Harley's example

Percentage Accurate: 90.9% → 95.5%

Time: 49.5s

Alternatives: 5

Speedup: 896.0×

• could not determine a ground truth

  1. c_p = 7.155249106866654e-237
  2. c_n = 1.4982820521974867e-58
  3. t = -1.7870816223005282e-246
  4. s = 9.398080861887953e+159

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: 90.9% 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: 95.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right)\\ t_2 := e^{-t}\\ t_3 := e^{-s}\\ t_4 := \frac{{\left(\frac{1}{1 + t\_3}\right)}^{c\_p} \cdot {\left(1 + \frac{1}{-1 - t\_3}\right)}^{c\_n}}{{\left(\frac{1}{1 + t\_2}\right)}^{c\_p} \cdot {\left(1 + \frac{1}{-1 - t\_2}\right)}^{c\_n}}\\ \mathbf{if}\;t\_4 \leq 2:\\ \;\;\;\;t\_4\\ \mathbf{else}:\\ \;\;\;\;{\left(t\_1 \cdot t\_1\right)}^{\left(-c\_p \cdot 0.5\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (let* ((t_1 (fma s (fma s (fma s -0.16666666666666666 0.5) -1.0) 2.0))
        (t_2 (exp (- t)))
        (t_3 (exp (- s)))
        (t_4
         (/
          (*
           (pow (/ 1.0 (+ 1.0 t_3)) c_p)
           (pow (+ 1.0 (/ 1.0 (- -1.0 t_3))) c_n))
          (*
           (pow (/ 1.0 (+ 1.0 t_2)) c_p)
           (pow (+ 1.0 (/ 1.0 (- -1.0 t_2))) c_n)))))
   (if (<= t_4 2.0) t_4 (pow (* t_1 t_1) (- (* c_p 0.5))))))

C

double code(double c_p, double c_n, double t, double s) {
	double t_1 = fma(s, fma(s, fma(s, -0.16666666666666666, 0.5), -1.0), 2.0);
	double t_2 = exp(-t);
	double t_3 = exp(-s);
	double t_4 = (pow((1.0 / (1.0 + t_3)), c_p) * pow((1.0 + (1.0 / (-1.0 - t_3))), c_n)) / (pow((1.0 / (1.0 + t_2)), c_p) * pow((1.0 + (1.0 / (-1.0 - t_2))), c_n));
	double tmp;
	if (t_4 <= 2.0) {
		tmp = t_4;
	} else {
		tmp = pow((t_1 * t_1), -(c_p * 0.5));
	}
	return tmp;
}

Julia

function code(c_p, c_n, t, s)
	t_1 = fma(s, fma(s, fma(s, -0.16666666666666666, 0.5), -1.0), 2.0)
	t_2 = exp(Float64(-t))
	t_3 = exp(Float64(-s))
	t_4 = Float64(Float64((Float64(1.0 / Float64(1.0 + t_3)) ^ c_p) * (Float64(1.0 + Float64(1.0 / Float64(-1.0 - t_3))) ^ c_n)) / Float64((Float64(1.0 / Float64(1.0 + t_2)) ^ c_p) * (Float64(1.0 + Float64(1.0 / Float64(-1.0 - t_2))) ^ c_n)))
	tmp = 0.0
	if (t_4 <= 2.0)
		tmp = t_4;
	else
		tmp = Float64(t_1 * t_1) ^ Float64(-Float64(c_p * 0.5));
	end
	return tmp
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := Block[{t$95$1 = N[(s * N[(s * N[(s * -0.16666666666666666 + 0.5), $MachinePrecision] + -1.0), $MachinePrecision] + 2.0), $MachinePrecision]}, Block[{t$95$2 = N[Exp[(-t)], $MachinePrecision]}, Block[{t$95$3 = N[Exp[(-s)], $MachinePrecision]}, Block[{t$95$4 = N[(N[(N[Power[N[(1.0 / N[(1.0 + t$95$3), $MachinePrecision]), $MachinePrecision], c$95$p], $MachinePrecision] * N[Power[N[(1.0 + N[(1.0 / N[(-1.0 - t$95$3), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision] / N[(N[Power[N[(1.0 / N[(1.0 + t$95$2), $MachinePrecision]), $MachinePrecision], c$95$p], $MachinePrecision] * N[Power[N[(1.0 + N[(1.0 / N[(-1.0 - t$95$2), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], c$95$n], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$4, 2.0], t$95$4, N[Power[N[(t$95$1 * t$95$1), $MachinePrecision], (-N[(c$95$p * 0.5), $MachinePrecision])], $MachinePrecision]]]]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 s))))) c_n)) (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 t))))) c_n))) < 2

