Harley's example

Percentage Accurate: 91.2% → 96.0%

Time: 2.3min

Alternatives: 6

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: 91.2% 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: 96.0% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := e^{-t}\\ \mathbf{if}\;-s \leq 400000000:\\ \;\;\;\;\frac{{0.5}^{c\_n}}{{\left(1 + \frac{1}{-1 - t\_1}\right)}^{c\_n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{1 - c\_p \cdot \log \left(1 + t\_1\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (let* ((t_1 (exp (- t))))
   (if (<= (- s) 400000000.0)
     (/ (pow 0.5 c_n) (pow (+ 1.0 (/ 1.0 (- -1.0 t_1))) c_n))
     (/
      (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
      (- 1.0 (* c_p (log (+ 1.0 t_1))))))))

C

double code(double c_p, double c_n, double t, double s) {
	double t_1 = exp(-t);
	double tmp;
	if (-s <= 400000000.0) {
		tmp = pow(0.5, c_n) / pow((1.0 + (1.0 / (-1.0 - t_1))), c_n);
	} else {
		tmp = pow((1.0 / (1.0 + exp(-s))), c_p) / (1.0 - (c_p * log((1.0 + t_1))));
	}
	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) :: t_1
    real(8) :: tmp
    t_1 = exp(-t)
    if (-s <= 400000000.0d0) then
        tmp = (0.5d0 ** c_n) / ((1.0d0 + (1.0d0 / ((-1.0d0) - t_1))) ** c_n)
    else
        tmp = ((1.0d0 / (1.0d0 + exp(-s))) ** c_p) / (1.0d0 - (c_p * log((1.0d0 + t_1))))
    end if
    code = tmp
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	double t_1 = Math.exp(-t);
	double tmp;
	if (-s <= 400000000.0) {
		tmp = Math.pow(0.5, c_n) / Math.pow((1.0 + (1.0 / (-1.0 - t_1))), c_n);
	} else {
		tmp = Math.pow((1.0 / (1.0 + Math.exp(-s))), c_p) / (1.0 - (c_p * Math.log((1.0 + t_1))));
	}
	return tmp;
}

Python

def code(c_p, c_n, t, s):
	t_1 = math.exp(-t)
	tmp = 0
	if -s <= 400000000.0:
		tmp = math.pow(0.5, c_n) / math.pow((1.0 + (1.0 / (-1.0 - t_1))), c_n)
	else:
		tmp = math.pow((1.0 / (1.0 + math.exp(-s))), c_p) / (1.0 - (c_p * math.log((1.0 + t_1))))
	return tmp

Julia

function code(c_p, c_n, t, s)
	t_1 = exp(Float64(-t))
	tmp = 0.0
	if (Float64(-s) <= 400000000.0)
		tmp = Float64((0.5 ^ c_n) / (Float64(1.0 + Float64(1.0 / Float64(-1.0 - t_1))) ^ c_n));
	else
		tmp = Float64((Float64(1.0 / Float64(1.0 + exp(Float64(-s)))) ^ c_p) / Float64(1.0 - Float64(c_p * log(Float64(1.0 + t_1)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c_p, c_n, t, s)
	t_1 = exp(-t);
	tmp = 0.0;
	if (-s <= 400000000.0)
		tmp = (0.5 ^ c_n) / ((1.0 + (1.0 / (-1.0 - t_1))) ^ c_n);
	else
		tmp = ((1.0 / (1.0 + exp(-s))) ^ c_p) / (1.0 - (c_p * log((1.0 + t_1))));
	end
	tmp_2 = tmp;
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := Block[{t$95$1 = N[Exp[(-t)], $MachinePrecision]}, If[LessEqual[(-s), 400000000.0], N[(N[Power[0.5, c$95$n], $MachinePrecision] / N[Power[N[(1.0 + N[(1.0 / N[(-1.0 - t$95$1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(1.0 / N[(1.0 + N[Exp[(-s)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$p], $MachinePrecision] / N[(1.0 - N[(c$95$p * N[Log[N[(1.0 + t$95$1), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (neg.f64 s) < 4e8

