Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D

Percentage Accurate: 99.5% → 99.7%

Time: 9.9s

Alternatives: 16

Speedup: 1.2×

• 21.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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 + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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 + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) (+ 4.0 (* z -6.0)) x))

C

double code(double x, double y, double z) {
	return fma((y - x), (4.0 + (z * -6.0)), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), Float64(4.0 + Float64(z * -6.0)), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. +-commutative 99.6%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

   3. fma-def 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

   4. sub-neg 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

   5. distribute-rgt-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

   6. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

   7. metadata-eval 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

   8. distribute-lft-neg-out 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

   9. distribute-rgt-neg-in 99.8%

      \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

   10. metadata-eval 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]

4. Final simplification 99.8%

   \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right) \]

Alternative 2: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.7 \cdot 10^{+187}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.55:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-246}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-299}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-218}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -2.7e+187)
     (* -6.0 (* y z))
     (if (<= z -0.55)
       t_0
       (if (<= z -7.4e-174)
         (* y 4.0)
         (if (<= z -2.6e-246)
           (* x -3.0)
           (if (<= z -1.5e-299)
             (* y 4.0)
             (if (<= z 8.5e-218)
               (* x -3.0)
               (if (<= z 4e-70)
                 (* y 4.0)
                 (if (<= z 1.3e-8)
                   (* x -3.0)
                   (if (<= z 0.55) (* y 4.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.7e+187) {
		tmp = -6.0 * (y * z);
	} else if (z <= -0.55) {
		tmp = t_0;
	} else if (z <= -7.4e-174) {
		tmp = y * 4.0;
	} else if (z <= -2.6e-246) {
		tmp = x * -3.0;
	} else if (z <= -1.5e-299) {
		tmp = y * 4.0;
	} else if (z <= 8.5e-218) {
		tmp = x * -3.0;
	} else if (z <= 4e-70) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-8) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	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 = 6.0d0 * (x * z)
    if (z <= (-2.7d+187)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-0.55d0)) then
        tmp = t_0
    else if (z <= (-7.4d-174)) then
        tmp = y * 4.0d0
    else if (z <= (-2.6d-246)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.5d-299)) then
        tmp = y * 4.0d0
    else if (z <= 8.5d-218) then
        tmp = x * (-3.0d0)
    else if (z <= 4d-70) then
        tmp = y * 4.0d0
    else if (z <= 1.3d-8) then
        tmp = x * (-3.0d0)
    else if (z <= 0.55d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.7e+187) {
		tmp = -6.0 * (y * z);
	} else if (z <= -0.55) {
		tmp = t_0;
	} else if (z <= -7.4e-174) {
		tmp = y * 4.0;
	} else if (z <= -2.6e-246) {
		tmp = x * -3.0;
	} else if (z <= -1.5e-299) {
		tmp = y * 4.0;
	} else if (z <= 8.5e-218) {
		tmp = x * -3.0;
	} else if (z <= 4e-70) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-8) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -2.7e+187:
		tmp = -6.0 * (y * z)
	elif z <= -0.55:
		tmp = t_0
	elif z <= -7.4e-174:
		tmp = y * 4.0
	elif z <= -2.6e-246:
		tmp = x * -3.0
	elif z <= -1.5e-299:
		tmp = y * 4.0
	elif z <= 8.5e-218:
		tmp = x * -3.0
	elif z <= 4e-70:
		tmp = y * 4.0
	elif z <= 1.3e-8:
		tmp = x * -3.0
	elif z <= 0.55:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.7e+187)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -0.55)
		tmp = t_0;
	elseif (z <= -7.4e-174)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.6e-246)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.5e-299)
		tmp = Float64(y * 4.0);
	elseif (z <= 8.5e-218)
		tmp = Float64(x * -3.0);
	elseif (z <= 4e-70)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.3e-8)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.55)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.7e+187)
		tmp = -6.0 * (y * z);
	elseif (z <= -0.55)
		tmp = t_0;
	elseif (z <= -7.4e-174)
		tmp = y * 4.0;
	elseif (z <= -2.6e-246)
		tmp = x * -3.0;
	elseif (z <= -1.5e-299)
		tmp = y * 4.0;
	elseif (z <= 8.5e-218)
		tmp = x * -3.0;
	elseif (z <= 4e-70)
		tmp = y * 4.0;
	elseif (z <= 1.3e-8)
		tmp = x * -3.0;
	elseif (z <= 0.55)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.7e+187], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.55], t$95$0, If[LessEqual[z, -7.4e-174], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.6e-246], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.5e-299], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8.5e-218], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4e-70], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.3e-8], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.70000000000000008e187

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 99.3%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 99.3%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 99.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 99.3%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 99.9%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 99.9%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 99.9%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   9. Taylor expanded in y around inf 66.9%

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

       1. *-commutative 66.9%

          \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   11. Simplified 66.9%

       \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]

   if -2.70000000000000008e187 < z < -0.55000000000000004 or 0.55000000000000004 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around 0 98.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

   5. Taylor expanded in z around inf 95.8%

      \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 95.8%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot 6} \]

      2. associate-*r* 95.9%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{x \cdot \left(z \cdot 6\right)} \]

      3. *-commutative 95.9%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{\left(z \cdot 6\right) \cdot x} \]

      4. associate-*l* 95.8%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{z \cdot \left(6 \cdot x\right)} \]

      5. *-commutative 95.8%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + z \cdot \color{blue}{\left(x \cdot 6\right)} \]

   7. Simplified 95.8%

      \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{z \cdot \left(x \cdot 6\right)} \]