   1. Initial program 99.6%

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

   if 2 < (/.f64 (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 s))))) c_n)) (*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (exp.f64 (neg.f64 t))))) c_n)))

   1. Initial program 0.5%

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

   3. Taylor expanded in c_p around 0

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

   5. Simplified 50.2%

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

   6. Taylor expanded in c_n around 0

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

      1. lower-pow.f64 N/A

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

      2. lower-/.f64 N/A

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

      3. neg-mul-1 N/A

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

      4. lower-+.f64 N/A

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

      5. lower-exp.f64 N/A

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

      6. neg-mul-1 N/A

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

      7. lower-neg.f64 65.3

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

   8. Simplified 65.3%

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

   9. Taylor expanded in s around 0

      \[\leadsto {\left(\frac{1}{\color{blue}{2 + s \cdot \left(s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) - 1\right)}}\right)}^{c\_p} \]
   10. Step-by-step derivation

       1. +-commutative N/A

          \[\leadsto {\left(\frac{1}{\color{blue}{s \cdot \left(s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) - 1\right) + 2}}\right)}^{c\_p} \]

       2. lower-fma.f64 N/A

          \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) - 1, 2\right)}}\right)}^{c\_p} \]

       3. sub-neg N/A

          \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \color{blue}{s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) + \left(\mathsf{neg}\left(1\right)\right)}, 2\right)}\right)}^{c\_p} \]

       4. metadata-eval N/A

          \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) + \color{blue}{-1}, 2\right)}\right)}^{c\_p} \]

       5. lower-fma.f64 N/A

          \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \color{blue}{\mathsf{fma}\left(s, \frac{1}{2} + \frac{-1}{6} \cdot s, -1\right)}, 2\right)}\right)}^{c\_p} \]

       6. +-commutative N/A

          \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \color{blue}{\frac{-1}{6} \cdot s + \frac{1}{2}}, -1\right), 2\right)}\right)}^{c\_p} \]

       7. *-commutative N/A

          \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \color{blue}{s \cdot \frac{-1}{6}} + \frac{1}{2}, -1\right), 2\right)}\right)}^{c\_p} \]

       8. lower-fma.f64 75.9

          \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \color{blue}{\mathsf{fma}\left(s, -0.16666666666666666, 0.5\right)}, -1\right), 2\right)}\right)}^{c\_p} \]

   11. Simplified 75.9%

       \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right)}}\right)}^{c\_p} \]
   12. Step-by-step derivation

       1. lift-fma.f64 N/A

          \[\leadsto {\left(\frac{1}{s \cdot \left(s \cdot \color{blue}{\mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right)} + -1\right) + 2}\right)}^{c\_p} \]

       2. lift-fma.f64 N/A

          \[\leadsto {\left(\frac{1}{s \cdot \color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right)} + 2}\right)}^{c\_p} \]

       3. lift-fma.f64 N/A

          \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}}\right)}^{c\_p} \]

       4. lift-/.f64 N/A

          \[\leadsto {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}}^{c\_p} \]

       5. sqr-pow N/A

          \[\leadsto \color{blue}{{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)}} \]

       6. lift-/.f64 N/A

          \[\leadsto {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}}^{\left(\frac{c\_p}{2}\right)} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \]

       7. inv-pow N/A

          \[\leadsto {\color{blue}{\left({\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{-1}\right)}}^{\left(\frac{c\_p}{2}\right)} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \]

       8. pow-pow N/A

          \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \]

       9. lift-/.f64 N/A

          \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)} \cdot {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}}^{\left(\frac{c\_p}{2}\right)} \]

       10. inv-pow N/A

           \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)} \cdot {\color{blue}{\left({\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{-1}\right)}}^{\left(\frac{c\_p}{2}\right)} \]

