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

Percentage Accurate: 99.5% → 99.8%

Time: 15.5s

Alternatives: 16

Speedup: 1.2×

• 21.0% 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: 99.8% 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 99.2%

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

   1. +-commutative 99.2%

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

   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-define 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. Add Preprocessing
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. +-commutative 99.2%

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

   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-define 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 3: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-134}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-61}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.5)
   (* x (* z 6.0))
   (if (<= z -5.5e-134)
     (* x -3.0)
     (if (<= z 5.5e-61)
       (* y 4.0)
       (if (<= z 0.65) (* x -3.0) (* z (* y -6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = x * (z * 6.0);
	} else if (z <= -5.5e-134) {
		tmp = x * -3.0;
	} else if (z <= 5.5e-61) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = z * (y * -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 <= (-0.5d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-5.5d-134)) then
        tmp = x * (-3.0d0)
    else if (z <= 5.5d-61) then
        tmp = y * 4.0d0
    else if (z <= 0.65d0) then
        tmp = x * (-3.0d0)
    else
        tmp = z * (y * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = x * (z * 6.0);
	} else if (z <= -5.5e-134) {
		tmp = x * -3.0;
	} else if (z <= 5.5e-61) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.5:
		tmp = x * (z * 6.0)
	elif z <= -5.5e-134:
		tmp = x * -3.0
	elif z <= 5.5e-61:
		tmp = y * 4.0
	elif z <= 0.65:
		tmp = x * -3.0
	else:
		tmp = z * (y * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.5)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -5.5e-134)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.5e-61)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.65)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(z * Float64(y * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.5)
		tmp = x * (z * 6.0);
	elseif (z <= -5.5e-134)
		tmp = x * -3.0;
	elseif (z <= 5.5e-61)
		tmp = y * 4.0;
	elseif (z <= 0.65)
		tmp = x * -3.0;
	else
		tmp = z * (y * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.5], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.5e-134], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.5e-61], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(x * -3.0), $MachinePrecision], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.5

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 52.5%

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

      1. *-lft-identity 52.5%

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

      2. *-commutative 52.5%

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

      3. associate-*r* 52.6%

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

      4. sub-neg 52.6%

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

      5. distribute-rgt-in 52.6%

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

      6. metadata-eval 52.6%

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

      7. neg-mul-1 52.6%

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

      8. associate-*r* 52.6%

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

      9. *-commutative 52.6%

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

      10. metadata-eval 52.6%

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

      11. distribute-lft-in 52.6%

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

      12. distribute-rgt-in 52.6%

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

      13. distribute-lft-in 52.6%

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

      14. metadata-eval 52.6%

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

      15. associate-+r+ 52.6%

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

      16. metadata-eval 52.6%

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

      17. associate-*r* 52.6%

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

      18. metadata-eval 52.6%

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

   7. Simplified 52.6%

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

   8. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-*r* 51.5%

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

   10. Simplified 51.5%

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

   if -0.5 < z < -5.5000000000000002e-134 or 5.4999999999999997e-61 < z < 0.650000000000000022

   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. +-commutative 99.3%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 60.5%

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

      1. *-lft-identity 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*r* 60.7%

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

      4. sub-neg 60.7%

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

      5. distribute-rgt-in 60.7%

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

      6. metadata-eval 60.7%

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

      7. neg-mul-1 60.7%

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

      8. associate-*r* 60.7%

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

      9. *-commutative 60.7%

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

      10. metadata-eval 60.7%

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

      11. distribute-lft-in 60.7%

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

      12. distribute-rgt-in 60.8%

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

      13. distribute-lft-in 60.8%

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

      14. metadata-eval 60.8%

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

      15. associate-+r+ 60.8%

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

      16. metadata-eval 60.8%

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

      17. associate-*r* 60.8%

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

      18. metadata-eval 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in z around 0 57.4%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 57.4%

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

   10. Simplified 57.4%

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

   if -5.5000000000000002e-134 < z < 5.4999999999999997e-61

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      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-define 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 88.5%

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

   7. Simplified 88.6%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 65.3%

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

   9. Taylor expanded in z around 0 65.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 65.3%

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

   11. Simplified 65.3%

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

   if 0.650000000000000022 < 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. +-commutative 99.8%

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

      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-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around -inf 86.5%

