Harley's example

Percentage Accurate: 91.0% → 95.9%

Time: 2.3min

Alternatives: 5

Speedup: 835.0×

• could not determine a ground truth

  1. c_p = 2.00000000000000007e154
  2. c_n = 2
  3. t = 0.0
  4. s = 0.0

Specification

\[0 < c\_p \land 0 < c\_n\]

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{1 + e^{-t}}\\ t_2 := \frac{1}{1 + e^{-s}}\\ \frac{{t\_2}^{c\_p} \cdot {\left(1 - t\_2\right)}^{c\_n}}{{t\_1}^{c\_p} \cdot {\left(1 - t\_1\right)}^{c\_n}} \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (let* ((t_1 (/ 1.0 (+ 1.0 (exp (- t))))) (t_2 (/ 1.0 (+ 1.0 (exp (- s))))))
   (/
    (* (pow t_2 c_p) (pow (- 1.0 t_2) c_n))
    (* (pow t_1 c_p) (pow (- 1.0 t_1) c_n)))))

C

double code(double c_p, double c_n, double t, double s) {
	double t_1 = 1.0 / (1.0 + exp(-t));
	double t_2 = 1.0 / (1.0 + exp(-s));
	return (pow(t_2, c_p) * pow((1.0 - t_2), c_n)) / (pow(t_1, c_p) * pow((1.0 - t_1), c_n));
}

Fortran

real(8) function code(c_p, c_n, t, s)
    real(8), intent (in) :: c_p
    real(8), intent (in) :: c_n
    real(8), intent (in) :: t
    real(8), intent (in) :: s
    real(8) :: t_1
    real(8) :: t_2
    t_1 = 1.0d0 / (1.0d0 + exp(-t))
    t_2 = 1.0d0 / (1.0d0 + exp(-s))
    code = ((t_2 ** c_p) * ((1.0d0 - t_2) ** c_n)) / ((t_1 ** c_p) * ((1.0d0 - t_1) ** c_n))
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	double t_1 = 1.0 / (1.0 + Math.exp(-t));
	double t_2 = 1.0 / (1.0 + Math.exp(-s));
	return (Math.pow(t_2, c_p) * Math.pow((1.0 - t_2), c_n)) / (Math.pow(t_1, c_p) * Math.pow((1.0 - t_1), c_n));
}

Python

def code(c_p, c_n, t, s):
	t_1 = 1.0 / (1.0 + math.exp(-t))
	t_2 = 1.0 / (1.0 + math.exp(-s))
	return (math.pow(t_2, c_p) * math.pow((1.0 - t_2), c_n)) / (math.pow(t_1, c_p) * math.pow((1.0 - t_1), c_n))

Julia

function code(c_p, c_n, t, s)
	t_1 = Float64(1.0 / Float64(1.0 + exp(Float64(-t))))
	t_2 = Float64(1.0 / Float64(1.0 + exp(Float64(-s))))
	return Float64(Float64((t_2 ^ c_p) * (Float64(1.0 - t_2) ^ c_n)) / Float64((t_1 ^ c_p) * (Float64(1.0 - t_1) ^ c_n)))
end

MATLAB

function tmp = code(c_p, c_n, t, s)
	t_1 = 1.0 / (1.0 + exp(-t));
	t_2 = 1.0 / (1.0 + exp(-s));
	tmp = ((t_2 ^ c_p) * ((1.0 - t_2) ^ c_n)) / ((t_1 ^ c_p) * ((1.0 - t_1) ^ c_n));
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := Block[{t$95$1 = N[(1.0 / N[(1.0 + N[Exp[(-t)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(1.0 + N[Exp[(-s)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[Power[t$95$2, c$95$p], $MachinePrecision] * N[Power[N[(1.0 - t$95$2), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision] / N[(N[Power[t$95$1, c$95$p], $MachinePrecision] * N[Power[N[(1.0 - t$95$1), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Initial Program: 91.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{1}{1 + e^{-t}}\\ t_2 := \frac{1}{1 + e^{-s}}\\ \frac{{t\_2}^{c\_p} \cdot {\left(1 - t\_2\right)}^{c\_n}}{{t\_1}^{c\_p} \cdot {\left(1 - t\_1\right)}^{c\_n}} \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (let* ((t_1 (/ 1.0 (+ 1.0 (exp (- t))))) (t_2 (/ 1.0 (+ 1.0 (exp (- s))))))
   (/
    (* (pow t_2 c_p) (pow (- 1.0 t_2) c_n))
    (* (pow t_1 c_p) (pow (- 1.0 t_1) c_n)))))