   8. Taylor expanded in y around 0 67.7%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   if -0.55000000000000004 < z < -7.40000000000000019e-174 or -2.5999999999999999e-246 < z < -1.49999999999999992e-299 or 8.5000000000000004e-218 < z < 3.99999999999999998e-70 or 1.3000000000000001e-8 < z < 0.55000000000000004

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 97.2%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around 0 63.5%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -7.40000000000000019e-174 < z < -2.5999999999999999e-246 or -1.49999999999999992e-299 < z < 8.5000000000000004e-218 or 3.99999999999999998e-70 < z < 1.3000000000000001e-8

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 77.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 77.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 77.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 77.7%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. neg-mul-1 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right)\right) \]

      5. associate-*r* 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right)\right) \]

      6. *-commutative 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      7. associate-+r+ 77.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      8. metadata-eval 77.7%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 77.7%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 77.5%

      \[\leadsto x \cdot \color{blue}{-3} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.7 \cdot 10^{+187}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.55:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.4 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-246}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-299}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-218}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.75 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -0.24:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-246}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-12}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -2.75e+187)
     (* z (* y -6.0))
     (if (<= z -0.24)
       t_0
       (if (<= z -3.9e-177)
         (* y 4.0)
         (if (<= z -2.6e-246)
           (* x -3.0)
           (if (<= z -7.5e-301)
             (* y 4.0)
             (if (<= z 1.36e-220)
               (* x -3.0)
               (if (<= z 2.55e-70)
                 (* y 4.0)
                 (if (<= z 1.5e-12)
                   (* x -3.0)
                   (if (<= z 0.5) (* y 4.0) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.75e+187) {
		tmp = z * (y * -6.0);
	} else if (z <= -0.24) {
		tmp = t_0;
	} else if (z <= -3.9e-177) {
		tmp = y * 4.0;
	} else if (z <= -2.6e-246) {
		tmp = x * -3.0;
	} else if (z <= -7.5e-301) {
		tmp = y * 4.0;
	} else if (z <= 1.36e-220) {
		tmp = x * -3.0;
	} else if (z <= 2.55e-70) {
		tmp = y * 4.0;
	} else if (z <= 1.5e-12) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	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 = 6.0d0 * (x * z)
    if (z <= (-2.75d+187)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-0.24d0)) then
        tmp = t_0
    else if (z <= (-3.9d-177)) then
        tmp = y * 4.0d0
    else if (z <= (-2.6d-246)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7.5d-301)) then
        tmp = y * 4.0d0
    else if (z <= 1.36d-220) then
        tmp = x * (-3.0d0)
    else if (z <= 2.55d-70) then
        tmp = y * 4.0d0
    else if (z <= 1.5d-12) then
        tmp = x * (-3.0d0)
    else if (z <= 0.5d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.75e+187) {
		tmp = z * (y * -6.0);
	} else if (z <= -0.24) {
		tmp = t_0;
	} else if (z <= -3.9e-177) {
		tmp = y * 4.0;
	} else if (z <= -2.6e-246) {
		tmp = x * -3.0;
	} else if (z <= -7.5e-301) {
		tmp = y * 4.0;
	} else if (z <= 1.36e-220) {
		tmp = x * -3.0;
	} else if (z <= 2.55e-70) {
		tmp = y * 4.0;
	} else if (z <= 1.5e-12) {
		tmp = x * -3.0;
	} else if (z <= 0.5) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -2.75e+187:
		tmp = z * (y * -6.0)
	elif z <= -0.24:
		tmp = t_0
	elif z <= -3.9e-177:
		tmp = y * 4.0
	elif z <= -2.6e-246:
		tmp = x * -3.0
	elif z <= -7.5e-301:
		tmp = y * 4.0
	elif z <= 1.36e-220:
		tmp = x * -3.0
	elif z <= 2.55e-70:
		tmp = y * 4.0
	elif z <= 1.5e-12:
		tmp = x * -3.0
	elif z <= 0.5:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.75e+187)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -0.24)
		tmp = t_0;
	elseif (z <= -3.9e-177)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.6e-246)
		tmp = Float64(x * -3.0);
	elseif (z <= -7.5e-301)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.36e-220)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.55e-70)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.5e-12)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.5)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.75e+187)
		tmp = z * (y * -6.0);
	elseif (z <= -0.24)
		tmp = t_0;
	elseif (z <= -3.9e-177)
		tmp = y * 4.0;
	elseif (z <= -2.6e-246)
		tmp = x * -3.0;
	elseif (z <= -7.5e-301)
		tmp = y * 4.0;
	elseif (z <= 1.36e-220)
		tmp = x * -3.0;
	elseif (z <= 2.55e-70)
		tmp = y * 4.0;
	elseif (z <= 1.5e-12)
		tmp = x * -3.0;
	elseif (z <= 0.5)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.75e+187], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.24], t$95$0, If[LessEqual[z, -3.9e-177], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.6e-246], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7.5e-301], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.36e-220], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.55e-70], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.5e-12], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.74999999999999999e187

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 99.3%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 99.3%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 99.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 99.3%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 99.9%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 99.9%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 99.9%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   9. Taylor expanded in y around inf 66.9%

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

       1. associate-*r* 66.9%

          \[\leadsto \color{blue}{\left(-6 \cdot y\right) \cdot z} \]

       2. *-commutative 66.9%

          \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   11. Simplified 66.9%

       \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   if -2.74999999999999999e187 < z < -0.23999999999999999 or 0.5 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around 0 98.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

   5. Taylor expanded in z around inf 95.8%

      \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 95.8%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot 6} \]

      2. associate-*r* 95.9%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{x \cdot \left(z \cdot 6\right)} \]

      3. *-commutative 95.9%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{\left(z \cdot 6\right) \cdot x} \]

