Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J

Percentage Accurate: 96.1% → 98.0%

Time: 7.3s

Alternatives: 13

Speedup: 0.8×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 96.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x (- 1.0 (* (- 1.0 y) z))))

C

double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (1.0d0 - ((1.0d0 - y) * z))
end function

Java

public static double code(double x, double y, double z) {
	return x * (1.0 - ((1.0 - y) * z));
}

Python

def code(x, y, z):
	return x * (1.0 - ((1.0 - y) * z))

Julia

function code(x, y, z)
	return Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * (1.0 - ((1.0 - y) * z));
end

Wolfram

code[x_, y_, z_] := N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \leq 2 \cdot 10^{+51}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + -1, x \cdot z, x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* x (- 1.0 (* (- 1.0 y) z))) 2e+51)
   (+ x (* z (- (* x y) x)))
   (fma (+ y -1.0) (* x z) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x * (1.0 - ((1.0 - y) * z))) <= 2e+51) {
		tmp = x + (z * ((x * y) - x));
	} else {
		tmp = fma((y + -1.0), (x * z), x);
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z))) <= 2e+51)
		tmp = Float64(x + Float64(z * Float64(Float64(x * y) - x)));
	else
		tmp = fma(Float64(y + -1.0), Float64(x * z), x);
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], 2e+51], N[(x + N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision] + x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z))) < 2e51

   1. Initial program 97.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 97.2%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(1 - y\right) \cdot z\right)\right)} \]

      2. +-commutative 97.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(-\left(1 - y\right) \cdot z\right) + 1\right)} \]

      3. distribute-rgt-neg-in 97.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right) \cdot \left(-z\right)} + 1\right) \]

      4. sub-neg 97.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      5. +-commutative 97.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right)} \cdot \left(-z\right) + 1\right) \]

      6. distribute-rgt1-in 97.2%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-z\right) + \left(-y\right) \cdot \left(-z\right)\right)} + 1\right) \]

      7. distribute-rgt-neg-in 97.2%

         \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-\left(-y\right) \cdot z\right)}\right) + 1\right) \]

      8. associate-+l+ 97.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(-z\right) + \left(\left(-\left(-y\right) \cdot z\right) + 1\right)\right)} \]

      9. associate-+l+ 97.2%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(-z\right) + \left(-\left(-y\right) \cdot z\right)\right) + 1\right)} \]

      10. distribute-rgt-neg-in 97.2%

          \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-y\right) \cdot \left(-z\right)}\right) + 1\right) \]

      11. distribute-rgt1-in 97.2%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right) \cdot \left(-z\right)} + 1\right) \]

      12. +-commutative 97.2%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      13. sub-neg 97.2%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right)} \cdot \left(-z\right) + 1\right) \]

      14. distribute-rgt-neg-in 97.2%

          \[\leadsto x \cdot \left(\color{blue}{\left(-\left(1 - y\right) \cdot z\right)} + 1\right) \]

      15. *-commutative 97.2%

          \[\leadsto x \cdot \left(\left(-\color{blue}{z \cdot \left(1 - y\right)}\right) + 1\right) \]

      16. distribute-rgt-neg-in 97.2%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot \left(-\left(1 - y\right)\right)} + 1\right) \]

      17. fma-def 97.2%

          \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
   4. Step-by-step derivation

      1. fma-udef 97.2%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(y + -1\right) + 1\right)} \]

      2. distribute-lft-in 97.2%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x \cdot 1} \]

      3. *-commutative 97.2%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{1 \cdot x} \]

      4. *-un-lft-identity 97.2%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{x} \]

   5. Applied egg-rr 97.2%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x} \]

   6. Taylor expanded in x around 0 99.4%

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} + x \]
   7. Step-by-step derivation

      1. sub-neg 99.4%

         \[\leadsto z \cdot \left(\color{blue}{\left(y + \left(-1\right)\right)} \cdot x\right) + x \]

      2. metadata-eval 99.4%

         \[\leadsto z \cdot \left(\left(y + \color{blue}{-1}\right) \cdot x\right) + x \]

      3. *-commutative 99.4%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y + -1\right)\right)} + x \]

      4. distribute-lft-in 99.4%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + x \cdot -1\right)} + x \]

      5. *-commutative 99.4%

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot x}\right) + x \]

      6. neg-mul-1 99.4%

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{\left(-x\right)}\right) + x \]

      7. unsub-neg 99.4%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y - x\right)} + x \]

      8. *-commutative 99.4%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - x\right) + x \]

   8. Simplified 99.4%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - x\right)} + x \]

   if 2e51 < (*.f64 x (-.f64 1 (*.f64 (-.f64 1 y) z)))

   1. Initial program 94.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. distribute-rgt-out-- 94.2%

         \[\leadsto \color{blue}{1 \cdot x - \left(\left(1 - y\right) \cdot z\right) \cdot x} \]

      2. *-lft-identity 94.2%

         \[\leadsto \color{blue}{x} - \left(\left(1 - y\right) \cdot z\right) \cdot x \]

      3. cancel-sign-sub-inv 94.2%

         \[\leadsto \color{blue}{x + \left(-\left(1 - y\right) \cdot z\right) \cdot x} \]

      4. +-commutative 94.2%

         \[\leadsto \color{blue}{\left(-\left(1 - y\right) \cdot z\right) \cdot x + x} \]

      5. distribute-lft-neg-in 94.2%

         \[\leadsto \color{blue}{\left(\left(-\left(1 - y\right)\right) \cdot z\right)} \cdot x + x \]

      6. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(-\left(1 - y\right)\right) \cdot \left(z \cdot x\right)} + x \]

      7. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-\left(1 - y\right), z \cdot x, x\right)} \]

      8. neg-sub0 99.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{0 - \left(1 - y\right)}, z \cdot x, x\right) \]

      9. associate--r- 99.9%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\left(0 - 1\right) + y}, z \cdot x, x\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(\color{blue}{-1} + y, z \cdot x, x\right) \]

      11. +-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(\color{blue}{y + -1}, z \cdot x, x\right) \]

      12. *-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(y + -1, \color{blue}{x \cdot z}, x\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y + -1, x \cdot z, x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \leq 2 \cdot 10^{+51}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(y + -1, x \cdot z, x\right)\\ \end{array} \]