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

   7. Simplified 86.5%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 56.7%

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

   9. Taylor expanded in z around inf 53.9%

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

   10. Taylor expanded in y around 0 53.8%

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

       1. associate-*r* 53.9%

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

       2. *-commutative 53.9%

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

       3. *-commutative 53.9%

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

   12. Simplified 53.9%

       \[\leadsto \color{blue}{z \cdot \left(y \cdot -6\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 4: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-134}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-59}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.5)
   (* x (* z 6.0))
   (if (<= z -7.2e-134)
     (* x -3.0)
     (if (<= z 6e-59) (* y 4.0) (if (<= z 0.5) (* x -3.0) (* y (* z -6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = x * (z * 6.0);
	} else if (z <= -7.2e-134) {
		tmp = x * -3.0;
	} else if (z <= 6e-59) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = y * (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 <= (-0.5d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-7.2d-134)) then
        tmp = x * (-3.0d0)
    else if (z <= 6d-59) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = y * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = x * (z * 6.0);
	} else if (z <= -7.2e-134) {
		tmp = x * -3.0;
	} else if (z <= 6e-59) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.5:
		tmp = x * (z * 6.0)
	elif z <= -7.2e-134:
		tmp = x * -3.0
	elif z <= 6e-59:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = y * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.5)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -7.2e-134)
		tmp = Float64(x * -3.0);
	elseif (z <= 6e-59)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.5)
		tmp = x * (z * 6.0);
	elseif (z <= -7.2e-134)
		tmp = x * -3.0;
	elseif (z <= 6e-59)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = y * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.5], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.2e-134], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6e-59], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.5

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 52.5%

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

      1. *-lft-identity 52.5%

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

      2. *-commutative 52.5%

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

      3. associate-*r* 52.6%

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

      4. sub-neg 52.6%

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

      5. distribute-rgt-in 52.6%

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

      6. metadata-eval 52.6%

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

      7. neg-mul-1 52.6%

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

      8. associate-*r* 52.6%

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

      9. *-commutative 52.6%

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

      10. metadata-eval 52.6%

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

      11. distribute-lft-in 52.6%

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

      12. distribute-rgt-in 52.6%

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

      13. distribute-lft-in 52.6%

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

      14. metadata-eval 52.6%

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

      15. associate-+r+ 52.6%

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

      16. metadata-eval 52.6%

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

      17. associate-*r* 52.6%

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

      18. metadata-eval 52.6%

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

   7. Simplified 52.6%

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

   8. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-*r* 51.5%

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

   10. Simplified 51.5%

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

   if -0.5 < z < -7.1999999999999998e-134 or 6.0000000000000002e-59 < z < 0.5

   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. +-commutative 99.3%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 60.5%

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

      1. *-lft-identity 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*r* 60.7%

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

      4. sub-neg 60.7%

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

      5. distribute-rgt-in 60.7%

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

      6. metadata-eval 60.7%

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

      7. neg-mul-1 60.7%

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

      8. associate-*r* 60.7%

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

      9. *-commutative 60.7%

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

      10. metadata-eval 60.7%

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

      11. distribute-lft-in 60.7%

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

      12. distribute-rgt-in 60.8%

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

      13. distribute-lft-in 60.8%

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

      14. metadata-eval 60.8%

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

      15. associate-+r+ 60.8%

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

      16. metadata-eval 60.8%

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

      17. associate-*r* 60.8%

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

      18. metadata-eval 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in z around 0 57.4%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 57.4%

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

   10. Simplified 57.4%

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

   if -7.1999999999999998e-134 < z < 6.0000000000000002e-59

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      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-define 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 88.5%

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

   7. Simplified 88.6%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 65.3%

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

   9. Taylor expanded in z around 0 65.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 65.3%

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

   11. Simplified 65.3%

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

   if 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. +-commutative 99.8%

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

      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-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around -inf 86.5%