   1. Initial program 92.4%

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

      1. associate-/l/ 92.4%

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

   3. Simplified 92.4%

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

   5. Taylor expanded in c_p around 0 98.4%

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

   6. Taylor expanded in s around 0 98.4%

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

   if 4e8 < (neg.f64 s)

   1. Initial program 62.5%

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

      1. associate-/l/ 62.5%

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

   3. Simplified 62.5%

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

   5. Taylor expanded in c_n around 0 62.5%

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

   6. Taylor expanded in c_p around 0 100.0%

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

      1. log-rec 100.0%

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

   8. Simplified 100.0%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-s \leq 400000000:\\ \;\;\;\;\frac{{0.5}^{c\_n}}{{\left(1 + \frac{1}{-1 - e^{-t}}\right)}^{c\_n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{1 - c\_p \cdot \log \left(1 + e^{-t}\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 95.0% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-s \leq 2 \cdot 10^{+43}:\\ \;\;\;\;\frac{{0.5}^{c\_n}}{{\left(1 + \frac{1}{-1 - e^{-t}}\right)}^{c\_n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{{0.5}^{c\_p}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (if (<= (- s) 2e+43)
   (/ (pow 0.5 c_n) (pow (+ 1.0 (/ 1.0 (- -1.0 (exp (- t))))) c_n))
   (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow 0.5 c_p))))

C

double code(double c_p, double c_n, double t, double s) {
	double tmp;
	if (-s <= 2e+43) {
		tmp = pow(0.5, c_n) / pow((1.0 + (1.0 / (-1.0 - exp(-t)))), c_n);
	} else {
		tmp = pow((1.0 / (1.0 + exp(-s))), c_p) / pow(0.5, c_p);
	}
	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 (-s <= 2d+43) then
        tmp = (0.5d0 ** c_n) / ((1.0d0 + (1.0d0 / ((-1.0d0) - exp(-t)))) ** c_n)
    else
        tmp = ((1.0d0 / (1.0d0 + exp(-s))) ** c_p) / (0.5d0 ** c_p)
    end if
    code = tmp
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	double tmp;
	if (-s <= 2e+43) {
		tmp = Math.pow(0.5, c_n) / Math.pow((1.0 + (1.0 / (-1.0 - Math.exp(-t)))), c_n);
	} else {
		tmp = Math.pow((1.0 / (1.0 + Math.exp(-s))), c_p) / Math.pow(0.5, c_p);
	}
	return tmp;
}

Python

def code(c_p, c_n, t, s):
	tmp = 0
	if -s <= 2e+43:
		tmp = math.pow(0.5, c_n) / math.pow((1.0 + (1.0 / (-1.0 - math.exp(-t)))), c_n)
	else:
		tmp = math.pow((1.0 / (1.0 + math.exp(-s))), c_p) / math.pow(0.5, c_p)
	return tmp

Julia

function code(c_p, c_n, t, s)
	tmp = 0.0
	if (Float64(-s) <= 2e+43)
		tmp = Float64((0.5 ^ c_n) / (Float64(1.0 + Float64(1.0 / Float64(-1.0 - exp(Float64(-t))))) ^ c_n));
	else
		tmp = Float64((Float64(1.0 / Float64(1.0 + exp(Float64(-s)))) ^ c_p) / (0.5 ^ c_p));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c_p, c_n, t, s)
	tmp = 0.0;
	if (-s <= 2e+43)
		tmp = (0.5 ^ c_n) / ((1.0 + (1.0 / (-1.0 - exp(-t)))) ^ c_n);
	else
		tmp = ((1.0 / (1.0 + exp(-s))) ^ c_p) / (0.5 ^ c_p);
	end
	tmp_2 = tmp;
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := If[LessEqual[(-s), 2e+43], N[(N[Power[0.5, c$95$n], $MachinePrecision] / N[Power[N[(1.0 + N[(1.0 / N[(-1.0 - N[Exp[(-t)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(1.0 / N[(1.0 + N[Exp[(-s)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$p], $MachinePrecision] / N[Power[0.5, c$95$p], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (neg.f64 s) < 2.00000000000000003e43

   1. Initial program 92.0%

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

      1. associate-/l/ 92.0%

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

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\frac{\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 + \frac{1}{-1 - e^{-s}}\right)}^{c\_n}}{{\left(1 + \frac{1}{-1 - e^{-t}}\right)}^{c\_n}}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p}}} \]
   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 s around 0 98.0%