Alternative 2: 97.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(z, y + -1, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 5e-45) (* x (fma z (+ y -1.0) 1.0)) (+ x (* z (- (* x y) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 5e-45) {
		tmp = x * fma(z, (y + -1.0), 1.0);
	} else {
		tmp = x + (z * ((x * y) - x));
	}
	return tmp;
}

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 5e-45)
		tmp = Float64(x * fma(z, Float64(y + -1.0), 1.0));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(x * y) - x)));
	end
	return tmp
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 5e-45], N[(x * N[(z * N[(y + -1.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.99999999999999976e-45

   1. Initial program 97.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 97.9%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(1 - y\right) \cdot z\right)\right)} \]

      2. +-commutative 97.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(-\left(1 - y\right) \cdot z\right) + 1\right)} \]

      3. distribute-rgt-neg-in 97.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right) \cdot \left(-z\right)} + 1\right) \]

      4. sub-neg 97.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      5. +-commutative 97.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right)} \cdot \left(-z\right) + 1\right) \]

      6. distribute-rgt1-in 97.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-z\right) + \left(-y\right) \cdot \left(-z\right)\right)} + 1\right) \]

      7. distribute-rgt-neg-in 97.9%

         \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-\left(-y\right) \cdot z\right)}\right) + 1\right) \]

      8. associate-+l+ 97.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(-z\right) + \left(\left(-\left(-y\right) \cdot z\right) + 1\right)\right)} \]

      9. associate-+l+ 97.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(-z\right) + \left(-\left(-y\right) \cdot z\right)\right) + 1\right)} \]

      10. distribute-rgt-neg-in 97.9%

          \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-y\right) \cdot \left(-z\right)}\right) + 1\right) \]

      11. distribute-rgt1-in 97.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right) \cdot \left(-z\right)} + 1\right) \]

      12. +-commutative 97.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      13. sub-neg 97.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right)} \cdot \left(-z\right) + 1\right) \]

      14. distribute-rgt-neg-in 97.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(-\left(1 - y\right) \cdot z\right)} + 1\right) \]

      15. *-commutative 97.9%

          \[\leadsto x \cdot \left(\left(-\color{blue}{z \cdot \left(1 - y\right)}\right) + 1\right) \]

      16. distribute-rgt-neg-in 97.9%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot \left(-\left(1 - y\right)\right)} + 1\right) \]

      17. fma-def 97.9%

          \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

   3. Simplified 97.9%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]

   if 4.99999999999999976e-45 < z

   1. Initial program 91.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 91.6%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(1 - y\right) \cdot z\right)\right)} \]

      2. +-commutative 91.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(-\left(1 - y\right) \cdot z\right) + 1\right)} \]

      3. distribute-rgt-neg-in 91.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right) \cdot \left(-z\right)} + 1\right) \]

      4. sub-neg 91.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      5. +-commutative 91.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right)} \cdot \left(-z\right) + 1\right) \]

      6. distribute-rgt1-in 91.6%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-z\right) + \left(-y\right) \cdot \left(-z\right)\right)} + 1\right) \]

      7. distribute-rgt-neg-in 91.6%

         \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-\left(-y\right) \cdot z\right)}\right) + 1\right) \]

      8. associate-+l+ 91.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(-z\right) + \left(\left(-\left(-y\right) \cdot z\right) + 1\right)\right)} \]

      9. associate-+l+ 91.6%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(-z\right) + \left(-\left(-y\right) \cdot z\right)\right) + 1\right)} \]

      10. distribute-rgt-neg-in 91.6%

          \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-y\right) \cdot \left(-z\right)}\right) + 1\right) \]

      11. distribute-rgt1-in 91.6%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right) \cdot \left(-z\right)} + 1\right) \]

      12. +-commutative 91.6%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      13. sub-neg 91.6%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right)} \cdot \left(-z\right) + 1\right) \]

      14. distribute-rgt-neg-in 91.6%

          \[\leadsto x \cdot \left(\color{blue}{\left(-\left(1 - y\right) \cdot z\right)} + 1\right) \]

      15. *-commutative 91.6%

          \[\leadsto x \cdot \left(\left(-\color{blue}{z \cdot \left(1 - y\right)}\right) + 1\right) \]

      16. distribute-rgt-neg-in 91.6%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot \left(-\left(1 - y\right)\right)} + 1\right) \]

      17. fma-def 91.6%

          \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

   3. Simplified 91.6%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
   4. Step-by-step derivation

      1. fma-udef 91.6%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(y + -1\right) + 1\right)} \]

      2. distribute-lft-in 91.6%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x \cdot 1} \]

      3. *-commutative 91.6%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{1 \cdot x} \]

      4. *-un-lft-identity 91.6%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{x} \]

   5. Applied egg-rr 91.6%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x} \]

   6. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} + x \]
   7. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto z \cdot \left(\color{blue}{\left(y + \left(-1\right)\right)} \cdot x\right) + x \]

      2. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\left(y + \color{blue}{-1}\right) \cdot x\right) + x \]

      3. *-commutative 99.9%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y + -1\right)\right)} + x \]

      4. distribute-lft-in 99.9%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + x \cdot -1\right)} + x \]

      5. *-commutative 99.9%

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot x}\right) + x \]

      6. neg-mul-1 99.9%

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{\left(-x\right)}\right) + x \]

      7. unsub-neg 99.9%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y - x\right)} + x \]

      8. *-commutative 99.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - x\right) + x \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - x\right)} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 5 \cdot 10^{-45}:\\ \;\;\;\;x \cdot \mathsf{fma}\left(z, y + -1, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \end{array} \]