      4. associate-*l* 95.8%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{z \cdot \left(6 \cdot x\right)} \]

      5. *-commutative 95.8%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + z \cdot \color{blue}{\left(x \cdot 6\right)} \]

   7. Simplified 95.8%

      \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{z \cdot \left(x \cdot 6\right)} \]

   8. Taylor expanded in y around 0 67.7%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   if -0.23999999999999999 < z < -3.90000000000000014e-177 or -2.5999999999999999e-246 < z < -7.5000000000000006e-301 or 1.3600000000000001e-220 < z < 2.55000000000000013e-70 or 1.5000000000000001e-12 < z < 0.5

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 97.2%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around 0 63.5%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -3.90000000000000014e-177 < z < -2.5999999999999999e-246 or -7.5000000000000006e-301 < z < 1.3600000000000001e-220 or 2.55000000000000013e-70 < z < 1.5000000000000001e-12

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 77.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 77.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 77.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 77.7%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. neg-mul-1 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right)\right) \]

      5. associate-*r* 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right)\right) \]

      6. *-commutative 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      7. associate-+r+ 77.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      8. metadata-eval 77.7%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 77.7%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 77.5%

      \[\leadsto x \cdot \color{blue}{-3} \]
3. Recombined 4 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.75 \cdot 10^{+187}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -0.24:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-246}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-220}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-12}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -0.017:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-303}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.46 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.1e+186)
   (* z (* y -6.0))
   (if (<= z -0.017)
     (* 6.0 (* x z))
     (if (<= z -6.2e-177)
       (* y 4.0)
       (if (<= z -2.45e-247)
         (* x -3.0)
         (if (<= z -9.5e-303)
           (* y 4.0)
           (if (<= z 4.5e-213)
             (* x -3.0)
             (if (<= z 2.46e-70)
               (* y 4.0)
               (if (<= z 8.5e-13)
                 (* x -3.0)
                 (if (<= z 0.56) (* y 4.0) (* z (* x 6.0))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+186) {
		tmp = z * (y * -6.0);
	} else if (z <= -0.017) {
		tmp = 6.0 * (x * z);
	} else if (z <= -6.2e-177) {
		tmp = y * 4.0;
	} else if (z <= -2.45e-247) {
		tmp = x * -3.0;
	} else if (z <= -9.5e-303) {
		tmp = y * 4.0;
	} else if (z <= 4.5e-213) {
		tmp = x * -3.0;
	} else if (z <= 2.46e-70) {
		tmp = y * 4.0;
	} else if (z <= 8.5e-13) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	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 <= (-4.1d+186)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-0.017d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-6.2d-177)) then
        tmp = y * 4.0d0
    else if (z <= (-2.45d-247)) then
        tmp = x * (-3.0d0)
    else if (z <= (-9.5d-303)) then
        tmp = y * 4.0d0
    else if (z <= 4.5d-213) then
        tmp = x * (-3.0d0)
    else if (z <= 2.46d-70) then
        tmp = y * 4.0d0
    else if (z <= 8.5d-13) then
        tmp = x * (-3.0d0)
    else if (z <= 0.56d0) then
        tmp = y * 4.0d0
    else
        tmp = z * (x * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.1e+186) {
		tmp = z * (y * -6.0);
	} else if (z <= -0.017) {
		tmp = 6.0 * (x * z);
	} else if (z <= -6.2e-177) {
		tmp = y * 4.0;
	} else if (z <= -2.45e-247) {
		tmp = x * -3.0;
	} else if (z <= -9.5e-303) {
		tmp = y * 4.0;
	} else if (z <= 4.5e-213) {
		tmp = x * -3.0;
	} else if (z <= 2.46e-70) {
		tmp = y * 4.0;
	} else if (z <= 8.5e-13) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.1e+186:
		tmp = z * (y * -6.0)
	elif z <= -0.017:
		tmp = 6.0 * (x * z)
	elif z <= -6.2e-177:
		tmp = y * 4.0
	elif z <= -2.45e-247:
		tmp = x * -3.0
	elif z <= -9.5e-303:
		tmp = y * 4.0
	elif z <= 4.5e-213:
		tmp = x * -3.0
	elif z <= 2.46e-70:
		tmp = y * 4.0
	elif z <= 8.5e-13:
		tmp = x * -3.0
	elif z <= 0.56:
		tmp = y * 4.0
	else:
		tmp = z * (x * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.1e+186)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -0.017)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -6.2e-177)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.45e-247)
		tmp = Float64(x * -3.0);
	elseif (z <= -9.5e-303)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.5e-213)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.46e-70)
		tmp = Float64(y * 4.0);
	elseif (z <= 8.5e-13)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.56)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(z * Float64(x * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.1e+186)
		tmp = z * (y * -6.0);
	elseif (z <= -0.017)
		tmp = 6.0 * (x * z);
	elseif (z <= -6.2e-177)
		tmp = y * 4.0;
	elseif (z <= -2.45e-247)
		tmp = x * -3.0;
	elseif (z <= -9.5e-303)
		tmp = y * 4.0;
	elseif (z <= 4.5e-213)
		tmp = x * -3.0;
	elseif (z <= 2.46e-70)
		tmp = y * 4.0;
	elseif (z <= 8.5e-13)
		tmp = x * -3.0;
	elseif (z <= 0.56)
		tmp = y * 4.0;
	else
		tmp = z * (x * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.1e+186], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.017], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.2e-177], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.45e-247], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -9.5e-303], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.5e-213], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.46e-70], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8.5e-13], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(y * 4.0), $MachinePrecision], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.1e186