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

   7. Simplified 86.5%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 56.7%

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

   9. Taylor expanded in z around inf 53.9%

      \[\leadsto y \cdot \color{blue}{\left(-6 \cdot z\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-134}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-59}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-134}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-59}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.5)
   (* x (* z 6.0))
   (if (<= z -9.5e-134)
     (* x -3.0)
     (if (<= z 3.9e-59)
       (* y 4.0)
       (if (<= z 0.64) (* x -3.0) (* -6.0 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = x * (z * 6.0);
	} else if (z <= -9.5e-134) {
		tmp = x * -3.0;
	} else if (z <= 3.9e-59) {
		tmp = y * 4.0;
	} else if (z <= 0.64) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.5d0)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-9.5d-134)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.9d-59) then
        tmp = y * 4.0d0
    else if (z <= 0.64d0) then
        tmp = x * (-3.0d0)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = x * (z * 6.0);
	} else if (z <= -9.5e-134) {
		tmp = x * -3.0;
	} else if (z <= 3.9e-59) {
		tmp = y * 4.0;
	} else if (z <= 0.64) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.5:
		tmp = x * (z * 6.0)
	elif z <= -9.5e-134:
		tmp = x * -3.0
	elif z <= 3.9e-59:
		tmp = y * 4.0
	elif z <= 0.64:
		tmp = x * -3.0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.5)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -9.5e-134)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.9e-59)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.64)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.5)
		tmp = x * (z * 6.0);
	elseif (z <= -9.5e-134)
		tmp = x * -3.0;
	elseif (z <= 3.9e-59)
		tmp = y * 4.0;
	elseif (z <= 0.64)
		tmp = x * -3.0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.5], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-134], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.9e-59], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.64], N[(x * -3.0), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.5

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 52.5%

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

      1. *-lft-identity 52.5%

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

      2. *-commutative 52.5%

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

      3. associate-*r* 52.6%

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

      4. sub-neg 52.6%

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

      5. distribute-rgt-in 52.6%

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

      6. metadata-eval 52.6%

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

      7. neg-mul-1 52.6%

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

      8. associate-*r* 52.6%

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

      9. *-commutative 52.6%

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

      10. metadata-eval 52.6%

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

      11. distribute-lft-in 52.6%

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

      12. distribute-rgt-in 52.6%

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

      13. distribute-lft-in 52.6%

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

      14. metadata-eval 52.6%

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

      15. associate-+r+ 52.6%

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

      16. metadata-eval 52.6%

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

      17. associate-*r* 52.6%

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

      18. metadata-eval 52.6%

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

   7. Simplified 52.6%

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

   8. Taylor expanded in z around inf 51.5%

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

      1. *-commutative 51.5%

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

      2. associate-*r* 51.5%

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

   10. Simplified 51.5%

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

   if -0.5 < z < -9.5000000000000008e-134 or 3.90000000000000019e-59 < z < 0.640000000000000013

   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. +-commutative 99.3%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 60.5%

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

      1. *-lft-identity 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*r* 60.7%

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

      4. sub-neg 60.7%

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

      5. distribute-rgt-in 60.7%

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

      6. metadata-eval 60.7%

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

      7. neg-mul-1 60.7%

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

      8. associate-*r* 60.7%

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

      9. *-commutative 60.7%

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

      10. metadata-eval 60.7%

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

      11. distribute-lft-in 60.7%

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

      12. distribute-rgt-in 60.8%

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

      13. distribute-lft-in 60.8%

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

      14. metadata-eval 60.8%

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

      15. associate-+r+ 60.8%

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

      16. metadata-eval 60.8%

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

      17. associate-*r* 60.8%

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

      18. metadata-eval 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in z around 0 57.4%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 57.4%

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

   10. Simplified 57.4%

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

   if -9.5000000000000008e-134 < z < 3.90000000000000019e-59

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      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-define 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 88.5%

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

   7. Simplified 88.6%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 65.3%

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

   9. Taylor expanded in z around 0 65.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 65.3%

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

   11. Simplified 65.3%

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

   if 0.640000000000000013 < 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. +-commutative 99.8%

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

      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-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around -inf 86.5%

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

   7. Simplified 86.5%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 56.7%

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

   9. Taylor expanded in z around inf 53.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 6: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-134}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-60}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.5)
   (* 6.0 (* x z))
   (if (<= z -2.6e-134)
     (* x -3.0)
     (if (<= z 6e-60)
       (* y 4.0)
       (if (<= z 0.65) (* x -3.0) (* -6.0 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= -2.6e-134) {
		tmp = x * -3.0;
	} else if (z <= 6e-60) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.5d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-2.6d-134)) then
        tmp = x * (-3.0d0)
    else if (z <= 6d-60) then
        tmp = y * 4.0d0
    else if (z <= 0.65d0) then
        tmp = x * (-3.0d0)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= -2.6e-134) {
		tmp = x * -3.0;
	} else if (z <= 6e-60) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.5:
		tmp = 6.0 * (x * z)
	elif z <= -2.6e-134:
		tmp = x * -3.0
	elif z <= 6e-60:
		tmp = y * 4.0
	elif z <= 0.65:
		tmp = x * -3.0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.5)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -2.6e-134)
		tmp = Float64(x * -3.0);
	elseif (z <= 6e-60)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.65)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.5)
		tmp = 6.0 * (x * z);
	elseif (z <= -2.6e-134)
		tmp = x * -3.0;
	elseif (z <= 6e-60)
		tmp = y * 4.0;
	elseif (z <= 0.65)
		tmp = x * -3.0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.5], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.6e-134], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6e-60], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(x * -3.0), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.5