Alternative 3: 63.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -x \cdot z\\ t_1 := x \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+43}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-76}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+54} \lor \neg \left(z \leq 5.8 \cdot 10^{+149}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x z))) (t_1 (* x (* y z))))
   (if (<= z -1.15e+43)
     t_0
     (if (<= z -3.9e-76)
       t_1
       (if (<= z 1.0)
         x
         (if (or (<= z 2.2e+54) (not (<= z 5.8e+149))) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = -(x * z);
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -1.15e+43) {
		tmp = t_0;
	} else if (z <= -3.9e-76) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x;
	} else if ((z <= 2.2e+54) || !(z <= 5.8e+149)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = -(x * z)
    t_1 = x * (y * z)
    if (z <= (-1.15d+43)) then
        tmp = t_0
    else if (z <= (-3.9d-76)) then
        tmp = t_1
    else if (z <= 1.0d0) then
        tmp = x
    else if ((z <= 2.2d+54) .or. (.not. (z <= 5.8d+149))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -(x * z);
	double t_1 = x * (y * z);
	double tmp;
	if (z <= -1.15e+43) {
		tmp = t_0;
	} else if (z <= -3.9e-76) {
		tmp = t_1;
	} else if (z <= 1.0) {
		tmp = x;
	} else if ((z <= 2.2e+54) || !(z <= 5.8e+149)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(x * z)
	t_1 = x * (y * z)
	tmp = 0
	if z <= -1.15e+43:
		tmp = t_0
	elif z <= -3.9e-76:
		tmp = t_1
	elif z <= 1.0:
		tmp = x
	elif (z <= 2.2e+54) or not (z <= 5.8e+149):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(x * z))
	t_1 = Float64(x * Float64(y * z))
	tmp = 0.0
	if (z <= -1.15e+43)
		tmp = t_0;
	elseif (z <= -3.9e-76)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x;
	elseif ((z <= 2.2e+54) || !(z <= 5.8e+149))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -(x * z);
	t_1 = x * (y * z);
	tmp = 0.0;
	if (z <= -1.15e+43)
		tmp = t_0;
	elseif (z <= -3.9e-76)
		tmp = t_1;
	elseif (z <= 1.0)
		tmp = x;
	elseif ((z <= 2.2e+54) || ~((z <= 5.8e+149)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(x * z), $MachinePrecision])}, Block[{t$95$1 = N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+43], t$95$0, If[LessEqual[z, -3.9e-76], t$95$1, If[LessEqual[z, 1.0], x, If[Or[LessEqual[z, 2.2e+54], N[Not[LessEqual[z, 5.8e+149]], $MachinePrecision]], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.1500000000000001e43 or 1 < z < 2.1999999999999999e54 or 5.8000000000000004e149 < z

   1. Initial program 94.7%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 98.0%

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} \]
   3. Step-by-step derivation

      1. *-commutative 98.0%

         \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot x\right) \cdot z} \]

      2. sub-neg 98.0%

         \[\leadsto \left(\color{blue}{\left(y + \left(-1\right)\right)} \cdot x\right) \cdot z \]

      3. metadata-eval 98.0%

         \[\leadsto \left(\left(y + \color{blue}{-1}\right) \cdot x\right) \cdot z \]

      4. associate-*l* 98.0%

         \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(x \cdot z\right)} \]

      5. *-commutative 98.0%

         \[\leadsto \left(y + -1\right) \cdot \color{blue}{\left(z \cdot x\right)} \]

   4. Simplified 98.0%

      \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(z \cdot x\right)} \]

   5. Taylor expanded in y around 0 68.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 68.1%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-in 68.1%

         \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   7. Simplified 68.1%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   if -1.1500000000000001e43 < z < -3.90000000000000025e-76 or 2.1999999999999999e54 < z < 5.8000000000000004e149

   1. Initial program 90.2%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 62.3%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 62.3%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   4. Simplified 62.3%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if -3.90000000000000025e-76 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 80.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 3 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+43}:\\ \;\;\;\;-x \cdot z\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{+54} \lor \neg \left(z \leq 5.8 \cdot 10^{+149}\right):\\ \;\;\;\;-x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 64.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -x \cdot z\\ \mathbf{if}\;z \leq -6.8 \cdot 10^{+42}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+50} \lor \neg \left(z \leq 1.8 \cdot 10^{+166}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (- (* x z))))
   (if (<= z -6.8e+42)
     t_0
     (if (<= z -3.2e-76)
       (* x (* y z))
       (if (<= z 1.0)
         x
         (if (or (<= z 1.4e+50) (not (<= z 1.8e+166))) t_0 (* y (* x z))))))))

C

double code(double x, double y, double z) {
	double t_0 = -(x * z);
	double tmp;
	if (z <= -6.8e+42) {
		tmp = t_0;
	} else if (z <= -3.2e-76) {
		tmp = x * (y * z);
	} else if (z <= 1.0) {
		tmp = x;
	} else if ((z <= 1.4e+50) || !(z <= 1.8e+166)) {
		tmp = t_0;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = -(x * z)
    if (z <= (-6.8d+42)) then
        tmp = t_0
    else if (z <= (-3.2d-76)) then
        tmp = x * (y * z)
    else if (z <= 1.0d0) then
        tmp = x
    else if ((z <= 1.4d+50) .or. (.not. (z <= 1.8d+166))) then
        tmp = t_0
    else
        tmp = y * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -(x * z);
	double tmp;
	if (z <= -6.8e+42) {
		tmp = t_0;
	} else if (z <= -3.2e-76) {
		tmp = x * (y * z);
	} else if (z <= 1.0) {
		tmp = x;
	} else if ((z <= 1.4e+50) || !(z <= 1.8e+166)) {
		tmp = t_0;
	} else {
		tmp = y * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -(x * z)
	tmp = 0
	if z <= -6.8e+42:
		tmp = t_0
	elif z <= -3.2e-76:
		tmp = x * (y * z)
	elif z <= 1.0:
		tmp = x
	elif (z <= 1.4e+50) or not (z <= 1.8e+166):
		tmp = t_0
	else:
		tmp = y * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-Float64(x * z))
	tmp = 0.0
	if (z <= -6.8e+42)
		tmp = t_0;
	elseif (z <= -3.2e-76)
		tmp = Float64(x * Float64(y * z));
	elseif (z <= 1.0)
		tmp = x;
	elseif ((z <= 1.4e+50) || !(z <= 1.8e+166))
		tmp = t_0;
	else
		tmp = Float64(y * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -(x * z);
	tmp = 0.0;
	if (z <= -6.8e+42)
		tmp = t_0;
	elseif (z <= -3.2e-76)
		tmp = x * (y * z);
	elseif (z <= 1.0)
		tmp = x;
	elseif ((z <= 1.4e+50) || ~((z <= 1.8e+166)))
		tmp = t_0;
	else
		tmp = y * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = (-N[(x * z), $MachinePrecision])}, If[LessEqual[z, -6.8e+42], t$95$0, If[LessEqual[z, -3.2e-76], N[(x * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.0], x, If[Or[LessEqual[z, 1.4e+50], N[Not[LessEqual[z, 1.8e+166]], $MachinePrecision]], t$95$0, N[(y * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.7999999999999995e42 or 1 < z < 1.3999999999999999e50 or 1.7999999999999999e166 < z

