChar / (Math.exp((((EAccept + Vef) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if Ev <= -1.35e+109:
		tmp = NaChar / (math.exp((((Ev + Vef) - mu) / KbT)) + 1.0)
	else:
		tmp = NaChar / (math.exp((((EAccept + Vef) - mu) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (Ev <= -1.35e+109)
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Ev + Vef) - mu) / KbT)) + 1.0));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(EAccept + Vef) - mu) / KbT)) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if (Ev <= -1.35e+109)
		tmp = NaChar / (exp((((Ev + Vef) - mu) / KbT)) + 1.0);
	else
		tmp = NaChar / (exp((((EAccept + Vef) - mu) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[Ev, -1.35e+109], N[(NaChar / N[(N[Exp[N[(N[(N[(Ev + Vef), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(N[(N[(EAccept + Vef), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if Ev < -1.35000000000000001e109

   1. Initial program 100.0%

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

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 54.8

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

   5. Applied rewrites 54.8%

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

   6. Taylor expanded in EAccept around 0

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

   8. Applied rewrites 50.5%

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

   if -1.35000000000000001e109 < Ev

   1. Initial program 100.0%

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

   3. Taylor expanded in 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. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 63.4

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

   5. Applied rewrites 63.4%

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

   6. Taylor expanded in Ev around 0

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

   8. Applied rewrites 58.1%

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

Alternative 17: 55.4% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;KbT \leq -4.5 \cdot 10^{+179}:\\ \;\;\;\;0.5 \cdot \left(NaChar + NdChar\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{NaChar}{e^{\frac{\left(Ev + Vef\right) - mu}{KbT}} + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (<= KbT -4.5e+179)
   (* 0.5 (+ NaChar NdChar))
   (/ NaChar (+ (exp (/ (- (+ Ev Vef) 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 tmp;
	if (KbT <= -4.5e+179) {
		tmp = 0.5 * (NaChar + NdChar);
	} else {
		tmp = NaChar / (exp((((Ev + Vef) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if (kbt <= (-4.5d+179)) then
        tmp = 0.5d0 * (nachar + ndchar)
    else
        tmp = nachar / (exp((((ev + vef) - 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 tmp;
	if (KbT <= -4.5e+179) {
		tmp = 0.5 * (NaChar + NdChar);
	} else {
		tmp = NaChar / (Math.exp((((Ev + Vef) - mu) / KbT)) + 1.0);
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if KbT <= -4.5e+179:
		tmp = 0.5 * (NaChar + NdChar)
	else:
		tmp = NaChar / (math.exp((((Ev + Vef) - mu) / KbT)) + 1.0)
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if (KbT <= -4.5e+179)
		tmp = Float64(0.5 * Float64(NaChar + NdChar));
	else
		tmp = Float64(NaChar / Float64(exp(Float64(Float64(Float64(Ev + Vef) - mu) / 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 (KbT <= -4.5e+179)
		tmp = 0.5 * (NaChar + NdChar);
	else
		tmp = NaChar / (exp((((Ev + Vef) - mu) / KbT)) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[LessEqual[KbT, -4.5e+179], N[(0.5 * N[(NaChar + NdChar), $MachinePrecision]), $MachinePrecision], N[(NaChar / N[(N[Exp[N[(N[(N[(Ev + Vef), $MachinePrecision] - mu), $MachinePrecision] / KbT), $MachinePrecision]], $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if KbT < -4.5000000000000003e179

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   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. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 81.0

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

   5. Applied rewrites 81.0%

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

   if -4.5000000000000003e179 < 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 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. +-commutative N/A

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

      3. lower-+.f64 N/A

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

      4. lower-exp.f64 N/A

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

      5. lower-/.f64 N/A

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

      6. lower--.f64 N/A

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

      7. +-commutative N/A

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

      8. lower-+.f64 N/A

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

      9. lower-+.f64 64.2

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

   5. Applied rewrites 64.2%

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

   6. Taylor expanded in EAccept around 0

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

   8. Applied rewrites 57.6%

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

Alternative 18: 23.1% accurate, 15.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;NdChar \leq -5.5 \cdot 10^{-126} \lor \neg \left(NdChar \leq 4.5 \cdot 10^{+47}\right):\\ \;\;\;\;0.5 \cdot NdChar\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NaChar\\ \end{array} \end{array} \]

FPCore

(FPCore (NdChar Ec Vef EDonor mu KbT NaChar Ev EAccept)
 :precision binary64
 (if (or (<= NdChar -5.5e-126) (not (<= NdChar 4.5e+47)))
   (* 0.5 NdChar)
   (* 0.5 NaChar)))

C

double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -5.5e-126) || !(NdChar <= 4.5e+47)) {
		tmp = 0.5 * NdChar;
	} else {
		tmp = 0.5 * NaChar;
	}
	return tmp;
}

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

real(8) function code(ndchar, ec, vef, edonor, mu, kbt, nachar, ev, eaccept)
use fmin_fmax_functions
    real(8), intent (in) :: ndchar
    real(8), intent (in) :: ec
    real(8), intent (in) :: vef
    real(8), intent (in) :: edonor
    real(8), intent (in) :: mu
    real(8), intent (in) :: kbt
    real(8), intent (in) :: nachar
    real(8), intent (in) :: ev
    real(8), intent (in) :: eaccept
    real(8) :: tmp
    if ((ndchar <= (-5.5d-126)) .or. (.not. (ndchar <= 4.5d+47))) then
        tmp = 0.5d0 * ndchar
    else
        tmp = 0.5d0 * nachar
    end if
    code = tmp
end function