   1. Initial program 99.9%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.9%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.9%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 99.3%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 99.3%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 99.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 99.3%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 99.9%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 99.9%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 99.9%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 99.9%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   9. Taylor expanded in y around inf 66.9%

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

       1. associate-*r* 66.9%

          \[\leadsto \color{blue}{\left(-6 \cdot y\right) \cdot z} \]

       2. *-commutative 66.9%

          \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   11. Simplified 66.9%

       \[\leadsto \color{blue}{z \cdot \left(-6 \cdot y\right)} \]

   if -4.1e186 < z < -0.017000000000000001

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around 0 99.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]

   5. Taylor expanded in z around inf 94.3%

      \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{6 \cdot \left(x \cdot z\right)} \]
   6. Step-by-step derivation

      1. *-commutative 94.3%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{\left(x \cdot z\right) \cdot 6} \]

      2. associate-*r* 94.3%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{x \cdot \left(z \cdot 6\right)} \]

      3. *-commutative 94.3%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{\left(z \cdot 6\right) \cdot x} \]

      4. associate-*l* 94.3%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{z \cdot \left(6 \cdot x\right)} \]

      5. *-commutative 94.3%

         \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + z \cdot \color{blue}{\left(x \cdot 6\right)} \]

   7. Simplified 94.3%

      \[\leadsto 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right) + \color{blue}{z \cdot \left(x \cdot 6\right)} \]

   8. Taylor expanded in y around 0 66.2%

      \[\leadsto \color{blue}{6 \cdot \left(x \cdot z\right)} \]

   if -0.017000000000000001 < z < -6.20000000000000036e-177 or -2.45e-247 < z < -9.4999999999999999e-303 or 4.5000000000000001e-213 < z < 2.4600000000000001e-70 or 8.5000000000000001e-13 < z < 0.56000000000000005

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 97.2%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around 0 63.5%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -6.20000000000000036e-177 < z < -2.45e-247 or -9.4999999999999999e-303 < z < 4.5000000000000001e-213 or 2.4600000000000001e-70 < z < 8.5000000000000001e-13

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 77.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 77.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 77.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 77.7%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. neg-mul-1 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right)\right) \]

      5. associate-*r* 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right)\right) \]

      6. *-commutative 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      7. associate-+r+ 77.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      8. metadata-eval 77.7%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 77.7%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 77.5%

      \[\leadsto x \cdot \color{blue}{-3} \]

   if 0.56000000000000005 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 98.9%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 98.9%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 98.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 98.9%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 99.1%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 99.1%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 99.1%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 99.1%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 99.1%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   9. Taylor expanded in y around 0 69.0%

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

       1. associate-*r* 69.1%

          \[\leadsto \color{blue}{\left(6 \cdot x\right) \cdot z} \]

       2. *-commutative 69.1%

          \[\leadsto \color{blue}{z \cdot \left(6 \cdot x\right)} \]

       3. *-commutative 69.1%

          \[\leadsto z \cdot \color{blue}{\left(x \cdot 6\right)} \]

   11. Simplified 69.1%

       \[\leadsto \color{blue}{z \cdot \left(x \cdot 6\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.1 \cdot 10^{+186}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -0.017:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.45 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-303}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-213}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.46 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-13}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 5: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0225:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-248}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-303}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-68}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0225)
     t_0
     (if (<= z -8e-177)
       (* y 4.0)
       (if (<= z -5.5e-248)
         (* x -3.0)
         (if (<= z 1.8e-303)
           (* y 4.0)
           (if (<= z 7e-215)
             (* x -3.0)
             (if (<= z 5.4e-68)
               (* y 4.0)
               (if (<= z 1.3e-8)
                 (* x -3.0)
                 (if (<= z 0.62) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0225) {
		tmp = t_0;
	} else if (z <= -8e-177) {
		tmp = y * 4.0;
	} else if (z <= -5.5e-248) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-303) {
		tmp = y * 4.0;
	} else if (z <= 7e-215) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-68) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-8) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	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 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.0225d0)) then
        tmp = t_0
    else if (z <= (-8d-177)) then
        tmp = y * 4.0d0
    else if (z <= (-5.5d-248)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.8d-303) then
        tmp = y * 4.0d0
    else if (z <= 7d-215) then
        tmp = x * (-3.0d0)
    else if (z <= 5.4d-68) then
        tmp = y * 4.0d0
    else if (z <= 1.3d-8) then
        tmp = x * (-3.0d0)
    else if (z <= 0.62d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0225) {
		tmp = t_0;
	} else if (z <= -8e-177) {
		tmp = y * 4.0;
	} else if (z <= -5.5e-248) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-303) {
		tmp = y * 4.0;
	} else if (z <= 7e-215) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-68) {
		tmp = y * 4.0;
	} else if (z <= 1.3e-8) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.0225:
		tmp = t_0
	elif z <= -8e-177:
		tmp = y * 4.0
	elif z <= -5.5e-248:
		tmp = x * -3.0
	elif z <= 1.8e-303:
		tmp = y * 4.0
	elif z <= 7e-215:
		tmp = x * -3.0
	elif z <= 5.4e-68:
		tmp = y * 4.0
	elif z <= 1.3e-8:
		tmp = x * -3.0
	elif z <= 0.62:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.0225)
		tmp = t_0;
	elseif (z <= -8e-177)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.5e-248)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.8e-303)
		tmp = Float64(y * 4.0);
	elseif (z <= 7e-215)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.4e-68)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.3e-8)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.62)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.0225)
		tmp = t_0;
	elseif (z <= -8e-177)
		tmp = y * 4.0;
	elseif (z <= -5.5e-248)
		tmp = x * -3.0;
	elseif (z <= 1.8e-303)
		tmp = y * 4.0;
	elseif (z <= 7e-215)
		tmp = x * -3.0;
	elseif (z <= 5.4e-68)
		tmp = y * 4.0;
	elseif (z <= 1.3e-8)
		tmp = x * -3.0;
	elseif (z <= 0.62)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0225], t$95$0, If[LessEqual[z, -8e-177], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.5e-248], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.8e-303], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7e-215], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.4e-68], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.3e-8], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.022499999999999999 or 0.619999999999999996 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 98.9%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 98.9%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 98.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 98.9%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 97.0%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 97.0%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 97.0%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 97.0%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 97.0%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   if -0.022499999999999999 < z < -7.99999999999999962e-177 or -5.49999999999999979e-248 < z < 1.7999999999999999e-303 or 7.0000000000000004e-215 < z < 5.4000000000000003e-68 or 1.3000000000000001e-8 < z < 0.619999999999999996