   1. Initial program 94.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 98.0%

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} \]
   3. Step-by-step derivation

      1. *-commutative 98.0%

         \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot x\right) \cdot z} \]

      2. sub-neg 98.0%

         \[\leadsto \left(\color{blue}{\left(y + \left(-1\right)\right)} \cdot x\right) \cdot z \]

      3. metadata-eval 98.0%

         \[\leadsto \left(\left(y + \color{blue}{-1}\right) \cdot x\right) \cdot z \]

      4. associate-*l* 98.0%

         \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(x \cdot z\right)} \]

      5. *-commutative 98.0%

         \[\leadsto \left(y + -1\right) \cdot \color{blue}{\left(z \cdot x\right)} \]

   4. Simplified 98.0%

      \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(z \cdot x\right)} \]

   5. Taylor expanded in y around 0 68.1%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 68.1%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-in 68.1%

         \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   7. Simplified 68.1%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   if -6.7999999999999995e42 < z < -3.1999999999999998e-76

   1. Initial program 99.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 63.3%

      \[\leadsto x \cdot \color{blue}{\left(y \cdot z\right)} \]
   3. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   4. Simplified 63.3%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y\right)} \]

   if -3.1999999999999998e-76 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 80.1%

      \[\leadsto \color{blue}{x} \]

   if 1.3999999999999999e50 < z < 1.7999999999999999e166

   1. Initial program 81.1%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 84.5%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.8 \cdot 10^{+42}:\\ \;\;\;\;-x \cdot z\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 1:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+50} \lor \neg \left(z \leq 1.8 \cdot 10^{+166}\right):\\ \;\;\;\;-x \cdot z\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 5: 94.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -960000000000 \lor \neg \left(y \leq 1.35 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -960000000000.0) (not (<= y 1.35e-30)))
   (* x (+ 1.0 (* y z)))
   (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -960000000000.0) || !(y <= 1.35e-30)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-960000000000.0d0)) .or. (.not. (y <= 1.35d-30))) then
        tmp = x * (1.0d0 + (y * z))
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -960000000000.0) || !(y <= 1.35e-30)) {
		tmp = x * (1.0 + (y * z));
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -960000000000.0) or not (y <= 1.35e-30):
		tmp = x * (1.0 + (y * z))
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -960000000000.0) || !(y <= 1.35e-30))
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -960000000000.0) || ~((y <= 1.35e-30)))
		tmp = x * (1.0 + (y * z));
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -960000000000.0], N[Not[LessEqual[y, 1.35e-30]], $MachinePrecision]], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6e11 or 1.34999999999999994e-30 < y

   1. Initial program 92.8%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 91.8%

      \[\leadsto x \cdot \left(1 - \color{blue}{-1 \cdot \left(y \cdot z\right)}\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 91.8%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(-y \cdot z\right)}\right) \]

      2. distribute-lft-neg-out 91.8%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(-y\right) \cdot z}\right) \]

      3. *-commutative 91.8%

         \[\leadsto x \cdot \left(1 - \color{blue}{z \cdot \left(-y\right)}\right) \]

   4. Simplified 91.8%

      \[\leadsto x \cdot \left(1 - \color{blue}{z \cdot \left(-y\right)}\right) \]
   5. Step-by-step derivation

      1. sub-neg 91.8%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-z \cdot \left(-y\right)\right)\right)} \]

      2. distribute-rgt-neg-out 91.8%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{\left(-z \cdot y\right)}\right)\right) \]

      3. remove-double-neg 91.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{z \cdot y}\right) \]

      4. +-commutative 91.8%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y + 1\right)} \]

   6. Applied egg-rr 91.8%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y + 1\right)} \]

   if -9.6e11 < y < 1.34999999999999994e-30

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 99.1%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]
   3. Step-by-step derivation

      1. sub-neg 99.1%

         \[\leadsto \color{blue}{\left(1 + \left(-z\right)\right)} \cdot x \]

      2. +-commutative 99.1%

         \[\leadsto \color{blue}{\left(\left(-z\right) + 1\right)} \cdot x \]

      3. distribute-rgt1-in 99.2%

         \[\leadsto \color{blue}{x + \left(-z\right) \cdot x} \]

      4. cancel-sign-sub-inv 99.2%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 99.2%

      \[\leadsto \color{blue}{x - z \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -960000000000 \lor \neg \left(y \leq 1.35 \cdot 10^{-30}\right):\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 6: 98.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+29} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -4.2e+29) (not (<= z 1.0)))
   (* (+ y -1.0) (* x z))
   (* x (+ 1.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e+29) || !(z <= 1.0)) {
		tmp = (y + -1.0) * (x * z);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-4.2d+29)) .or. (.not. (z <= 1.0d0))) then
        tmp = (y + (-1.0d0)) * (x * z)
    else
        tmp = x * (1.0d0 + (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -4.2e+29) || !(z <= 1.0)) {
		tmp = (y + -1.0) * (x * z);
	} else {
		tmp = x * (1.0 + (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -4.2e+29) or not (z <= 1.0):
		tmp = (y + -1.0) * (x * z)
	else:
		tmp = x * (1.0 + (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -4.2e+29) || !(z <= 1.0))
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	else
		tmp = Float64(x * Float64(1.0 + Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -4.2e+29) || ~((z <= 1.0)))
		tmp = (y + -1.0) * (x * z);
	else
		tmp = x * (1.0 + (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -4.2e+29], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -4.2000000000000003e29 or 1 < z

   1. Initial program 91.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 98.4%

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} \]
   3. Step-by-step derivation

      1. *-commutative 98.4%

         \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot x\right) \cdot z} \]

      2. sub-neg 98.4%

         \[\leadsto \left(\color{blue}{\left(y + \left(-1\right)\right)} \cdot x\right) \cdot z \]

      3. metadata-eval 98.4%

         \[\leadsto \left(\left(y + \color{blue}{-1}\right) \cdot x\right) \cdot z \]

      4. associate-*l* 98.5%

         \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(x \cdot z\right)} \]

      5. *-commutative 98.5%

         \[\leadsto \left(y + -1\right) \cdot \color{blue}{\left(z \cdot x\right)} \]