C

double code(double c_p, double c_n, double t, double s) {
	double t_1 = 1.0 / (1.0 + exp(-t));
	double t_2 = 1.0 / (1.0 + exp(-s));
	return (pow(t_2, c_p) * pow((1.0 - t_2), c_n)) / (pow(t_1, c_p) * pow((1.0 - t_1), c_n));
}

Fortran

real(8) function code(c_p, c_n, t, s)
    real(8), intent (in) :: c_p
    real(8), intent (in) :: c_n
    real(8), intent (in) :: t
    real(8), intent (in) :: s
    real(8) :: t_1
    real(8) :: t_2
    t_1 = 1.0d0 / (1.0d0 + exp(-t))
    t_2 = 1.0d0 / (1.0d0 + exp(-s))
    code = ((t_2 ** c_p) * ((1.0d0 - t_2) ** c_n)) / ((t_1 ** c_p) * ((1.0d0 - t_1) ** c_n))
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	double t_1 = 1.0 / (1.0 + Math.exp(-t));
	double t_2 = 1.0 / (1.0 + Math.exp(-s));
	return (Math.pow(t_2, c_p) * Math.pow((1.0 - t_2), c_n)) / (Math.pow(t_1, c_p) * Math.pow((1.0 - t_1), c_n));
}

Python

def code(c_p, c_n, t, s):
	t_1 = 1.0 / (1.0 + math.exp(-t))
	t_2 = 1.0 / (1.0 + math.exp(-s))
	return (math.pow(t_2, c_p) * math.pow((1.0 - t_2), c_n)) / (math.pow(t_1, c_p) * math.pow((1.0 - t_1), c_n))

Julia

function code(c_p, c_n, t, s)
	t_1 = Float64(1.0 / Float64(1.0 + exp(Float64(-t))))
	t_2 = Float64(1.0 / Float64(1.0 + exp(Float64(-s))))
	return Float64(Float64((t_2 ^ c_p) * (Float64(1.0 - t_2) ^ c_n)) / Float64((t_1 ^ c_p) * (Float64(1.0 - t_1) ^ c_n)))
end

MATLAB

function tmp = code(c_p, c_n, t, s)
	t_1 = 1.0 / (1.0 + exp(-t));
	t_2 = 1.0 / (1.0 + exp(-s));
	tmp = ((t_2 ^ c_p) * ((1.0 - t_2) ^ c_n)) / ((t_1 ^ c_p) * ((1.0 - t_1) ^ c_n));
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := Block[{t$95$1 = N[(1.0 / N[(1.0 + N[Exp[(-t)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(1.0 / N[(1.0 + N[Exp[(-s)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[Power[t$95$2, c$95$p], $MachinePrecision] * N[Power[N[(1.0 - t$95$2), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision] / N[(N[Power[t$95$1, c$95$p], $MachinePrecision] * N[Power[N[(1.0 - t$95$1), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Alternative 1: 95.9% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-s}\\ \mathbf{if}\;c\_n \leq 1000:\\ \;\;\;\;\frac{{\left(1 + \frac{1}{-1 - t\_1}\right)}^{c\_n}}{{0.5}^{c\_n} + t \cdot \left(-0.5 \cdot \left(c\_n \cdot {0.5}^{c\_n}\right) + t \cdot \left(t \cdot \left({0.5}^{c\_n} \cdot \left(-0.020833333333333332 \cdot {c\_n}^{3} + 0.0625 \cdot {c\_n}^{2}\right)\right) + {0.5}^{c\_n} \cdot \left(c\_n \cdot -0.125 + {c\_n}^{2} \cdot 0.125\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + t\_1}\right)}^{c\_p}}{1 - c\_p \cdot \mathsf{log1p}\left(e^{-t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (let* ((t_1 (exp (- s))))
   (if (<= c_n 1000.0)
     (/
      (pow (+ 1.0 (/ 1.0 (- -1.0 t_1))) c_n)
      (+
       (pow 0.5 c_n)
       (*
        t
        (+
         (* -0.5 (* c_n (pow 0.5 c_n)))
         (*
          t
          (+
           (*
            t
            (*
             (pow 0.5 c_n)
             (+
              (* -0.020833333333333332 (pow c_n 3.0))
              (* 0.0625 (pow c_n 2.0)))))
           (* (pow 0.5 c_n) (+ (* c_n -0.125) (* (pow c_n 2.0) 0.125)))))))))
     (/ (pow (/ 1.0 (+ 1.0 t_1)) c_p) (- 1.0 (* c_p (log1p (exp (- t)))))))))