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 97.2%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around 0 63.5%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -7.99999999999999962e-177 < z < -5.49999999999999979e-248 or 1.7999999999999999e-303 < z < 7.0000000000000004e-215 or 5.4000000000000003e-68 < z < 1.3000000000000001e-8

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 77.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 77.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 77.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 77.7%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. neg-mul-1 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right)\right) \]

      5. associate-*r* 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right)\right) \]

      6. *-commutative 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      7. associate-+r+ 77.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      8. metadata-eval 77.7%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 77.7%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 77.5%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0225:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-248}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-303}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-68}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-8}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 6: 74.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -500:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-173}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-308}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-218}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-69}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6800:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -500.0)
     t_1
     (if (<= z -1.45e-173)
       t_0
       (if (<= z -1.55e-247)
         (* x -3.0)
         (if (<= z 2.6e-308)
           (* y 4.0)
           (if (<= z 2.8e-218)
             (* x -3.0)
             (if (<= z 7.2e-69)
               (* y 4.0)
               (if (<= z 1.75e-13)
                 (* x -3.0)
                 (if (<= z 6800.0) t_0 t_1))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -500.0) {
		tmp = t_1;
	} else if (z <= -1.45e-173) {
		tmp = t_0;
	} else if (z <= -1.55e-247) {
		tmp = x * -3.0;
	} else if (z <= 2.6e-308) {
		tmp = y * 4.0;
	} else if (z <= 2.8e-218) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-69) {
		tmp = y * 4.0;
	} else if (z <= 1.75e-13) {
		tmp = x * -3.0;
	} else if (z <= 6800.0) {
		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 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-500.0d0)) then
        tmp = t_1
    else if (z <= (-1.45d-173)) then
        tmp = t_0
    else if (z <= (-1.55d-247)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.6d-308) then
        tmp = y * 4.0d0
    else if (z <= 2.8d-218) then
        tmp = x * (-3.0d0)
    else if (z <= 7.2d-69) then
        tmp = y * 4.0d0
    else if (z <= 1.75d-13) then
        tmp = x * (-3.0d0)
    else if (z <= 6800.0d0) 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 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -500.0) {
		tmp = t_1;
	} else if (z <= -1.45e-173) {
		tmp = t_0;
	} else if (z <= -1.55e-247) {
		tmp = x * -3.0;
	} else if (z <= 2.6e-308) {
		tmp = y * 4.0;
	} else if (z <= 2.8e-218) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-69) {
		tmp = y * 4.0;
	} else if (z <= 1.75e-13) {
		tmp = x * -3.0;
	} else if (z <= 6800.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -500.0:
		tmp = t_1
	elif z <= -1.45e-173:
		tmp = t_0
	elif z <= -1.55e-247:
		tmp = x * -3.0
	elif z <= 2.6e-308:
		tmp = y * 4.0
	elif z <= 2.8e-218:
		tmp = x * -3.0
	elif z <= 7.2e-69:
		tmp = y * 4.0
	elif z <= 1.75e-13:
		tmp = x * -3.0
	elif z <= 6800.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -500.0)
		tmp = t_1;
	elseif (z <= -1.45e-173)
		tmp = t_0;
	elseif (z <= -1.55e-247)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.6e-308)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.8e-218)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.2e-69)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.75e-13)
		tmp = Float64(x * -3.0);
	elseif (z <= 6800.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -500.0)
		tmp = t_1;
	elseif (z <= -1.45e-173)
		tmp = t_0;
	elseif (z <= -1.55e-247)
		tmp = x * -3.0;
	elseif (z <= 2.6e-308)
		tmp = y * 4.0;
	elseif (z <= 2.8e-218)
		tmp = x * -3.0;
	elseif (z <= 7.2e-69)
		tmp = y * 4.0;
	elseif (z <= 1.75e-13)
		tmp = x * -3.0;
	elseif (z <= 6800.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -500.0], t$95$1, If[LessEqual[z, -1.45e-173], t$95$0, If[LessEqual[z, -1.55e-247], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.6e-308], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.8e-218], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.2e-69], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.75e-13], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6800.0], t$95$0, t$95$1]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -500 or 6800 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 98.9%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 98.9%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 98.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 98.9%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 98.1%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 98.1%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 98.1%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 98.1%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 98.1%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   if -500 < z < -1.4499999999999999e-173 or 1.7500000000000001e-13 < z < 6800

   1. Initial program 99.3%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. flip-+ 53.2%

         \[\leadsto \color{blue}{\frac{x \cdot x - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      2. div-inv 53.0%

         \[\leadsto \color{blue}{\left(x \cdot x - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      3. pow2 53.0%

         \[\leadsto \left(x \cdot x - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. associate-*l* 53.1%

         \[\leadsto \left(x \cdot x - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 53.2%

         \[\leadsto \left(x \cdot x - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   5. Applied egg-rr 53.2%

      \[\leadsto \color{blue}{\left(x \cdot x - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Taylor expanded in x around 0 62.5%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   if -1.4499999999999999e-173 < z < -1.55000000000000008e-247 or 2.6e-308 < z < 2.80000000000000009e-218 or 7.20000000000000035e-69 < z < 1.7500000000000001e-13