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 52.5%

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

      1. *-lft-identity 52.5%

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

      2. *-commutative 52.5%

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

      3. associate-*r* 52.6%

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

      4. sub-neg 52.6%

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

      5. distribute-rgt-in 52.6%

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

      6. metadata-eval 52.6%

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

      7. neg-mul-1 52.6%

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

      8. associate-*r* 52.6%

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

      9. *-commutative 52.6%

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

      10. metadata-eval 52.6%

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

      11. distribute-lft-in 52.6%

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

      12. distribute-rgt-in 52.6%

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

      13. distribute-lft-in 52.6%

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

      14. metadata-eval 52.6%

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

      15. associate-+r+ 52.6%

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

      16. metadata-eval 52.6%

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

      17. associate-*r* 52.6%

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

      18. metadata-eval 52.6%

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

   7. Simplified 52.6%

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

   8. Taylor expanded in z around inf 51.5%

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

   if -0.5 < z < -2.60000000000000023e-134 or 6.00000000000000038e-60 < z < 0.650000000000000022

   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. +-commutative 99.3%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 60.5%

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

      1. *-lft-identity 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*r* 60.7%

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

      4. sub-neg 60.7%

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

      5. distribute-rgt-in 60.7%

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

      6. metadata-eval 60.7%

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

      7. neg-mul-1 60.7%

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

      8. associate-*r* 60.7%

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

      9. *-commutative 60.7%

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

      10. metadata-eval 60.7%

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

      11. distribute-lft-in 60.7%

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

      12. distribute-rgt-in 60.8%

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

      13. distribute-lft-in 60.8%

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

      14. metadata-eval 60.8%

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

      15. associate-+r+ 60.8%

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

      16. metadata-eval 60.8%

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

      17. associate-*r* 60.8%

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

      18. metadata-eval 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in z around 0 57.4%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 57.4%

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

   10. Simplified 57.4%

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

   if -2.60000000000000023e-134 < z < 6.00000000000000038e-60

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      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-define 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 88.5%

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

   7. Simplified 88.6%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 65.3%

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

   9. Taylor expanded in z around 0 65.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 65.3%

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

   11. Simplified 65.3%

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

   if 0.650000000000000022 < 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. +-commutative 99.8%

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

      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-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around -inf 86.5%

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

   7. Simplified 86.5%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 56.7%

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

   9. Taylor expanded in z around inf 53.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 7: 50.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.4 \cdot 10^{-134}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-60}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.5)
     t_0
     (if (<= z -8.4e-134)
       (* x -3.0)
       (if (<= z 7.2e-60) (* y 4.0) (if (<= z 0.65) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -8.4e-134) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-60) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} 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 <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-8.4d-134)) then
        tmp = x * (-3.0d0)
    else if (z <= 7.2d-60) then
        tmp = y * 4.0d0
    else if (z <= 0.65d0) then
        tmp = x * (-3.0d0)
    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 <= -0.5) {
		tmp = t_0;
	} else if (z <= -8.4e-134) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-60) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.5:
		tmp = t_0
	elif z <= -8.4e-134:
		tmp = x * -3.0
	elif z <= 7.2e-60:
		tmp = y * 4.0
	elif z <= 0.65:
		tmp = x * -3.0
	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 <= -0.5)
		tmp = t_0;
	elseif (z <= -8.4e-134)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.2e-60)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.65)
		tmp = Float64(x * -3.0);
	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 <= -0.5)
		tmp = t_0;
	elseif (z <= -8.4e-134)
		tmp = x * -3.0;
	elseif (z <= 7.2e-60)
		tmp = y * 4.0;
	elseif (z <= 0.65)
		tmp = x * -3.0;
	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, -0.5], t$95$0, If[LessEqual[z, -8.4e-134], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.2e-60], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.650000000000000022 < 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. +-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* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around -inf 89.1%