       11. pow-pow N/A

           \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)} \cdot \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \]

       12. pow-prod-down N/A

           \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \]

       13. lower-pow.f64 N/A

           \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \]

   13. Applied egg-rr 81.5%

       \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right)\right)}^{\left(-c\_p \cdot 0.5\right)}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 + \frac{1}{-1 - e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 + \frac{1}{-1 - e^{-t}}\right)}^{c\_n}} \leq 2:\\ \;\;\;\;\frac{{\left(\frac{1}{1 + e^{-s}}\right)}^{c\_p} \cdot {\left(1 + \frac{1}{-1 - e^{-s}}\right)}^{c\_n}}{{\left(\frac{1}{1 + e^{-t}}\right)}^{c\_p} \cdot {\left(1 + \frac{1}{-1 - e^{-t}}\right)}^{c\_n}}\\ \mathbf{else}:\\ \;\;\;\;{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right)\right)}^{\left(-c\_p \cdot 0.5\right)}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.5% accurate, 6.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right)\\ {\left(t\_1 \cdot t\_1\right)}^{\left(-c\_p \cdot 0.5\right)} \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (let* ((t_1 (fma s (fma s (fma s -0.16666666666666666 0.5) -1.0) 2.0)))
   (pow (* t_1 t_1) (- (* c_p 0.5)))))

C

double code(double c_p, double c_n, double t, double s) {
	double t_1 = fma(s, fma(s, fma(s, -0.16666666666666666, 0.5), -1.0), 2.0);
	return pow((t_1 * t_1), -(c_p * 0.5));
}

Julia

function code(c_p, c_n, t, s)
	t_1 = fma(s, fma(s, fma(s, -0.16666666666666666, 0.5), -1.0), 2.0)
	return Float64(t_1 * t_1) ^ Float64(-Float64(c_p * 0.5))
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := Block[{t$95$1 = N[(s * N[(s * N[(s * -0.16666666666666666 + 0.5), $MachinePrecision] + -1.0), $MachinePrecision] + 2.0), $MachinePrecision]}, N[Power[N[(t$95$1 * t$95$1), $MachinePrecision], (-N[(c$95$p * 0.5), $MachinePrecision])], $MachinePrecision]]

Derivation

1. Initial program 92.6%

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

3. Taylor expanded in c_p around 0

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

5. Simplified 93.8%

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

6. Taylor expanded in c_n around 0

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

   1. lower-pow.f64 N/A

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

   2. lower-/.f64 N/A

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

   3. neg-mul-1 N/A

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

   4. lower-+.f64 N/A

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

   5. lower-exp.f64 N/A

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

   6. neg-mul-1 N/A

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

   7. lower-neg.f64 93.4

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

8. Simplified 93.4%

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

9. Taylor expanded in s around 0

   \[\leadsto {\left(\frac{1}{\color{blue}{2 + s \cdot \left(s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) - 1\right)}}\right)}^{c\_p} \]
10. Step-by-step derivation

    1. +-commutative N/A

       \[\leadsto {\left(\frac{1}{\color{blue}{s \cdot \left(s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) - 1\right) + 2}}\right)}^{c\_p} \]

    2. lower-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) - 1, 2\right)}}\right)}^{c\_p} \]

    3. sub-neg N/A

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \color{blue}{s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) + \left(\mathsf{neg}\left(1\right)\right)}, 2\right)}\right)}^{c\_p} \]

    4. metadata-eval N/A

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, s \cdot \left(\frac{1}{2} + \frac{-1}{6} \cdot s\right) + \color{blue}{-1}, 2\right)}\right)}^{c\_p} \]

    5. lower-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \color{blue}{\mathsf{fma}\left(s, \frac{1}{2} + \frac{-1}{6} \cdot s, -1\right)}, 2\right)}\right)}^{c\_p} \]

    6. +-commutative N/A

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \color{blue}{\frac{-1}{6} \cdot s + \frac{1}{2}}, -1\right), 2\right)}\right)}^{c\_p} \]

    7. *-commutative N/A

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \color{blue}{s \cdot \frac{-1}{6}} + \frac{1}{2}, -1\right), 2\right)}\right)}^{c\_p} \]