   4. Simplified 98.5%

      \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(z \cdot x\right)} \]

   if -4.2000000000000003e29 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 99.0%

      \[\leadsto x \cdot \left(1 - \color{blue}{-1 \cdot \left(y \cdot z\right)}\right) \]
   3. Step-by-step derivation

      1. mul-1-neg 99.0%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(-y \cdot z\right)}\right) \]

      2. distribute-lft-neg-out 99.0%

         \[\leadsto x \cdot \left(1 - \color{blue}{\left(-y\right) \cdot z}\right) \]

      3. *-commutative 99.0%

         \[\leadsto x \cdot \left(1 - \color{blue}{z \cdot \left(-y\right)}\right) \]

   4. Simplified 99.0%

      \[\leadsto x \cdot \left(1 - \color{blue}{z \cdot \left(-y\right)}\right) \]
   5. Step-by-step derivation

      1. sub-neg 99.0%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-z \cdot \left(-y\right)\right)\right)} \]

      2. distribute-rgt-neg-out 99.0%

         \[\leadsto x \cdot \left(1 + \left(-\color{blue}{\left(-z \cdot y\right)}\right)\right) \]

      3. remove-double-neg 99.0%

         \[\leadsto x \cdot \left(1 + \color{blue}{z \cdot y}\right) \]

      4. +-commutative 99.0%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot y + 1\right)} \]

   6. Applied egg-rr 99.0%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot y + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.2 \cdot 10^{+29} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + y \cdot z\right)\\ \end{array} \]

Alternative 7: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 8.8 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 8.8e+15) (* x (- 1.0 (* (- 1.0 y) z))) (* (+ y -1.0) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 8.8e+15) {
		tmp = x * (1.0 - ((1.0 - y) * z));
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 8.8d+15) then
        tmp = x * (1.0d0 - ((1.0d0 - y) * z))
    else
        tmp = (y + (-1.0d0)) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 8.8e+15) {
		tmp = x * (1.0 - ((1.0 - y) * z));
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 8.8e+15:
		tmp = x * (1.0 - ((1.0 - y) * z))
	else:
		tmp = (y + -1.0) * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 8.8e+15)
		tmp = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 8.8e+15)
		tmp = x * (1.0 - ((1.0 - y) * z));
	else
		tmp = (y + -1.0) * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 8.8e+15], N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 8.8e15

   1. Initial program 98.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   if 8.8e15 < z

   1. Initial program 89.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} \]
   3. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot x\right) \cdot z} \]

      2. sub-neg 99.9%

         \[\leadsto \left(\color{blue}{\left(y + \left(-1\right)\right)} \cdot x\right) \cdot z \]

      3. metadata-eval 99.9%

         \[\leadsto \left(\left(y + \color{blue}{-1}\right) \cdot x\right) \cdot z \]

      4. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(x \cdot z\right)} \]

      5. *-commutative 99.9%

         \[\leadsto \left(y + -1\right) \cdot \color{blue}{\left(z \cdot x\right)} \]

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(z \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 8.8 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 8: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.5 \cdot 10^{+17}:\\ \;\;\;\;x - x \cdot \left(\left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.5e+17) (- x (* x (* (- 1.0 y) z))) (* (+ y -1.0) (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.5e+17) {
		tmp = x - (x * ((1.0 - y) * z));
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 1.5d+17) then
        tmp = x - (x * ((1.0d0 - y) * z))
    else
        tmp = (y + (-1.0d0)) * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.5e+17) {
		tmp = x - (x * ((1.0 - y) * z));
	} else {
		tmp = (y + -1.0) * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.5e+17:
		tmp = x - (x * ((1.0 - y) * z))
	else:
		tmp = (y + -1.0) * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.5e+17)
		tmp = Float64(x - Float64(x * Float64(Float64(1.0 - y) * z)));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.5e+17)
		tmp = x - (x * ((1.0 - y) * z));
	else
		tmp = (y + -1.0) * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.5e+17], N[(x - N[(x * N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.5e17

   1. Initial program 98.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 98.0%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(1 - y\right) \cdot z\right)\right)} \]

      2. +-commutative 98.0%

         \[\leadsto x \cdot \color{blue}{\left(\left(-\left(1 - y\right) \cdot z\right) + 1\right)} \]

      3. distribute-rgt-neg-in 98.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right) \cdot \left(-z\right)} + 1\right) \]

      4. sub-neg 98.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      5. +-commutative 98.0%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right)} \cdot \left(-z\right) + 1\right) \]

      6. distribute-rgt1-in 98.1%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-z\right) + \left(-y\right) \cdot \left(-z\right)\right)} + 1\right) \]

      7. distribute-rgt-neg-in 98.1%

         \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-\left(-y\right) \cdot z\right)}\right) + 1\right) \]

      8. associate-+l+ 98.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(-z\right) + \left(\left(-\left(-y\right) \cdot z\right) + 1\right)\right)} \]

      9. associate-+l+ 98.1%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(-z\right) + \left(-\left(-y\right) \cdot z\right)\right) + 1\right)} \]

      10. distribute-rgt-neg-in 98.1%

          \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-y\right) \cdot \left(-z\right)}\right) + 1\right) \]

      11. distribute-rgt1-in 98.0%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right) \cdot \left(-z\right)} + 1\right) \]

      12. +-commutative 98.0%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      13. sub-neg 98.0%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right)} \cdot \left(-z\right) + 1\right) \]

      14. distribute-rgt-neg-in 98.0%

          \[\leadsto x \cdot \left(\color{blue}{\left(-\left(1 - y\right) \cdot z\right)} + 1\right) \]

      15. *-commutative 98.0%

          \[\leadsto x \cdot \left(\left(-\color{blue}{z \cdot \left(1 - y\right)}\right) + 1\right) \]

      16. distribute-rgt-neg-in 98.0%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot \left(-\left(1 - y\right)\right)} + 1\right) \]

      17. fma-def 98.1%

          \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

   3. Simplified 98.1%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
   4. Step-by-step derivation

      1. fma-udef 98.0%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(y + -1\right) + 1\right)} \]

      2. distribute-lft-in 98.1%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x \cdot 1} \]

      3. *-commutative 98.1%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{1 \cdot x} \]

      4. *-un-lft-identity 98.1%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{x} \]

   5. Applied egg-rr 98.1%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x} \]

   if 1.5e17 < z

   1. Initial program 89.5%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} \]
   3. Step-by-step derivation

      1. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot x\right) \cdot z} \]