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

   7. Simplified 88.2%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 53.8%

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

   9. Taylor expanded in z around inf 50.7%

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

   if -0.5 < z < -8.3999999999999996e-134 or 7.2e-60 < z < 0.650000000000000022

   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. +-commutative 99.3%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 60.5%

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

      1. *-lft-identity 60.5%

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

      2. *-commutative 60.5%

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

      3. associate-*r* 60.7%

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

      4. sub-neg 60.7%

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

      5. distribute-rgt-in 60.7%

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

      6. metadata-eval 60.7%

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

      7. neg-mul-1 60.7%

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

      8. associate-*r* 60.7%

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

      9. *-commutative 60.7%

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

      10. metadata-eval 60.7%

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

      11. distribute-lft-in 60.7%

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

      12. distribute-rgt-in 60.8%

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

      13. distribute-lft-in 60.8%

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

      14. metadata-eval 60.8%

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

      15. associate-+r+ 60.8%

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

      16. metadata-eval 60.8%

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

      17. associate-*r* 60.8%

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

      18. metadata-eval 60.8%

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

   7. Simplified 60.8%

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

   8. Taylor expanded in z around 0 57.4%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 57.4%

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

   10. Simplified 57.4%

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

   if -8.3999999999999996e-134 < z < 7.2e-60

   1. Initial program 98.5%

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

      1. +-commutative 98.5%

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

      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-define 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 88.5%

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

   7. Simplified 88.6%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 65.3%

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

   9. Taylor expanded in z around 0 65.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 65.3%

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

   11. Simplified 65.3%

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

Alternative 8: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.66 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.66) (not (<= z 0.6)))
   (+ x (* (- y x) (* z -6.0)))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.66) || !(z <= 0.6)) {
		tmp = x + ((y - x) * (z * -6.0));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	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 <= (-0.66d0)) .or. (.not. (z <= 0.6d0))) then
        tmp = x + ((y - x) * (z * (-6.0d0)))
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.66) || !(z <= 0.6)) {
		tmp = x + ((y - x) * (z * -6.0));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.66) or not (z <= 0.6):
		tmp = x + ((y - x) * (z * -6.0))
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.66) || !(z <= 0.6))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.66) || ~((z <= 0.6)))
		tmp = x + ((y - x) * (z * -6.0));
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.66], N[Not[LessEqual[z, 0.6]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.660000000000000031 or 0.599999999999999978 < 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. +-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* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 95.6%

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

   if -0.660000000000000031 < z < 0.599999999999999978

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      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-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 99.3%

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

      1. associate-*r* 99.4%

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

      2. associate-*r* 98.8%

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

      3. *-commutative 98.8%

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

      4. distribute-rgt-out 98.8%

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

      5. *-commutative 98.8%

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

   9. Simplified 98.8%

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

   10. Taylor expanded in z around 0 96.8%

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

   11. Taylor expanded in x around 0 97.9%

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

4. Final simplification 96.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.66 \lor \neg \left(z \leq 0.58\right):\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.66) (not (<= z 0.58)))
   (+ x (* -6.0 (* (- y x) z)))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.66) || !(z <= 0.58)) {
		tmp = x + (-6.0 * ((y - x) * z));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	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 <= (-0.66d0)) .or. (.not. (z <= 0.58d0))) then
        tmp = x + ((-6.0d0) * ((y - x) * z))
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.66) || !(z <= 0.58)) {
		tmp = x + (-6.0 * ((y - x) * z));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.66) or not (z <= 0.58):
		tmp = x + (-6.0 * ((y - x) * z))
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.66) || !(z <= 0.58))
		tmp = Float64(x + Float64(-6.0 * Float64(Float64(y - x) * z)));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.66) || ~((z <= 0.58)))
		tmp = x + (-6.0 * ((y - x) * z));
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.66], N[Not[LessEqual[z, 0.58]], $MachinePrecision]], N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.660000000000000031 or 0.57999999999999996 < 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. Add Preprocessing

   5. Taylor expanded in z around inf 95.5%

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

   if -0.660000000000000031 < z < 0.57999999999999996

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      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-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 99.3%