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 77.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 77.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 77.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 77.7%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. neg-mul-1 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right)\right) \]

      5. associate-*r* 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right)\right) \]

      6. *-commutative 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      7. associate-+r+ 77.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      8. metadata-eval 77.7%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 77.7%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 77.5%

      \[\leadsto x \cdot \color{blue}{-3} \]

   if -1.55000000000000008e-247 < z < 2.6e-308 or 2.80000000000000009e-218 < z < 7.20000000000000035e-69

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 100.0%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around 0 68.0%

      \[\leadsto \color{blue}{4 \cdot y} \]
3. Recombined 4 regimes into one program.

4. Final simplification 83.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -500:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-173}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-308}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{-218}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-69}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6800:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-307}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-218}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-10}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.66)
     t_0
     (if (<= z -1.45e-174)
       (* y 4.0)
       (if (<= z -3e-247)
         (* x -3.0)
         (if (<= z -1.95e-307)
           (* y 4.0)
           (if (<= z 3.9e-218)
             (* x -3.0)
             (if (<= z 1.85e-70)
               (* y 4.0)
               (if (<= z 1.5e-10)
                 (* x -3.0)
                 (if (<= z 0.66) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -1.45e-174) {
		tmp = y * 4.0;
	} else if (z <= -3e-247) {
		tmp = x * -3.0;
	} else if (z <= -1.95e-307) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-218) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-70) {
		tmp = y * 4.0;
	} else if (z <= 1.5e-10) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	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 = (-6.0d0) * (y * z)
    if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= (-1.45d-174)) then
        tmp = y * 4.0d0
    else if (z <= (-3d-247)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.95d-307)) then
        tmp = y * 4.0d0
    else if (z <= 3.9d-218) then
        tmp = x * (-3.0d0)
    else if (z <= 1.85d-70) then
        tmp = y * 4.0d0
    else if (z <= 1.5d-10) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -1.45e-174) {
		tmp = y * 4.0;
	} else if (z <= -3e-247) {
		tmp = x * -3.0;
	} else if (z <= -1.95e-307) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-218) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-70) {
		tmp = y * 4.0;
	} else if (z <= 1.5e-10) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.66:
		tmp = t_0
	elif z <= -1.45e-174:
		tmp = y * 4.0
	elif z <= -3e-247:
		tmp = x * -3.0
	elif z <= -1.95e-307:
		tmp = y * 4.0
	elif z <= 3.9e-218:
		tmp = x * -3.0
	elif z <= 1.85e-70:
		tmp = y * 4.0
	elif z <= 1.5e-10:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -1.45e-174)
		tmp = Float64(y * 4.0);
	elseif (z <= -3e-247)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.95e-307)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.9e-218)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.85e-70)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.5e-10)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -1.45e-174)
		tmp = y * 4.0;
	elseif (z <= -3e-247)
		tmp = x * -3.0;
	elseif (z <= -1.95e-307)
		tmp = y * 4.0;
	elseif (z <= 3.9e-218)
		tmp = x * -3.0;
	elseif (z <= 1.85e-70)
		tmp = y * 4.0;
	elseif (z <= 1.5e-10)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, -1.45e-174], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3e-247], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.95e-307], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.9e-218], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.85e-70], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.5e-10], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031 or 0.660000000000000031 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 98.9%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 98.9%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 98.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 98.9%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 97.0%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 97.0%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 97.0%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 97.0%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 97.0%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   9. Taylor expanded in y around inf 40.1%

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

       1. *-commutative 40.1%

          \[\leadsto -6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   11. Simplified 40.1%

       \[\leadsto \color{blue}{-6 \cdot \left(z \cdot y\right)} \]

   if -0.660000000000000031 < z < -1.45000000000000005e-174 or -2.9999999999999997e-247 < z < -1.95e-307 or 3.9e-218 < z < 1.85e-70 or 1.5e-10 < z < 0.660000000000000031

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 97.2%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around 0 63.5%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -1.45000000000000005e-174 < z < -2.9999999999999997e-247 or -1.95e-307 < z < 3.9e-218 or 1.85e-70 < z < 1.5e-10

   1. Initial program 99.4%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 77.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 77.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 77.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 77.7%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. neg-mul-1 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right)\right) \]

      5. associate-*r* 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right)\right) \]

      6. *-commutative 77.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      7. associate-+r+ 77.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      8. metadata-eval 77.7%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 77.7%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 77.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 77.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 77.5%

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

4. Final simplification 54.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-174}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-307}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-218}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-70}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-10}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 8: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.52) (+ x (* (- y x) 4.0)) (+ x (* z (* (- y x) -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (z * ((y - x) * -6.0));
	}
	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 <= (-0.55d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.52d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x + (z * ((y - x) * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (z * ((y - x) * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.52:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x + (z * ((y - x) * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.52)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.52)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x + (z * ((y - x) * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.52], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 98.9%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 98.9%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 98.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 98.9%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 95.6%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 95.6%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 95.6%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 95.6%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 95.6%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   if -0.55000000000000004 < z < 0.52000000000000002

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 98.0%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   if 0.52000000000000002 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around inf 99.1%