      2. sub-neg 99.9%

         \[\leadsto \left(\color{blue}{\left(y + \left(-1\right)\right)} \cdot x\right) \cdot z \]

      3. metadata-eval 99.9%

         \[\leadsto \left(\left(y + \color{blue}{-1}\right) \cdot x\right) \cdot z \]

      4. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(x \cdot z\right)} \]

      5. *-commutative 99.9%

         \[\leadsto \left(y + -1\right) \cdot \color{blue}{\left(z \cdot x\right)} \]

   4. Simplified 99.9%

      \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(z \cdot x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.5 \cdot 10^{+17}:\\ \;\;\;\;x - x \cdot \left(\left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 9: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 10^{-79}:\\ \;\;\;\;x - x \cdot \left(\left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1e-79) (- x (* x (* (- 1.0 y) z))) (+ x (* z (- (* x y) x)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1e-79) {
		tmp = x - (x * ((1.0 - y) * z));
	} else {
		tmp = x + (z * ((x * y) - x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= 1d-79) then
        tmp = x - (x * ((1.0d0 - y) * z))
    else
        tmp = x + (z * ((x * y) - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1e-79) {
		tmp = x - (x * ((1.0 - y) * z));
	} else {
		tmp = x + (z * ((x * y) - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1e-79:
		tmp = x - (x * ((1.0 - y) * z))
	else:
		tmp = x + (z * ((x * y) - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1e-79)
		tmp = Float64(x - Float64(x * Float64(Float64(1.0 - y) * z)));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(x * y) - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1e-79)
		tmp = x - (x * ((1.0 - y) * z));
	else
		tmp = x + (z * ((x * y) - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1e-79], N[(x - N[(x * N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1e-79

   1. Initial program 97.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 97.9%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(1 - y\right) \cdot z\right)\right)} \]

      2. +-commutative 97.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(-\left(1 - y\right) \cdot z\right) + 1\right)} \]

      3. distribute-rgt-neg-in 97.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right) \cdot \left(-z\right)} + 1\right) \]

      4. sub-neg 97.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      5. +-commutative 97.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right)} \cdot \left(-z\right) + 1\right) \]

      6. distribute-rgt1-in 97.9%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-z\right) + \left(-y\right) \cdot \left(-z\right)\right)} + 1\right) \]

      7. distribute-rgt-neg-in 97.9%

         \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-\left(-y\right) \cdot z\right)}\right) + 1\right) \]

      8. associate-+l+ 97.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(-z\right) + \left(\left(-\left(-y\right) \cdot z\right) + 1\right)\right)} \]

      9. associate-+l+ 97.9%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(-z\right) + \left(-\left(-y\right) \cdot z\right)\right) + 1\right)} \]

      10. distribute-rgt-neg-in 97.9%

          \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-y\right) \cdot \left(-z\right)}\right) + 1\right) \]

      11. distribute-rgt1-in 97.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right) \cdot \left(-z\right)} + 1\right) \]

      12. +-commutative 97.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      13. sub-neg 97.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right)} \cdot \left(-z\right) + 1\right) \]

      14. distribute-rgt-neg-in 97.9%

          \[\leadsto x \cdot \left(\color{blue}{\left(-\left(1 - y\right) \cdot z\right)} + 1\right) \]

      15. *-commutative 97.9%

          \[\leadsto x \cdot \left(\left(-\color{blue}{z \cdot \left(1 - y\right)}\right) + 1\right) \]

      16. distribute-rgt-neg-in 97.9%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot \left(-\left(1 - y\right)\right)} + 1\right) \]

      17. fma-def 97.9%

          \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

   3. Simplified 97.9%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
   4. Step-by-step derivation

      1. fma-udef 97.9%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(y + -1\right) + 1\right)} \]

      2. distribute-lft-in 97.9%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x \cdot 1} \]

      3. *-commutative 97.9%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{1 \cdot x} \]

      4. *-un-lft-identity 97.9%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{x} \]

   5. Applied egg-rr 97.9%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x} \]

   if 1e-79 < z

   1. Initial program 92.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]
   2. Step-by-step derivation

      1. sub-neg 92.3%

         \[\leadsto x \cdot \color{blue}{\left(1 + \left(-\left(1 - y\right) \cdot z\right)\right)} \]

      2. +-commutative 92.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(-\left(1 - y\right) \cdot z\right) + 1\right)} \]

      3. distribute-rgt-neg-in 92.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right) \cdot \left(-z\right)} + 1\right) \]

      4. sub-neg 92.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      5. +-commutative 92.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right)} \cdot \left(-z\right) + 1\right) \]

      6. distribute-rgt1-in 92.3%

         \[\leadsto x \cdot \left(\color{blue}{\left(\left(-z\right) + \left(-y\right) \cdot \left(-z\right)\right)} + 1\right) \]

      7. distribute-rgt-neg-in 92.3%

         \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-\left(-y\right) \cdot z\right)}\right) + 1\right) \]

      8. associate-+l+ 92.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(-z\right) + \left(\left(-\left(-y\right) \cdot z\right) + 1\right)\right)} \]

      9. associate-+l+ 92.3%

         \[\leadsto x \cdot \color{blue}{\left(\left(\left(-z\right) + \left(-\left(-y\right) \cdot z\right)\right) + 1\right)} \]

      10. distribute-rgt-neg-in 92.3%

          \[\leadsto x \cdot \left(\left(\left(-z\right) + \color{blue}{\left(-y\right) \cdot \left(-z\right)}\right) + 1\right) \]

      11. distribute-rgt1-in 92.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(\left(-y\right) + 1\right) \cdot \left(-z\right)} + 1\right) \]

      12. +-commutative 92.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 + \left(-y\right)\right)} \cdot \left(-z\right) + 1\right) \]

      13. sub-neg 92.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(1 - y\right)} \cdot \left(-z\right) + 1\right) \]

      14. distribute-rgt-neg-in 92.3%

          \[\leadsto x \cdot \left(\color{blue}{\left(-\left(1 - y\right) \cdot z\right)} + 1\right) \]

      15. *-commutative 92.3%

          \[\leadsto x \cdot \left(\left(-\color{blue}{z \cdot \left(1 - y\right)}\right) + 1\right) \]