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

   if 2.00000000000000003e43 < (neg.f64 s)

   1. Initial program 71.4%

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

      1. associate-/l/ 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in c_n around 0 71.4%

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

   6. Taylor expanded in t around 0 85.7%

      \[\leadsto \color{blue}{\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{{0.5}^{c\_p}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;-s \leq 2 \cdot 10^{+43}:\\ \;\;\;\;\frac{{0.5}^{c\_n}}{{\left(1 + \frac{1}{-1 - e^{-t}}\right)}^{c\_n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{{0.5}^{c\_p}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 94.7% accurate, 2.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;-s \leq 1.8 \cdot 10^{+43}:\\ \;\;\;\;\frac{{0.5}^{c\_n}}{{\left(0.5 + t \cdot -0.25\right)}^{c\_n}}\\ \mathbf{else}:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{{0.5}^{c\_p}}\\ \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (if (<= (- s) 1.8e+43)
   (/ (pow 0.5 c_n) (pow (+ 0.5 (* t -0.25)) c_n))
   (/ (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow 0.5 c_p))))

C

double code(double c_p, double c_n, double t, double s) {
	double tmp;
	if (-s <= 1.8e+43) {
		tmp = pow(0.5, c_n) / pow((0.5 + (t * -0.25)), c_n);
	} else {
		tmp = pow((1.0 / (1.0 + exp(-s))), c_p) / pow(0.5, c_p);
	}
	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 (-s <= 1.8d+43) then
        tmp = (0.5d0 ** c_n) / ((0.5d0 + (t * (-0.25d0))) ** c_n)
    else
        tmp = ((1.0d0 / (1.0d0 + exp(-s))) ** c_p) / (0.5d0 ** c_p)
    end if
    code = tmp
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	double tmp;
	if (-s <= 1.8e+43) {
		tmp = Math.pow(0.5, c_n) / Math.pow((0.5 + (t * -0.25)), c_n);
	} else {
		tmp = Math.pow((1.0 / (1.0 + Math.exp(-s))), c_p) / Math.pow(0.5, c_p);
	}
	return tmp;
}

Python

def code(c_p, c_n, t, s):
	tmp = 0
	if -s <= 1.8e+43:
		tmp = math.pow(0.5, c_n) / math.pow((0.5 + (t * -0.25)), c_n)
	else:
		tmp = math.pow((1.0 / (1.0 + math.exp(-s))), c_p) / math.pow(0.5, c_p)
	return tmp

Julia

function code(c_p, c_n, t, s)
	tmp = 0.0
	if (Float64(-s) <= 1.8e+43)
		tmp = Float64((0.5 ^ c_n) / (Float64(0.5 + Float64(t * -0.25)) ^ c_n));
	else
		tmp = Float64((Float64(1.0 / Float64(1.0 + exp(Float64(-s)))) ^ c_p) / (0.5 ^ c_p));
	end
	return tmp
end

MATLAB

function tmp_2 = code(c_p, c_n, t, s)
	tmp = 0.0;
	if (-s <= 1.8e+43)
		tmp = (0.5 ^ c_n) / ((0.5 + (t * -0.25)) ^ c_n);
	else
		tmp = ((1.0 / (1.0 + exp(-s))) ^ c_p) / (0.5 ^ c_p);
	end
	tmp_2 = tmp;
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := If[LessEqual[(-s), 1.8e+43], N[(N[Power[0.5, c$95$n], $MachinePrecision] / N[Power[N[(0.5 + N[(t * -0.25), $MachinePrecision]), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(1.0 / N[(1.0 + N[Exp[(-s)], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$p], $MachinePrecision] / N[Power[0.5, c$95$p], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (neg.f64 s) < 1.80000000000000005e43

   1. Initial program 92.0%

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

      1. associate-/l/ 92.0%

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

   3. Simplified 92.0%

      \[\leadsto \color{blue}{\frac{\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 + \frac{1}{-1 - e^{-s}}\right)}^{c\_n}}{{\left(1 + \frac{1}{-1 - e^{-t}}\right)}^{c\_n}}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p}}} \]
   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 s around 0 98.0%