    8. lower-fma.f64 94.5

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \color{blue}{\mathsf{fma}\left(s, -0.16666666666666666, 0.5\right)}, -1\right), 2\right)}\right)}^{c\_p} \]

11. Simplified 94.5%

    \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right)}}\right)}^{c\_p} \]
12. Step-by-step derivation

    1. lift-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{s \cdot \left(s \cdot \color{blue}{\mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right)} + -1\right) + 2}\right)}^{c\_p} \]

    2. lift-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{s \cdot \color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right)} + 2}\right)}^{c\_p} \]

    3. lift-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}}\right)}^{c\_p} \]

    4. lift-/.f64 N/A

       \[\leadsto {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}}^{c\_p} \]

    5. sqr-pow N/A

       \[\leadsto \color{blue}{{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)}} \]

    6. lift-/.f64 N/A

       \[\leadsto {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}}^{\left(\frac{c\_p}{2}\right)} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \]

    7. inv-pow N/A

       \[\leadsto {\color{blue}{\left({\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{-1}\right)}}^{\left(\frac{c\_p}{2}\right)} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \]

    8. pow-pow N/A

       \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \]

    9. lift-/.f64 N/A

       \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)} \cdot {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)}\right)}}^{\left(\frac{c\_p}{2}\right)} \]

    10. inv-pow N/A

        \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)} \cdot {\color{blue}{\left({\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{-1}\right)}}^{\left(\frac{c\_p}{2}\right)} \]

    11. pow-pow N/A

        \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)} \cdot \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \]

    12. pow-prod-down N/A

        \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \]

    13. lower-pow.f64 N/A

        \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{-1}{6}, \frac{1}{2}\right), -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \]

13. Applied egg-rr 95.6%

    \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(s, \mathsf{fma}\left(s, -0.16666666666666666, 0.5\right), -1\right), 2\right)\right)}^{\left(-c\_p \cdot 0.5\right)}} \]
14. Add Preprocessing

Alternative 3: 93.3% accurate, 6.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \mathsf{fma}\left(s, \mathsf{fma}\left(s, 0.5, -1\right), 2\right)\\ {\left(t\_1 \cdot t\_1\right)}^{\left(-c\_p \cdot 0.5\right)} \end{array} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (let* ((t_1 (fma s (fma s 0.5 -1.0) 2.0))) (pow (* t_1 t_1) (- (* c_p 0.5)))))

C

double code(double c_p, double c_n, double t, double s) {
	double t_1 = fma(s, fma(s, 0.5, -1.0), 2.0);
	return pow((t_1 * t_1), -(c_p * 0.5));
}

Julia

function code(c_p, c_n, t, s)
	t_1 = fma(s, fma(s, 0.5, -1.0), 2.0)
	return Float64(t_1 * t_1) ^ Float64(-Float64(c_p * 0.5))
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := Block[{t$95$1 = N[(s * N[(s * 0.5 + -1.0), $MachinePrecision] + 2.0), $MachinePrecision]}, N[Power[N[(t$95$1 * t$95$1), $MachinePrecision], (-N[(c$95$p * 0.5), $MachinePrecision])], $MachinePrecision]]

Derivation

1. Initial program 92.6%

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

3. Taylor expanded in c_p around 0

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

5. Simplified 93.8%

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

6. Taylor expanded in c_n around 0

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

   1. lower-pow.f64 N/A

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

   2. lower-/.f64 N/A

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

   3. neg-mul-1 N/A

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

   4. lower-+.f64 N/A

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

   5. lower-exp.f64 N/A

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

   6. neg-mul-1 N/A

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

   7. lower-neg.f64 93.4

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

8. Simplified 93.4%

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

9. Taylor expanded in s around 0

   \[\leadsto {\left(\frac{1}{\color{blue}{2 + s \cdot \left(\frac{1}{2} \cdot s - 1\right)}}\right)}^{c\_p} \]
10. Step-by-step derivation

    1. +-commutative N/A

       \[\leadsto {\left(\frac{1}{\color{blue}{s \cdot \left(\frac{1}{2} \cdot s - 1\right) + 2}}\right)}^{c\_p} \]

    2. lower-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \frac{1}{2} \cdot s - 1, 2\right)}}\right)}^{c\_p} \]