      16. distribute-rgt-neg-in 92.3%

          \[\leadsto x \cdot \left(\color{blue}{z \cdot \left(-\left(1 - y\right)\right)} + 1\right) \]

      17. fma-def 92.3%

          \[\leadsto x \cdot \color{blue}{\mathsf{fma}\left(z, -\left(1 - y\right), 1\right)} \]

   3. Simplified 92.3%

      \[\leadsto \color{blue}{x \cdot \mathsf{fma}\left(z, y + -1, 1\right)} \]
   4. Step-by-step derivation

      1. fma-udef 92.3%

         \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(y + -1\right) + 1\right)} \]

      2. distribute-lft-in 92.3%

         \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x \cdot 1} \]

      3. *-commutative 92.3%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{1 \cdot x} \]

      4. *-un-lft-identity 92.3%

         \[\leadsto x \cdot \left(z \cdot \left(y + -1\right)\right) + \color{blue}{x} \]

   5. Applied egg-rr 92.3%

      \[\leadsto \color{blue}{x \cdot \left(z \cdot \left(y + -1\right)\right) + x} \]

   6. Taylor expanded in x around 0 99.9%

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} + x \]
   7. Step-by-step derivation

      1. sub-neg 99.9%

         \[\leadsto z \cdot \left(\color{blue}{\left(y + \left(-1\right)\right)} \cdot x\right) + x \]

      2. metadata-eval 99.9%

         \[\leadsto z \cdot \left(\left(y + \color{blue}{-1}\right) \cdot x\right) + x \]

      3. *-commutative 99.9%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot \left(y + -1\right)\right)} + x \]

      4. distribute-lft-in 99.9%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y + x \cdot -1\right)} + x \]

      5. *-commutative 99.9%

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{-1 \cdot x}\right) + x \]

      6. neg-mul-1 99.9%

         \[\leadsto z \cdot \left(x \cdot y + \color{blue}{\left(-x\right)}\right) + x \]

      7. unsub-neg 99.9%

         \[\leadsto z \cdot \color{blue}{\left(x \cdot y - x\right)} + x \]

      8. *-commutative 99.9%

         \[\leadsto z \cdot \left(\color{blue}{y \cdot x} - x\right) + x \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x - x\right)} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 10^{-79}:\\ \;\;\;\;x - x \cdot \left(\left(1 - y\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot y - x\right)\\ \end{array} \]

Alternative 10: 82.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+35} \lor \neg \left(y \leq 6.7 \cdot 10^{+165}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1e+35) (not (<= y 6.7e+165))) (* z (* x y)) (* x (- 1.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+35) || !(y <= 6.7e+165)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1d+35)) .or. (.not. (y <= 6.7d+165))) then
        tmp = z * (x * y)
    else
        tmp = x * (1.0d0 - z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1e+35) || !(y <= 6.7e+165)) {
		tmp = z * (x * y);
	} else {
		tmp = x * (1.0 - z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1e+35) or not (y <= 6.7e+165):
		tmp = z * (x * y)
	else:
		tmp = x * (1.0 - z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1e+35) || !(y <= 6.7e+165))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x * Float64(1.0 - z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1e+35) || ~((y <= 6.7e+165)))
		tmp = z * (x * y);
	else
		tmp = x * (1.0 - z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1e+35], N[Not[LessEqual[y, 6.7e+165]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.9999999999999997e34 or 6.70000000000000037e165 < y

   1. Initial program 90.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 79.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 76.9%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 76.9%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

      3. associate-*l* 82.0%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   4. Simplified 82.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if -9.9999999999999997e34 < y < 6.70000000000000037e165

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 91.0%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \cdot 10^{+35} \lor \neg \left(y \leq 6.7 \cdot 10^{+165}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - z\right)\\ \end{array} \]

Alternative 11: 82.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+36} \lor \neg \left(y \leq 6.7 \cdot 10^{+165}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3e+36) (not (<= y 6.7e+165))) (* z (* x y)) (- x (* x z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+36) || !(y <= 6.7e+165)) {
		tmp = z * (x * y);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3d+36)) .or. (.not. (y <= 6.7d+165))) then
        tmp = z * (x * y)
    else
        tmp = x - (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3e+36) || !(y <= 6.7e+165)) {
		tmp = z * (x * y);
	} else {
		tmp = x - (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3e+36) or not (y <= 6.7e+165):
		tmp = z * (x * y)
	else:
		tmp = x - (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3e+36) || !(y <= 6.7e+165))
		tmp = Float64(z * Float64(x * y));
	else
		tmp = Float64(x - Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3e+36) || ~((y <= 6.7e+165)))
		tmp = z * (x * y);
	else
		tmp = x - (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3e+36], N[Not[LessEqual[y, 6.7e+165]], $MachinePrecision]], N[(z * N[(x * y), $MachinePrecision]), $MachinePrecision], N[(x - N[(x * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3e36 or 6.70000000000000037e165 < y

   1. Initial program 90.6%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around inf 79.0%

      \[\leadsto \color{blue}{y \cdot \left(z \cdot x\right)} \]
   3. Step-by-step derivation

      1. associate-*r* 76.9%

         \[\leadsto \color{blue}{\left(y \cdot z\right) \cdot x} \]

      2. *-commutative 76.9%

         \[\leadsto \color{blue}{\left(z \cdot y\right)} \cdot x \]

      3. associate-*l* 82.0%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   4. Simplified 82.0%

      \[\leadsto \color{blue}{z \cdot \left(y \cdot x\right)} \]

   if -3e36 < y < 6.70000000000000037e165

   1. Initial program 99.3%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in y around 0 91.0%

      \[\leadsto \color{blue}{\left(1 - z\right) \cdot x} \]
   3. Step-by-step derivation

      1. sub-neg 91.0%

         \[\leadsto \color{blue}{\left(1 + \left(-z\right)\right)} \cdot x \]

      2. +-commutative 91.0%

         \[\leadsto \color{blue}{\left(\left(-z\right) + 1\right)} \cdot x \]

      3. distribute-rgt1-in 91.0%

         \[\leadsto \color{blue}{x + \left(-z\right) \cdot x} \]

      4. cancel-sign-sub-inv 91.0%

         \[\leadsto \color{blue}{x - z \cdot x} \]

   4. Simplified 91.0%

      \[\leadsto \color{blue}{x - z \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+36} \lor \neg \left(y \leq 6.7 \cdot 10^{+165}\right):\\ \;\;\;\;z \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x - x \cdot z\\ \end{array} \]