C

double code(double c_p, double c_n, double t, double s) {
	double t_1 = exp(-s);
	double tmp;
	if (c_n <= 1000.0) {
		tmp = pow((1.0 + (1.0 / (-1.0 - t_1))), c_n) / (pow(0.5, c_n) + (t * ((-0.5 * (c_n * pow(0.5, c_n))) + (t * ((t * (pow(0.5, c_n) * ((-0.020833333333333332 * pow(c_n, 3.0)) + (0.0625 * pow(c_n, 2.0))))) + (pow(0.5, c_n) * ((c_n * -0.125) + (pow(c_n, 2.0) * 0.125))))))));
	} else {
		tmp = pow((1.0 / (1.0 + t_1)), c_p) / (1.0 - (c_p * log1p(exp(-t))));
	}
	return tmp;
}

Java

public static double code(double c_p, double c_n, double t, double s) {
	double t_1 = Math.exp(-s);
	double tmp;
	if (c_n <= 1000.0) {
		tmp = Math.pow((1.0 + (1.0 / (-1.0 - t_1))), c_n) / (Math.pow(0.5, c_n) + (t * ((-0.5 * (c_n * Math.pow(0.5, c_n))) + (t * ((t * (Math.pow(0.5, c_n) * ((-0.020833333333333332 * Math.pow(c_n, 3.0)) + (0.0625 * Math.pow(c_n, 2.0))))) + (Math.pow(0.5, c_n) * ((c_n * -0.125) + (Math.pow(c_n, 2.0) * 0.125))))))));
	} else {
		tmp = Math.pow((1.0 / (1.0 + t_1)), c_p) / (1.0 - (c_p * Math.log1p(Math.exp(-t))));
	}
	return tmp;
}

Python

def code(c_p, c_n, t, s):
	t_1 = math.exp(-s)
	tmp = 0
	if c_n <= 1000.0:
		tmp = math.pow((1.0 + (1.0 / (-1.0 - t_1))), c_n) / (math.pow(0.5, c_n) + (t * ((-0.5 * (c_n * math.pow(0.5, c_n))) + (t * ((t * (math.pow(0.5, c_n) * ((-0.020833333333333332 * math.pow(c_n, 3.0)) + (0.0625 * math.pow(c_n, 2.0))))) + (math.pow(0.5, c_n) * ((c_n * -0.125) + (math.pow(c_n, 2.0) * 0.125))))))))
	else:
		tmp = math.pow((1.0 / (1.0 + t_1)), c_p) / (1.0 - (c_p * math.log1p(math.exp(-t))))
	return tmp