    3. sub-neg N/A

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \color{blue}{\frac{1}{2} \cdot s + \left(\mathsf{neg}\left(1\right)\right)}, 2\right)}\right)}^{c\_p} \]

    4. metadata-eval N/A

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \frac{1}{2} \cdot s + \color{blue}{-1}, 2\right)}\right)}^{c\_p} \]

    5. lower-fma.f64 94.5

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \color{blue}{\mathsf{fma}\left(0.5, s, -1\right)}, 2\right)}\right)}^{c\_p} \]

11. Simplified 94.5%

    \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(0.5, s, -1\right), 2\right)}}\right)}^{c\_p} \]
12. Step-by-step derivation

    1. lift-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{s \cdot \color{blue}{\mathsf{fma}\left(\frac{1}{2}, s, -1\right)} + 2}\right)}^{c\_p} \]

    2. lift-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}}\right)}^{c\_p} \]

    3. lift-/.f64 N/A

       \[\leadsto {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}}^{c\_p} \]

    4. sqr-pow N/A

       \[\leadsto \color{blue}{{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)}} \]

    5. lift-/.f64 N/A

       \[\leadsto {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}}^{\left(\frac{c\_p}{2}\right)} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \]

    6. inv-pow N/A

       \[\leadsto {\color{blue}{\left({\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{-1}\right)}}^{\left(\frac{c\_p}{2}\right)} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \]

    7. pow-pow N/A

       \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \cdot {\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}^{\left(\frac{c\_p}{2}\right)} \]

    8. lift-/.f64 N/A

       \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)} \cdot {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}}^{\left(\frac{c\_p}{2}\right)} \]

    9. inv-pow N/A

       \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)} \cdot {\color{blue}{\left({\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{-1}\right)}}^{\left(\frac{c\_p}{2}\right)} \]

    10. pow-pow N/A

        \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)} \cdot \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \]

    11. pow-prod-down N/A

        \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \]

    12. lower-pow.f64 N/A

        \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{\left(-1 \cdot \frac{c\_p}{2}\right)}} \]

13. Applied egg-rr 94.9%

    \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, 0.5, -1\right), 2\right) \cdot \mathsf{fma}\left(s, \mathsf{fma}\left(s, 0.5, -1\right), 2\right)\right)}^{\left(-c\_p \cdot 0.5\right)}} \]
14. Add Preprocessing

Alternative 4: 92.8% accurate, 7.7× speedup

Math

\[\begin{array}{l} \\ {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, 0.5, -1\right), 2\right)\right)}^{\left(-c\_p\right)} \end{array} \]

FPCore

(FPCore (c_p c_n t s)
 :precision binary64
 (pow (fma s (fma s 0.5 -1.0) 2.0) (- c_p)))

C

double code(double c_p, double c_n, double t, double s) {
	return pow(fma(s, fma(s, 0.5, -1.0), 2.0), -c_p);
}

Julia

function code(c_p, c_n, t, s)
	return fma(s, fma(s, 0.5, -1.0), 2.0) ^ Float64(-c_p)
end

Wolfram

code[c$95$p_, c$95$n_, t_, s_] := N[Power[N[(s * N[(s * 0.5 + -1.0), $MachinePrecision] + 2.0), $MachinePrecision], (-c$95$p)], $MachinePrecision]

Derivation

1. Initial program 92.6%

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

3. Taylor expanded in c_p around 0

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

5. Simplified 93.8%

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

6. Taylor expanded in c_n around 0

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

   1. lower-pow.f64 N/A

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

   2. lower-/.f64 N/A

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

   3. neg-mul-1 N/A

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

   4. lower-+.f64 N/A

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

   5. lower-exp.f64 N/A

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

   6. neg-mul-1 N/A

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

   7. lower-neg.f64 93.4

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

8. Simplified 93.4%

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

9. Taylor expanded in s around 0

   \[\leadsto {\left(\frac{1}{\color{blue}{2 + s \cdot \left(\frac{1}{2} \cdot s - 1\right)}}\right)}^{c\_p} \]
10. Step-by-step derivation