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

      1. associate-*r* 99.2%

         \[\leadsto x + \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.2%

         \[\leadsto x + \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

      3. associate-*l* 99.2%

         \[\leadsto x + \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

   6. Simplified 99.2%

      \[\leadsto x + \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 9: 97.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.62) (+ x (* (- y x) 4.0)) (+ x (* (- y x) (* z -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.62) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + ((y - x) * (z * -6.0));
	}
	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 <= (-0.58d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.62d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x + ((y - x) * (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.62) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + ((y - x) * (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.62:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x + ((y - x) * (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.62)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.62)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x + ((y - x) * (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.62], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 98.9%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 98.9%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 98.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 98.9%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 95.6%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 95.6%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 95.6%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 95.6%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 95.6%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   if -0.57999999999999996 < z < 0.619999999999999996

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 98.0%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   if 0.619999999999999996 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around inf 99.1%

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

      1. associate-*r* 99.2%

         \[\leadsto x + \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.2%

         \[\leadsto x + \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 99.2%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(z \cdot -6\right)} \]

      4. *-commutative 99.2%

         \[\leadsto x + \left(y - x\right) \cdot \color{blue}{\left(-6 \cdot z\right)} \]

   6. Simplified 99.2%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(-6 \cdot z\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 10: 75.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+94} \lor \neg \left(y \leq 1.7 \cdot 10^{+32}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.2e+94) (not (<= y 1.7e+32)))
   (* 6.0 (* y (- 0.6666666666666666 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+94) || !(y <= 1.7e+32)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	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 <= (-5.2d+94)) .or. (.not. (y <= 1.7d+32))) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.2e+94) || !(y <= 1.7e+32)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.2e+94) or not (y <= 1.7e+32):
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.2e+94) || !(y <= 1.7e+32))
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.2e+94) || ~((y <= 1.7e+32)))
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.2e+94], N[Not[LessEqual[y, 1.7e+32]], $MachinePrecision]], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999998e94 or 1.69999999999999989e32 < y

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. flip-+ 19.6%

         \[\leadsto \color{blue}{\frac{x \cdot x - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      2. div-inv 19.5%

         \[\leadsto \color{blue}{\left(x \cdot x - \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right) \cdot \left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      3. pow2 19.5%

         \[\leadsto \left(x \cdot x - \color{blue}{{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)\right)}^{2}}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      4. associate-*l* 19.5%

         \[\leadsto \left(x \cdot x - {\color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}}^{2}\right) \cdot \frac{1}{x - \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

      5. associate-*l* 19.6%

         \[\leadsto \left(x \cdot x - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   5. Applied egg-rr 19.6%

      \[\leadsto \color{blue}{\left(x \cdot x - {\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}^{2}\right) \cdot \frac{1}{x - \left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}} \]

   6. Taylor expanded in x around 0 84.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]

   if -5.1999999999999998e94 < y < 1.69999999999999989e32

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 79.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 79.4%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 79.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 79.4%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. neg-mul-1 79.4%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right)\right) \]

      5. associate-*r* 79.4%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right)\right) \]

      6. *-commutative 79.4%

         \[\leadsto x \cdot \left(1 + \left(-4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      7. associate-+r+ 79.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      8. metadata-eval 79.5%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 79.5%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 79.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 79.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 79.5%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+94} \lor \neg \left(y \leq 1.7 \cdot 10^{+32}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]

Alternative 11: 75.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+94} \lor \neg \left(y \leq 6 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -5.3e+94) (not (<= y 6e+31)))
   (* y (+ 4.0 (* z -6.0)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.3e+94) || !(y <= 6e+31)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	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 <= (-5.3d+94)) .or. (.not. (y <= 6d+31))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -5.3e+94) || !(y <= 6e+31)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -5.3e+94) or not (y <= 6e+31):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -5.3e+94) || !(y <= 6e+31))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -5.3e+94) || ~((y <= 6e+31)))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -5.3e+94], N[Not[LessEqual[y, 6e+31]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.30000000000000003e94 or 5.99999999999999978e31 < y

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-def 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{4} + \left(-z\right) \cdot 6, x\right) \]

      8. distribute-lft-neg-out 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{\left(-z \cdot 6\right)}, x\right) \]

      9. distribute-rgt-neg-in 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 4 + \color{blue}{z \cdot \left(-6\right)}, x\right) \]

      10. metadata-eval 99.9%

          \[\leadsto \mathsf{fma}\left(y - x, 4 + z \cdot \color{blue}{-6}, x\right) \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 4 + z \cdot -6, x\right)} \]

   4. Taylor expanded in y around inf 84.8%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   if -5.30000000000000003e94 < y < 5.99999999999999978e31

   1. Initial program 99.6%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 79.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 79.4%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 79.4%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 79.4%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. neg-mul-1 79.4%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right)\right) \]

      5. associate-*r* 79.4%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right)\right) \]

      6. *-commutative 79.4%

         \[\leadsto x \cdot \left(1 + \left(-4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      7. associate-+r+ 79.5%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      8. metadata-eval 79.5%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 79.5%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 79.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 79.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 79.5%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 81.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.3 \cdot 10^{+94} \lor \neg \left(y \leq 6 \cdot 10^{+31}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]

Alternative 12: 97.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.5)))
   (* -6.0 (* (- y x) z))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.5)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	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 <= (-0.58d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.5)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.5):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.5))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.5)))
		tmp = -6.0 * ((y - x) * z);
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.5 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]
   4. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x} \]

      2. *-commutative 99.8%

         \[\leadsto \color{blue}{\left(0.6666666666666666 - z\right) \cdot \left(\left(y - x\right) \cdot 6\right)} + x \]

      3. add-cube-cbrt 98.9%

         \[\leadsto \left(0.6666666666666666 - z\right) \cdot \color{blue}{\left(\left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)} + x \]