Julia

function code(c_p, c_n, t, s)
	t_1 = exp(Float64(-s))
	tmp = 0.0
	if (c_n <= 1000.0)
		tmp = Float64((Float64(1.0 + Float64(1.0 / Float64(-1.0 - t_1))) ^ c_n) / Float64((0.5 ^ c_n) + Float64(t * Float64(Float64(-0.5 * Float64(c_n * (0.5 ^ c_n))) + Float64(t * Float64(Float64(t * Float64((0.5 ^ c_n) * Float64(Float64(-0.020833333333333332 * (c_n ^ 3.0)) + Float64(0.0625 * (c_n ^ 2.0))))) + Float64((0.5 ^ c_n) * Float64(Float64(c_n * -0.125) + Float64((c_n ^ 2.0) * 0.125)))))))));
	else
		tmp = Float64((Float64(1.0 / Float64(1.0 + t_1)) ^ c_p) / Float64(1.0 - Float64(c_p * log1p(exp(Float64(-t))))));
	end
	return tmp
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := Block[{t$95$1 = N[Exp[(-s)], $MachinePrecision]}, If[LessEqual[c$95$n, 1000.0], N[(N[Power[N[(1.0 + N[(1.0 / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$n], $MachinePrecision] / N[(N[Power[0.5, c$95$n], $MachinePrecision] + N[(t * N[(N[(-0.5 * N[(c$95$n * N[Power[0.5, c$95$n], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(t * N[(N[(t * N[(N[Power[0.5, c$95$n], $MachinePrecision] * N[(N[(-0.020833333333333332 * N[Power[c$95$n, 3.0], $MachinePrecision]), $MachinePrecision] + N[(0.0625 * N[Power[c$95$n, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[Power[0.5, c$95$n], $MachinePrecision] * N[(N[(c$95$n * -0.125), $MachinePrecision] + N[(N[Power[c$95$n, 2.0], $MachinePrecision] * 0.125), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(1.0 / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision], c$95$p], $MachinePrecision] / N[(1.0 - N[(c$95$p * N[Log[1 + N[Exp[(-t)], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c_n < 1e3

   1. Initial program 95.9%

      \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}} \]
   2. Step-by-step derivation

      1. associate-/l* 95.9%

         \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]
   4. Add Preprocessing

   5. Taylor expanded in c_p around 0 98.0%

      \[\leadsto \color{blue}{\frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   6. Taylor expanded in t around 0 98.4%

      \[\leadsto \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{\color{blue}{t \cdot \left(-0.5 \cdot \left(c\_n \cdot {0.5}^{c\_n}\right) + t \cdot \left(t \cdot \left(\left(-0.020833333333333332 \cdot {c\_n}^{3} + 0.0625 \cdot {c\_n}^{2}\right) \cdot {0.5}^{c\_n}\right) + \left(-0.125 \cdot c\_n + 0.125 \cdot {c\_n}^{2}\right) \cdot {0.5}^{c\_n}\right)\right) + {0.5}^{c\_n}}} \]

   if 1e3 < c_n

   1. Initial program 0.0%

      \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}} \]
   2. Step-by-step derivation

      1. associate-/l* 0.0%

         \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   3. Simplified 0.0%

      \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]
   4. Add Preprocessing

   5. Taylor expanded in c_n around 0 51.2%

      \[\leadsto \color{blue}{\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p}}} \]

   6. Taylor expanded in c_p around 0 75.8%

      \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{\color{blue}{1 + c\_p \cdot \log \left(\frac{1}{1 + e^{-t}}\right)}} \]
   7. Step-by-step derivation

      1. log-rec 75.8%

         \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{1 + c\_p \cdot \color{blue}{\left(-\log \left(1 + e^{-t}\right)\right)}} \]

      2. log1p-undefine 75.8%

         \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{1 + c\_p \cdot \left(-\color{blue}{\mathsf{log1p}\left(e^{-t}\right)}\right)} \]

   8. Simplified 75.8%

      \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{\color{blue}{1 + c\_p \cdot \left(-\mathsf{log1p}\left(e^{-t}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c\_n \leq 1000:\\ \;\;\;\;\frac{{\left(1 + \frac{1}{-1 - e^{-s}}\right)}^{c\_n}}{{0.5}^{c\_n} + t \cdot \left(-0.5 \cdot \left(c\_n \cdot {0.5}^{c\_n}\right) + t \cdot \left(t \cdot \left({0.5}^{c\_n} \cdot \left(-0.020833333333333332 \cdot {c\_n}^{3} + 0.0625 \cdot {c\_n}^{2}\right)\right) + {0.5}^{c\_n} \cdot \left(c\_n \cdot -0.125 + {c\_n}^{2} \cdot 0.125\right)\right)\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{1 - c\_p \cdot \mathsf{log1p}\left(e^{-t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.6% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-s}\\ \mathbf{if}\;c\_n \leq 4.3:\\ \;\;\;\;\frac{{\left(1 + \frac{1}{-1 - t\_1}\right)}^{c\_n}}{{0.5}^{c\_n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + t\_1}\right)}^{c\_p}}{1 - c\_p \cdot \mathsf{log1p}\left(e^{-t}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (let* ((t_1 (exp (- s))))
   (if (<= c_n 4.3)
     (/ (pow (+ 1.0 (/ 1.0 (- -1.0 t_1))) c_n) (pow 0.5 c_n))
     (/ (pow (/ 1.0 (+ 1.0 t_1)) c_p) (- 1.0 (* c_p (log1p (exp (- t)))))))))