Java

public static double code(double NdChar, double Ec, double Vef, double EDonor, double mu, double KbT, double NaChar, double Ev, double EAccept) {
	double tmp;
	if ((NdChar <= -5.5e-126) || !(NdChar <= 4.5e+47)) {
		tmp = 0.5 * NdChar;
	} else {
		tmp = 0.5 * NaChar;
	}
	return tmp;
}

Python

def code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept):
	tmp = 0
	if (NdChar <= -5.5e-126) or not (NdChar <= 4.5e+47):
		tmp = 0.5 * NdChar
	else:
		tmp = 0.5 * NaChar
	return tmp

Julia

function code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0
	if ((NdChar <= -5.5e-126) || !(NdChar <= 4.5e+47))
		tmp = Float64(0.5 * NdChar);
	else
		tmp = Float64(0.5 * NaChar);
	end
	return tmp
end

MATLAB

function tmp_2 = code(NdChar, Ec, Vef, EDonor, mu, KbT, NaChar, Ev, EAccept)
	tmp = 0.0;
	if ((NdChar <= -5.5e-126) || ~((NdChar <= 4.5e+47)))
		tmp = 0.5 * NdChar;
	else
		tmp = 0.5 * NaChar;
	end
	tmp_2 = tmp;
end

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := If[Or[LessEqual[NdChar, -5.5e-126], N[Not[LessEqual[NdChar, 4.5e+47]], $MachinePrecision]], N[(0.5 * NdChar), $MachinePrecision], N[(0.5 * NaChar), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if NdChar < -5.49999999999999987e-126 or 4.49999999999999979e47 < 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 KbT around inf

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

      1. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 23.6

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

   5. Applied rewrites 23.6%

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

   6. Taylor expanded in NdChar around inf

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

   8. Applied rewrites 22.3%

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

   if -5.49999999999999987e-126 < NdChar < 4.49999999999999979e47

   1. Initial program 100.0%

      \[\frac{NdChar}{1 + e^{\frac{-\left(\left(\left(Ec - Vef\right) - EDonor\right) - mu\right)}{KbT}}} + \frac{NaChar}{1 + e^{\frac{\left(\left(Ev + Vef\right) + EAccept\right) + \left(-mu\right)}{KbT}}} \]
   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. distribute-lft-out N/A

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

      2. lower-*.f64 N/A

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

      3. lower-+.f64 33.8

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

   5. Applied rewrites 33.8%

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

   6. Taylor expanded in NdChar around 0

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

   8. Applied rewrites 30.5%

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

4. Final simplification 26.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;NdChar \leq -5.5 \cdot 10^{-126} \lor \neg \left(NdChar \leq 4.5 \cdot 10^{+47}\right):\\ \;\;\;\;0.5 \cdot NdChar\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot NaChar\\ \end{array} \]
5. Add Preprocessing

Alternative 19: 28.6% accurate, 30.7× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[NdChar_, Ec_, Vef_, EDonor_, mu_, KbT_, NaChar_, Ev_, EAccept_] := N[(0.5 * N[(NaChar + NdChar), $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. distribute-lft-out N/A

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

   2. lower-*.f64 N/A

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

   3. lower-+.f64 28.6

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

5. Applied rewrites 28.6%

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

Alternative 20: 18.7% accurate, 46.0× speedup

Math

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

FPCore

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

C

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

Fortran

module fmin_fmax_functions
    implicit none
    private
    public fmax
    public fmin

    interface fmax
        module procedure fmax88
        module procedure fmax44
        module procedure fmax84
        module procedure fmax48
    end interface
    interface fmin
        module procedure fmin88
        module procedure fmin44
        module procedure fmin84
        module procedure fmin48
    end interface
contains
    real(8) function fmax88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(4) function fmax44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, max(x, y), y /= y), x /= x)
    end function
    real(8) function fmax84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, max(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmax48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), max(dble(x), y), y /= y), x /= x)
    end function
    real(8) function fmin88(x, y) result (res)
        real(8), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(4) function fmin44(x, y) result (res)
        real(4), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(y, merge(x, min(x, y), y /= y), x /= x)
    end function
    real(8) function fmin84(x, y) result(res)
        real(8), intent (in) :: x
        real(4), intent (in) :: y
        res = merge(dble(y), merge(x, min(x, dble(y)), y /= y), x /= x)
    end function
    real(8) function fmin48(x, y) result(res)
        real(4), intent (in) :: x
        real(8), intent (in) :: y
        res = merge(y, merge(dble(x), min(dble(x), y), y /= y), x /= x)
    end function
end module

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in KbT around inf

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

   1. distribute-lft-out N/A

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

   2. lower-*.f64 N/A

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

   3. lower-+.f64 28.6

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

5. Applied rewrites 28.6%

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

6. Taylor expanded in NdChar around 0

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

8. Applied rewrites 19.2%

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

Reproduce

herbie shell --seed 2025017 
(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))))))