Alternative 12: 64.6% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{-6} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;-x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1.86e-6) (not (<= z 1.0))) (- (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.86e-6) || !(z <= 1.0)) {
		tmp = -(x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-1.86d-6)) .or. (.not. (z <= 1.0d0))) then
        tmp = -(x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1.86e-6) || !(z <= 1.0)) {
		tmp = -(x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1.86e-6) or not (z <= 1.0):
		tmp = -(x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1.86e-6) || !(z <= 1.0))
		tmp = Float64(-Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -1.86e-6) || ~((z <= 1.0)))
		tmp = -(x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1.86e-6], N[Not[LessEqual[z, 1.0]], $MachinePrecision]], (-N[(x * z), $MachinePrecision]), x]

Derivation

1. Split input into 2 regimes

2. if z < -1.86e-6 or 1 < z

   1. Initial program 92.0%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around inf 98.5%

      \[\leadsto \color{blue}{z \cdot \left(\left(y - 1\right) \cdot x\right)} \]
   3. Step-by-step derivation

      1. *-commutative 98.5%

         \[\leadsto \color{blue}{\left(\left(y - 1\right) \cdot x\right) \cdot z} \]

      2. sub-neg 98.5%

         \[\leadsto \left(\color{blue}{\left(y + \left(-1\right)\right)} \cdot x\right) \cdot z \]

      3. metadata-eval 98.5%

         \[\leadsto \left(\left(y + \color{blue}{-1}\right) \cdot x\right) \cdot z \]

      4. associate-*l* 98.5%

         \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(x \cdot z\right)} \]

      5. *-commutative 98.5%

         \[\leadsto \left(y + -1\right) \cdot \color{blue}{\left(z \cdot x\right)} \]

   4. Simplified 98.5%

      \[\leadsto \color{blue}{\left(y + -1\right) \cdot \left(z \cdot x\right)} \]

   5. Taylor expanded in y around 0 58.9%

      \[\leadsto \color{blue}{-1 \cdot \left(z \cdot x\right)} \]
   6. Step-by-step derivation

      1. neg-mul-1 58.9%

         \[\leadsto \color{blue}{-z \cdot x} \]

      2. distribute-rgt-neg-in 58.9%

         \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   7. Simplified 58.9%

      \[\leadsto \color{blue}{z \cdot \left(-x\right)} \]

   if -1.86e-6 < z < 1

   1. Initial program 99.9%

      \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

   2. Taylor expanded in z around 0 75.4%

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

4. Final simplification 67.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.86 \cdot 10^{-6} \lor \neg \left(z \leq 1\right):\\ \;\;\;\;-x \cdot z\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 38.7% accurate, 9.0× speedup

Math

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

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 96.3%

   \[x \cdot \left(1 - \left(1 - y\right) \cdot z\right) \]

2. Taylor expanded in z around 0 42.1%

   \[\leadsto \color{blue}{x} \]

3. Final simplification 42.1%

   \[\leadsto x \]

Developer target: 99.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(1 - \left(1 - y\right) \cdot z\right)\\ t_1 := x + \left(1 - y\right) \cdot \left(\left(-z\right) \cdot x\right)\\ \mathbf{if}\;t_0 < -1.618195973607049 \cdot 10^{+50}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;t_0 < 3.892237649663903 \cdot 10^{+134}:\\ \;\;\;\;\left(x \cdot y\right) \cdot z - \left(x \cdot z - x\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (- 1.0 (* (- 1.0 y) z))))
        (t_1 (+ x (* (- 1.0 y) (* (- z) x)))))
   (if (< t_0 -1.618195973607049e+50)
     t_1
     (if (< t_0 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) t_1))))

C

double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (1.0d0 - ((1.0d0 - y) * z))
    t_1 = x + ((1.0d0 - y) * (-z * x))
    if (t_0 < (-1.618195973607049d+50)) then
        tmp = t_1
    else if (t_0 < 3.892237649663903d+134) then
        tmp = ((x * y) * z) - ((x * z) - x)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (1.0 - ((1.0 - y) * z));
	double t_1 = x + ((1.0 - y) * (-z * x));
	double tmp;
	if (t_0 < -1.618195973607049e+50) {
		tmp = t_1;
	} else if (t_0 < 3.892237649663903e+134) {
		tmp = ((x * y) * z) - ((x * z) - x);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (1.0 - ((1.0 - y) * z))
	t_1 = x + ((1.0 - y) * (-z * x))
	tmp = 0
	if t_0 < -1.618195973607049e+50:
		tmp = t_1
	elif t_0 < 3.892237649663903e+134:
		tmp = ((x * y) * z) - ((x * z) - x)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(1.0 - Float64(Float64(1.0 - y) * z)))
	t_1 = Float64(x + Float64(Float64(1.0 - y) * Float64(Float64(-z) * x)))
	tmp = 0.0
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = Float64(Float64(Float64(x * y) * z) - Float64(Float64(x * z) - x));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (1.0 - ((1.0 - y) * z));
	t_1 = x + ((1.0 - y) * (-z * x));
	tmp = 0.0;
	if (t_0 < -1.618195973607049e+50)
		tmp = t_1;
	elseif (t_0 < 3.892237649663903e+134)
		tmp = ((x * y) * z) - ((x * z) - x);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(1.0 - N[(N[(1.0 - y), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x + N[(N[(1.0 - y), $MachinePrecision] * N[((-z) * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Less[t$95$0, -1.618195973607049e+50], t$95$1, If[Less[t$95$0, 3.892237649663903e+134], N[(N[(N[(x * y), $MachinePrecision] * z), $MachinePrecision] - N[(N[(x * z), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision], t$95$1]]]]

Reproduce

herbie shell --seed 2023240 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSV:hsv from colour-2.3.3, J"
  :precision binary64

  :herbie-target
  (if (< (* x (- 1.0 (* (- 1.0 y) z))) -1.618195973607049e+50) (+ x (* (- 1.0 y) (* (- z) x))) (if (< (* x (- 1.0 (* (- 1.0 y) z))) 3.892237649663903e+134) (- (* (* x y) z) (- (* x z) x)) (+ x (* (- 1.0 y) (* (- z) x)))))

  (* x (- 1.0 (* (- 1.0 y) z))))