C

double code(double c_p, double c_n, double t, double s) {
	double t_1 = exp(-s);
	double tmp;
	if (c_n <= 4.3) {
		tmp = pow((1.0 + (1.0 / (-1.0 - t_1))), c_n) / pow(0.5, c_n);
	} else {
		tmp = pow((1.0 / (1.0 + t_1)), c_p) / (1.0 - (c_p * log1p(exp(-t))));
	}
	return tmp;
}

Java

public static double code(double c_p, double c_n, double t, double s) {
	double t_1 = Math.exp(-s);
	double tmp;
	if (c_n <= 4.3) {
		tmp = Math.pow((1.0 + (1.0 / (-1.0 - t_1))), c_n) / Math.pow(0.5, c_n);
	} else {
		tmp = Math.pow((1.0 / (1.0 + t_1)), c_p) / (1.0 - (c_p * Math.log1p(Math.exp(-t))));
	}
	return tmp;
}

Python

def code(c_p, c_n, t, s):
	t_1 = math.exp(-s)
	tmp = 0
	if c_n <= 4.3:
		tmp = math.pow((1.0 + (1.0 / (-1.0 - t_1))), c_n) / math.pow(0.5, c_n)
	else:
		tmp = math.pow((1.0 / (1.0 + t_1)), c_p) / (1.0 - (c_p * math.log1p(math.exp(-t))))
	return tmp

Julia

function code(c_p, c_n, t, s)
	t_1 = exp(Float64(-s))
	tmp = 0.0
	if (c_n <= 4.3)
		tmp = Float64((Float64(1.0 + Float64(1.0 / Float64(-1.0 - t_1))) ^ c_n) / (0.5 ^ c_n));
	else
		tmp = Float64((Float64(1.0 / Float64(1.0 + t_1)) ^ c_p) / Float64(1.0 - Float64(c_p * log1p(exp(Float64(-t))))));
	end
	return tmp
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := Block[{t$95$1 = N[Exp[(-s)], $MachinePrecision]}, If[LessEqual[c$95$n, 4.3], N[(N[Power[N[(1.0 + N[(1.0 / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$n], $MachinePrecision] / N[Power[0.5, c$95$n], $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(1.0 / N[(1.0 + t$95$1), $MachinePrecision]), $MachinePrecision], c$95$p], $MachinePrecision] / N[(1.0 - N[(c$95$p * N[Log[1 + N[Exp[(-t)], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if c_n < 4.29999999999999982

   1. Initial program 96.3%

      \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}} \]
   2. Step-by-step derivation

      1. associate-/l* 96.3%

         \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   3. Simplified 96.3%

      \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]
   4. Add Preprocessing

   5. Taylor expanded in c_p around 0 98.0%

      \[\leadsto \color{blue}{\frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   6. Taylor expanded in t around 0 98.4%

      \[\leadsto \color{blue}{\frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{0.5}^{c\_n}}} \]

   if 4.29999999999999982 < c_n

   1. Initial program 18.1%

      \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}} \]
   2. Step-by-step derivation

      1. associate-/l* 18.1%

         \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   3. Simplified 18.1%

      \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]
   4. Add Preprocessing

   5. Taylor expanded in c_n around 0 53.5%

      \[\leadsto \color{blue}{\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p}}} \]

   6. Taylor expanded in c_p around 0 78.1%

      \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{\color{blue}{1 + c\_p \cdot \log \left(\frac{1}{1 + e^{-t}}\right)}} \]
   7. Step-by-step derivation

      1. log-rec 78.1%

         \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{1 + c\_p \cdot \color{blue}{\left(-\log \left(1 + e^{-t}\right)\right)}} \]

      2. log1p-undefine 78.1%

         \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{1 + c\_p \cdot \left(-\color{blue}{\mathsf{log1p}\left(e^{-t}\right)}\right)} \]