    1. +-commutative N/A

       \[\leadsto {\left(\frac{1}{\color{blue}{s \cdot \left(\frac{1}{2} \cdot s - 1\right) + 2}}\right)}^{c\_p} \]

    2. lower-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \frac{1}{2} \cdot s - 1, 2\right)}}\right)}^{c\_p} \]

    3. sub-neg N/A

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \color{blue}{\frac{1}{2} \cdot s + \left(\mathsf{neg}\left(1\right)\right)}, 2\right)}\right)}^{c\_p} \]

    4. metadata-eval N/A

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \frac{1}{2} \cdot s + \color{blue}{-1}, 2\right)}\right)}^{c\_p} \]

    5. lower-fma.f64 94.5

       \[\leadsto {\left(\frac{1}{\mathsf{fma}\left(s, \color{blue}{\mathsf{fma}\left(0.5, s, -1\right)}, 2\right)}\right)}^{c\_p} \]

11. Simplified 94.5%

    \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(0.5, s, -1\right), 2\right)}}\right)}^{c\_p} \]
12. Step-by-step derivation

    1. lift-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{s \cdot \color{blue}{\mathsf{fma}\left(\frac{1}{2}, s, -1\right)} + 2}\right)}^{c\_p} \]

    2. lift-fma.f64 N/A

       \[\leadsto {\left(\frac{1}{\color{blue}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}}\right)}^{c\_p} \]

    3. lift-/.f64 N/A

       \[\leadsto {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}}^{c\_p} \]

    4. lift-/.f64 N/A

       \[\leadsto {\color{blue}{\left(\frac{1}{\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)}\right)}}^{c\_p} \]

    5. inv-pow N/A

       \[\leadsto {\color{blue}{\left({\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{-1}\right)}}^{c\_p} \]

    6. pow-pow N/A

       \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{\left(-1 \cdot c\_p\right)}} \]

    7. lower-pow.f64 N/A

       \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(\frac{1}{2}, s, -1\right), 2\right)\right)}^{\left(-1 \cdot c\_p\right)}} \]

    8. lift-fma.f64 N/A

       \[\leadsto {\left(\mathsf{fma}\left(s, \color{blue}{\frac{1}{2} \cdot s + -1}, 2\right)\right)}^{\left(-1 \cdot c\_p\right)} \]

    9. *-commutative N/A

       \[\leadsto {\left(\mathsf{fma}\left(s, \color{blue}{s \cdot \frac{1}{2}} + -1, 2\right)\right)}^{\left(-1 \cdot c\_p\right)} \]

    10. lower-fma.f64 N/A

        \[\leadsto {\left(\mathsf{fma}\left(s, \color{blue}{\mathsf{fma}\left(s, \frac{1}{2}, -1\right)}, 2\right)\right)}^{\left(-1 \cdot c\_p\right)} \]

    11. neg-mul-1 N/A

        \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, \frac{1}{2}, -1\right), 2\right)\right)}^{\color{blue}{\left(\mathsf{neg}\left(c\_p\right)\right)}} \]

    12. lower-neg.f64 94.5

        \[\leadsto {\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, 0.5, -1\right), 2\right)\right)}^{\color{blue}{\left(-c\_p\right)}} \]

13. Applied egg-rr 94.5%

    \[\leadsto \color{blue}{{\left(\mathsf{fma}\left(s, \mathsf{fma}\left(s, 0.5, -1\right), 2\right)\right)}^{\left(-c\_p\right)}} \]
14. Add Preprocessing

Alternative 5: 94.4% accurate, 896.0× 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 92.6%

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

3. Taylor expanded in c_p around 0

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

   1. lower-/.f64 N/A

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

   2. lower-pow.f64 N/A

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

   3. sub-neg N/A

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

   4. lower-+.f64 N/A

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

   5. distribute-neg-frac N/A

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

   6. metadata-eval N/A

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

   7. lower-/.f64 N/A

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

   8. lower-+.f64 N/A

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

   9. lower-exp.f64 N/A

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

   10. lower-neg.f64 N/A

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

   11. lower-pow.f64 N/A

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

5. Simplified 92.7%

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

6. Taylor expanded in c_n around 0

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

8. Simplified 91.9%

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

Developer Target 1: 96.6% accurate, 1.4× 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 2024210 
(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))))