      4. associate-*r* 98.9%

         \[\leadsto \color{blue}{\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right)\right) \cdot \sqrt[3]{\left(y - x\right) \cdot 6}} + x \]

      5. fma-def 98.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \left(\sqrt[3]{\left(y - x\right) \cdot 6} \cdot \sqrt[3]{\left(y - x\right) \cdot 6}\right), \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

      6. pow2 98.9%

         \[\leadsto \mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot \color{blue}{{\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right) \]

   5. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(0.6666666666666666 - z\right) \cdot {\left(\sqrt[3]{\left(y - x\right) \cdot 6}\right)}^{2}, \sqrt[3]{\left(y - x\right) \cdot 6}, x\right)} \]

   6. Taylor expanded in z around inf 97.0%

      \[\leadsto \color{blue}{-6 \cdot \left({1}^{0.3333333333333333} \cdot \left(z \cdot \left(y - x\right)\right)\right)} \]
   7. Step-by-step derivation

      1. pow-base-1 97.0%

         \[\leadsto -6 \cdot \left(\color{blue}{1} \cdot \left(z \cdot \left(y - x\right)\right)\right) \]

      2. *-lft-identity 97.0%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot \left(y - x\right)\right)} \]

      3. *-commutative 97.0%

         \[\leadsto -6 \cdot \color{blue}{\left(\left(y - x\right) \cdot z\right)} \]

   8. Simplified 97.0%

      \[\leadsto \color{blue}{-6 \cdot \left(\left(y - x\right) \cdot z\right)} \]

   if -0.57999999999999996 < z < 0.5

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 98.0%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]

Alternative 13: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- 0.6666666666666666 z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - 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 + (((y - x) * 6.0d0) * (0.6666666666666666d0 - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(0.6666666666666666 - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * (0.6666666666666666 - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

4. Final simplification 99.6%

   \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \]

Alternative 14: 38.0% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-46}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-25}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.2e-46) (* y 4.0) (if (<= y 1.26e-25) (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e-46) {
		tmp = y * 4.0;
	} else if (y <= 1.26e-25) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	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 <= (-5.2d-46)) then
        tmp = y * 4.0d0
    else if (y <= 1.26d-25) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.2e-46) {
		tmp = y * 4.0;
	} else if (y <= 1.26e-25) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.2e-46:
		tmp = y * 4.0
	elif y <= 1.26e-25:
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.2e-46)
		tmp = Float64(y * 4.0);
	elseif (y <= 1.26e-25)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.2e-46)
		tmp = y * 4.0;
	elseif (y <= 1.26e-25)
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.2e-46], N[(y * 4.0), $MachinePrecision], If[LessEqual[y, 1.26e-25], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -5.2000000000000004e-46 or 1.26e-25 < y

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 53.6%

      \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

   5. Taylor expanded in x around 0 43.7%

      \[\leadsto \color{blue}{4 \cdot y} \]

   if -5.2000000000000004e-46 < y < 1.26e-25

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
   2. Step-by-step derivation

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 86.7%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 86.7%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 86.7%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 86.7%

         \[\leadsto x \cdot \left(1 + \left(\color{blue}{-4} + \left(-z\right) \cdot -6\right)\right) \]

      4. neg-mul-1 86.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{\left(-1 \cdot z\right)} \cdot -6\right)\right) \]

      5. associate-*r* 86.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + \color{blue}{-1 \cdot \left(z \cdot -6\right)}\right)\right) \]

      6. *-commutative 86.7%

         \[\leadsto x \cdot \left(1 + \left(-4 + -1 \cdot \color{blue}{\left(-6 \cdot z\right)}\right)\right) \]

      7. associate-+r+ 86.7%

         \[\leadsto x \cdot \color{blue}{\left(\left(1 + -4\right) + -1 \cdot \left(-6 \cdot z\right)\right)} \]

      8. metadata-eval 86.7%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 86.7%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 86.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 86.7%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 86.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 43.1%

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

4. Final simplification 43.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{-46}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 1.26 \cdot 10^{-25}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]

Alternative 15: 25.5% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ y \cdot 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y 4.0))

C

double code(double x, double y, double z) {
	return y * 4.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y * 4.0d0
end function

Java

public static double code(double x, double y, double z) {
	return y * 4.0;
}

Python

def code(x, y, z):
	return y * 4.0

Julia

function code(x, y, z)
	return Float64(y * 4.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = y * 4.0;
end

Wolfram

code[x_, y_, z_] := N[(y * 4.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

4. Taylor expanded in z around 0 51.9%

   \[\leadsto x + \color{blue}{4 \cdot \left(y - x\right)} \]

5. Taylor expanded in x around 0 27.0%

   \[\leadsto \color{blue}{4 \cdot y} \]

6. Final simplification 27.0%

   \[\leadsto y \cdot 4 \]

Alternative 16: 2.6% accurate, 13.0× 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 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
2. Step-by-step derivation

   1. metadata-eval 99.6%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.6%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

4. Taylor expanded in z around inf 49.2%

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

   1. associate-*r* 49.2%

      \[\leadsto x + \color{blue}{\left(-6 \cdot z\right) \cdot \left(y - x\right)} \]

   2. *-commutative 49.2%

      \[\leadsto x + \color{blue}{\left(z \cdot -6\right)} \cdot \left(y - x\right) \]

   3. associate-*l* 49.2%

      \[\leadsto x + \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

6. Simplified 49.2%

   \[\leadsto x + \color{blue}{z \cdot \left(-6 \cdot \left(y - x\right)\right)} \]

7. Taylor expanded in z around 0 2.8%

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

8. Final simplification 2.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))