   8. Simplified 78.1%

      \[\leadsto \frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{\color{blue}{1 + c\_p \cdot \left(-\mathsf{log1p}\left(e^{-t}\right)\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;c\_n \leq 4.3:\\ \;\;\;\;\frac{{\left(1 + \frac{1}{-1 - e^{-s}}\right)}^{c\_n}}{{0.5}^{c\_n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{1 - c\_p \cdot \mathsf{log1p}\left(e^{-t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 95.5% accurate, 3.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-t \leq 5 \cdot 10^{-42}:\\ \;\;\;\;1 + -0.5 \cdot \left(c\_n \cdot s\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{{0.5}^{c\_n}}{1 + c\_n \cdot \log 0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (if (<= (- t) 5e-42)
   (+ 1.0 (* -0.5 (* c_n s)))
   (/ (pow 0.5 c_n) (+ 1.0 (* c_n (log 0.5))))))

C

double code(double c_p, double c_n, double t, double s) {
	double tmp;
	if (-t <= 5e-42) {
		tmp = 1.0 + (-0.5 * (c_n * s));
	} else {
		tmp = pow(0.5, c_n) / (1.0 + (c_n * log(0.5)));
	}
	return tmp;
}

Fortran

real(8) function code(c_p, c_n, t, s)
    real(8), intent (in) :: c_p
    real(8), intent (in) :: c_n
    real(8), intent (in) :: t
    real(8), intent (in) :: s
    real(8) :: tmp
    if (-t <= 5d-42) then
        tmp = 1.0d0 + ((-0.5d0) * (c_n * s))
    else
        tmp = (0.5d0 ** c_n) / (1.0d0 + (c_n * log(0.5d0)))
    end if
    code = tmp
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	double tmp;
	if (-t <= 5e-42) {
		tmp = 1.0 + (-0.5 * (c_n * s));
	} else {
		tmp = Math.pow(0.5, c_n) / (1.0 + (c_n * Math.log(0.5)));
	}
	return tmp;
}

Python

def code(c_p, c_n, t, s):
	tmp = 0
	if -t <= 5e-42:
		tmp = 1.0 + (-0.5 * (c_n * s))
	else:
		tmp = math.pow(0.5, c_n) / (1.0 + (c_n * math.log(0.5)))
	return tmp

Julia

function code(c_p, c_n, t, s)
	tmp = 0.0
	if (Float64(-t) <= 5e-42)
		tmp = Float64(1.0 + Float64(-0.5 * Float64(c_n * s)));
	else
		tmp = Float64((0.5 ^ c_n) / Float64(1.0 + Float64(c_n * log(0.5))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c_p, c_n, t, s)
	tmp = 0.0;
	if (-t <= 5e-42)
		tmp = 1.0 + (-0.5 * (c_n * s));
	else
		tmp = (0.5 ^ c_n) / (1.0 + (c_n * log(0.5)));
	end
	tmp_2 = tmp;
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := If[LessEqual[(-t), 5e-42], N[(1.0 + N[(-0.5 * N[(c$95$n * s), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[0.5, c$95$n], $MachinePrecision] / N[(1.0 + N[(c$95$n * N[Log[0.5], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (neg.f64 t) < 5.00000000000000003e-42

   1. Initial program 93.9%

      \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}} \]
   2. Step-by-step derivation

      1. associate-/l* 93.9%

         \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   3. Simplified 93.9%

      \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]
   4. Add Preprocessing

   5. Taylor expanded in c_p around 0 95.2%

      \[\leadsto \color{blue}{\frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   6. Taylor expanded in t around 0 95.4%

      \[\leadsto \color{blue}{\frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{0.5}^{c\_n}}} \]

   7. Taylor expanded in s around 0 97.6%

      \[\leadsto \color{blue}{1 + -0.5 \cdot \left(c\_n \cdot s\right)} \]

   if 5.00000000000000003e-42 < (neg.f64 t)

   1. Initial program 70.4%

      \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}} \]
   2. Step-by-step derivation

      1. associate-/l* 70.4%

         \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   3. Simplified 70.4%

      \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]
   4. Add Preprocessing

   5. Taylor expanded in c_p around 0 89.3%

      \[\leadsto \color{blue}{\frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

   6. Taylor expanded in c_n around 0 93.1%

      \[\leadsto \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{\color{blue}{1 + c\_n \cdot \log \left(1 - \frac{1}{1 + e^{-t}}\right)}} \]
   7. Step-by-step derivation