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

   7. Taylor expanded in t around 0 98.0%

      \[\leadsto \frac{{0.5}^{c\_n}}{{\color{blue}{\left(0.5 + -0.25 \cdot t\right)}}^{c\_n}} \]
   8. Step-by-step derivation

      1. *-commutative 98.0%

         \[\leadsto \frac{{0.5}^{c\_n}}{{\left(0.5 + \color{blue}{t \cdot -0.25}\right)}^{c\_n}} \]

   9. Simplified 98.0%

      \[\leadsto \frac{{0.5}^{c\_n}}{{\color{blue}{\left(0.5 + t \cdot -0.25\right)}}^{c\_n}} \]

   if 1.80000000000000005e43 < (neg.f64 s)

   1. Initial program 71.4%

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

      1. associate-/l/ 71.4%

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

   3. Simplified 71.4%

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

   5. Taylor expanded in c_n around 0 71.4%

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

   6. Taylor expanded in t around 0 85.7%

      \[\leadsto \color{blue}{\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p}}{{0.5}^{c\_p}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 93.5% accurate, 4.0× speedup

Math

\[\begin{array}{l} \\ \frac{{0.5}^{c\_n}}{{\left(0.5 + t \cdot -0.25\right)}^{c\_n}} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (/ (pow 0.5 c_n) (pow (+ 0.5 (* t -0.25)) c_n)))

C

double code(double c_p, double c_n, double t, double s) {
	return pow(0.5, c_n) / pow((0.5 + (t * -0.25)), 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 = (0.5d0 ** c_n) / ((0.5d0 + (t * (-0.25d0))) ** c_n)
end function

Java

public static double code(double c_p, double c_n, double t, double s) {
	return Math.pow(0.5, c_n) / Math.pow((0.5 + (t * -0.25)), c_n);
}

Python

def code(c_p, c_n, t, s):
	return math.pow(0.5, c_n) / math.pow((0.5 + (t * -0.25)), c_n)

Julia

function code(c_p, c_n, t, s)
	return Float64((0.5 ^ c_n) / (Float64(0.5 + Float64(t * -0.25)) ^ c_n))
end

MATLAB

function tmp = code(c_p, c_n, t, s)
	tmp = (0.5 ^ c_n) / ((0.5 + (t * -0.25)) ^ c_n);
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := N[(N[Power[0.5, c$95$n], $MachinePrecision] / N[Power[N[(0.5 + N[(t * -0.25), $MachinePrecision]), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 91.5%

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

   1. associate-/l/ 91.5%

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

3. Simplified 91.5%

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

5. Taylor expanded in c_p around 0 95.4%

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

6. Taylor expanded in s around 0 95.4%

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

7. Taylor expanded in t around 0 95.4%

   \[\leadsto \frac{{0.5}^{c\_n}}{{\color{blue}{\left(0.5 + -0.25 \cdot t\right)}}^{c\_n}} \]
8. Step-by-step derivation

   1. *-commutative 95.4%

      \[\leadsto \frac{{0.5}^{c\_n}}{{\left(0.5 + \color{blue}{t \cdot -0.25}\right)}^{c\_n}} \]

9. Simplified 95.4%

   \[\leadsto \frac{{0.5}^{c\_n}}{{\color{blue}{\left(0.5 + t \cdot -0.25\right)}}^{c\_n}} \]
10. Add Preprocessing

Alternative 5: 94.3% accurate, 119.3× speedup

Math

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

FPCore

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

C

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

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 * (c_n * t))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 91.5%

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

   1. associate-/l/ 91.5%

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

3. Simplified 91.5%

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

5. Taylor expanded in c_p around 0 95.4%

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

6. Taylor expanded in s around 0 95.4%

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

7. Taylor expanded in t around 0 94.6%

   \[\leadsto \color{blue}{1 + 0.5 \cdot \left(c\_n \cdot t\right)} \]
8. Add Preprocessing

Alternative 6: 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 91.5%

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

   1. associate-/l/ 91.5%

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

3. Simplified 91.5%

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

5. Taylor expanded in c_p around 0 95.4%

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

6. Taylor expanded in c_n around 0 94.6%

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

Developer Target 1: 96.2% 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 2024136 
(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))))