      1. sub-neg 93.1%

         \[\leadsto \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{1 + c\_n \cdot \log \color{blue}{\left(1 + \left(-\frac{1}{1 + e^{-t}}\right)\right)}} \]

      2. log1p-undefine 93.1%

         \[\leadsto \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{1 + c\_n \cdot \color{blue}{\mathsf{log1p}\left(-\frac{1}{1 + e^{-t}}\right)}} \]

      3. distribute-neg-frac 93.1%

         \[\leadsto \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{1 + c\_n \cdot \mathsf{log1p}\left(\color{blue}{\frac{-1}{1 + e^{-t}}}\right)} \]

      4. metadata-eval 93.1%

         \[\leadsto \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{1 + c\_n \cdot \mathsf{log1p}\left(\frac{\color{blue}{-1}}{1 + e^{-t}}\right)} \]

   8. Simplified 93.1%

      \[\leadsto \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{\color{blue}{1 + c\_n \cdot \mathsf{log1p}\left(\frac{-1}{1 + e^{-t}}\right)}} \]

   9. Taylor expanded in s around 0 93.1%

      \[\leadsto \frac{\color{blue}{{0.5}^{c\_n}}}{1 + c\_n \cdot \mathsf{log1p}\left(\frac{-1}{1 + e^{-t}}\right)} \]

   10. Taylor expanded in t around 0 93.1%

       \[\leadsto \frac{{0.5}^{c\_n}}{1 + \color{blue}{c\_n \cdot \log 0.5}} \]
   11. Step-by-step derivation

       1. *-commutative 93.1%

          \[\leadsto \frac{{0.5}^{c\_n}}{1 + \color{blue}{\log 0.5 \cdot c\_n}} \]

   12. Simplified 93.1%

       \[\leadsto \frac{{0.5}^{c\_n}}{1 + \color{blue}{\log 0.5 \cdot c\_n}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-t \leq 5 \cdot 10^{-42}:\\ \;\;\;\;1 + -0.5 \cdot \left(c\_n \cdot s\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{{0.5}^{c\_n}}{1 + c\_n \cdot \log 0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.4% accurate, 119.3× speedup

Math

\[\begin{array}{l} \\ 1 + -0.5 \cdot \left(t \cdot c\_p\right) \end{array} \]

FPCore

(FPCore (c_p c_n t s) :precision binary64 (+ 1.0 (* -0.5 (* t c_p))))

C

double code(double c_p, double c_n, double t, double s) {
	return 1.0 + (-0.5 * (t * c_p));
}

Fortran

real(8) function code(c_p, c_n, t, s)
    real(8), intent (in) :: c_p
    real(8), intent (in) :: c_n
    real(8), intent (in) :: t
    real(8), intent (in) :: s
    code = 1.0d0 + ((-0.5d0) * (t * c_p))
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	return 1.0 + (-0.5 * (t * c_p));
}

Python

def code(c_p, c_n, t, s):
	return 1.0 + (-0.5 * (t * c_p))

Julia

function code(c_p, c_n, t, s)
	return Float64(1.0 + Float64(-0.5 * Float64(t * c_p)))
end

MATLAB

function tmp = code(c_p, c_n, t, s)
	tmp = 1.0 + (-0.5 * (t * c_p));
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := N[(1.0 + N[(-0.5 * N[(t * c$95$p), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.4%

   \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}} \]
2. Step-by-step derivation

   1. associate-/l* 91.4%

      \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

3. Simplified 91.4%

   \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]
4. Add Preprocessing

5. Taylor expanded in c_n around 0 94.0%

   \[\leadsto \color{blue}{\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p}}} \]

6. Taylor expanded in s around 0 92.9%

   \[\leadsto \color{blue}{\frac{{0.5}^{c\_p}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p}}} \]

7. Taylor expanded in t around 0 95.2%

   \[\leadsto \color{blue}{1 + -0.5 \cdot \left(c\_p \cdot t\right)} \]

8. Final simplification 95.2%

   \[\leadsto 1 + -0.5 \cdot \left(t \cdot c\_p\right) \]
9. Add Preprocessing

Alternative 5: 94.3% accurate, 835.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (c_p c_n t s) :precision binary64 1.0)

C

double code(double c_p, double c_n, double t, double s) {
	return 1.0;
}

Fortran

real(8) function code(c_p, c_n, t, s)
    real(8), intent (in) :: c_p
    real(8), intent (in) :: c_n
    real(8), intent (in) :: t
    real(8), intent (in) :: s
    code = 1.0d0
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	return 1.0;
}

Python

def code(c_p, c_n, t, s):
	return 1.0

Julia

function code(c_p, c_n, t, s)
	return 1.0
end

MATLAB

function tmp = code(c_p, c_n, t, s)
	tmp = 1.0;
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := 1.0

Derivation

1. Initial program 91.4%

   \[\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}} \]
2. Step-by-step derivation

   1. associate-/l* 91.4%

      \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

3. Simplified 91.4%

   \[\leadsto \color{blue}{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot \frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]
4. Add Preprocessing

5. Taylor expanded in c_p around 0 94.6%

   \[\leadsto \color{blue}{\frac{{\left(1 - \frac{1}{1 + e^{-s}}\right)}^{c\_n}}{{\left(1 - \frac{1}{1 + e^{-t}}\right)}^{c\_n}}} \]

6. Taylor expanded in c_n around 0 95.2%

   \[\leadsto \color{blue}{1} \]
7. Add Preprocessing

Developer Target 1: 96.5% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ {\left(\frac{1 + e^{-t}}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(\frac{1 + e^{t}}{1 + e^{s}}\right)}^{c\_n} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (*
  (pow (/ (+ 1.0 (exp (- t))) (+ 1.0 (exp (- s)))) c_p)
  (pow (/ (+ 1.0 (exp t)) (+ 1.0 (exp s))) c_n)))

C

double code(double c_p, double c_n, double t, double s) {
	return pow(((1.0 + exp(-t)) / (1.0 + exp(-s))), c_p) * pow(((1.0 + exp(t)) / (1.0 + exp(s))), c_n);
}

Fortran

real(8) function code(c_p, c_n, t, s)
    real(8), intent (in) :: c_p
    real(8), intent (in) :: c_n
    real(8), intent (in) :: t
    real(8), intent (in) :: s
    code = (((1.0d0 + exp(-t)) / (1.0d0 + exp(-s))) ** c_p) * (((1.0d0 + exp(t)) / (1.0d0 + exp(s))) ** c_n)
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	return Math.pow(((1.0 + Math.exp(-t)) / (1.0 + Math.exp(-s))), c_p) * Math.pow(((1.0 + Math.exp(t)) / (1.0 + Math.exp(s))), c_n);
}

Python

def code(c_p, c_n, t, s):
	return math.pow(((1.0 + math.exp(-t)) / (1.0 + math.exp(-s))), c_p) * math.pow(((1.0 + math.exp(t)) / (1.0 + math.exp(s))), c_n)

Julia

function code(c_p, c_n, t, s)
	return Float64((Float64(Float64(1.0 + exp(Float64(-t))) / Float64(1.0 + exp(Float64(-s)))) ^ c_p) * (Float64(Float64(1.0 + exp(t)) / Float64(1.0 + exp(s))) ^ c_n))
end

MATLAB

function tmp = code(c_p, c_n, t, s)
	tmp = (((1.0 + exp(-t)) / (1.0 + exp(-s))) ^ c_p) * (((1.0 + exp(t)) / (1.0 + exp(s))) ^ c_n);
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := N[(N[Power[N[(N[(1.0 + N[Exp[(-t)], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[Exp[(-s)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$p], $MachinePrecision] * N[Power[N[(N[(1.0 + N[Exp[t], $MachinePrecision]), $MachinePrecision] / N[(1.0 + N[Exp[s], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024158 
(FPCore (c_p c_n t s)
  :name "Harley's example"
  :precision binary64
  :pre (and (< 0.0 c_p) (< 0.0 c_n))

  :alt
  (! :herbie-platform default (* (pow (/ (+ 1 (exp (- t))) (+ 1 (exp (- s)))) c_p) (pow (/ (+ 1 (exp t)) (+ 1 (exp s))) c_n)))

  (/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n))))