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

      1. associate-*r* 99.4%

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

      2. associate-*r* 98.8%

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

      3. *-commutative 98.8%

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

      4. distribute-rgt-out 98.8%

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

      5. *-commutative 98.8%

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

   9. Simplified 98.8%

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

   10. Taylor expanded in z around 0 96.8%

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

   11. Taylor expanded in x around 0 97.9%

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

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66 \lor \neg \left(z \leq 0.58\right):\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-81} \lor \neg \left(y \leq 1.05 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.5e-81) (not (<= y 1.05e-29)))
   (* y (* 6.0 (- 0.6666666666666666 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.5e-81) || !(y <= 1.05e-29)) {
		tmp = y * (6.0 * (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 <= (-9.5d-81)) .or. (.not. (y <= 1.05d-29))) then
        tmp = y * (6.0d0 * (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 <= -9.5e-81) || !(y <= 1.05e-29)) {
		tmp = y * (6.0 * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.5e-81) or not (y <= 1.05e-29):
		tmp = y * (6.0 * (0.6666666666666666 - z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.5e-81) || !(y <= 1.05e-29))
		tmp = Float64(y * Float64(6.0 * 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 <= -9.5e-81) || ~((y <= 1.05e-29)))
		tmp = y * (6.0 * (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, -9.5e-81], N[Not[LessEqual[y, 1.05e-29]], $MachinePrecision]], N[(y * N[(6.0 * 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 < -9.49999999999999917e-81 or 1.04999999999999995e-29 < y

   1. Initial program 99.0%

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

      1. +-commutative 99.0%

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

      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-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around -inf 98.5%

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

   7. Simplified 97.8%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 79.8%

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

      1. sub-neg 79.8%

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

      2. metadata-eval 79.8%

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

      3. distribute-rgt-neg-in 79.8%

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

      4. distribute-lft-in 79.8%

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

      5. sub-neg 79.8%

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

      6. *-commutative 79.8%

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

   10. Applied egg-rr 79.8%

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

   if -9.49999999999999917e-81 < y < 1.04999999999999995e-29

   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. +-commutative 99.5%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 78.3%

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

      1. *-lft-identity 78.3%

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

      2. *-commutative 78.3%

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

      3. associate-*r* 78.6%

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

      4. sub-neg 78.6%

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

      5. distribute-rgt-in 78.6%

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

      6. metadata-eval 78.6%

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

      7. neg-mul-1 78.6%

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

      8. associate-*r* 78.6%

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

      9. *-commutative 78.6%

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

      10. metadata-eval 78.6%

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

      11. distribute-lft-in 78.6%

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

      12. distribute-rgt-in 78.7%

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

      13. distribute-lft-in 78.7%

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

      14. metadata-eval 78.7%

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

      15. associate-+r+ 78.7%

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

      16. metadata-eval 78.7%

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

      17. associate-*r* 78.7%

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

      18. metadata-eval 78.7%

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

   7. Simplified 78.7%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.5 \cdot 10^{-81} \lor \neg \left(y \leq 1.05 \cdot 10^{-29}\right):\\ \;\;\;\;y \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+106} \lor \neg \left(y \leq 1.7 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.8e+106) (not (<= y 1.7e+41)))
   (* y 4.0)
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.8e+106) || !(y <= 1.7e+41)) {
		tmp = y * 4.0;
	} 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 <= (-1.8d+106)) .or. (.not. (y <= 1.7d+41))) then
        tmp = y * 4.0d0
    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 <= -1.8e+106) || !(y <= 1.7e+41)) {
		tmp = y * 4.0;
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.8e+106) or not (y <= 1.7e+41):
		tmp = y * 4.0
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.8e+106) || !(y <= 1.7e+41))
		tmp = Float64(y * 4.0);
	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 <= -1.8e+106) || ~((y <= 1.7e+41)))
		tmp = y * 4.0;
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.8e+106], N[Not[LessEqual[y, 1.7e+41]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e106 or 1.69999999999999999e41 < y

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      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-define 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 98.9%

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

   7. Simplified 97.9%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 88.9%

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

   9. Taylor expanded in z around 0 53.8%

      \[\leadsto \color{blue}{4 \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 53.8%

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

   11. Simplified 53.8%

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

   if -1.8e106 < y < 1.69999999999999999e41

   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. +-commutative 99.5%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 67.5%

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

      1. *-lft-identity 67.5%

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

      2. *-commutative 67.5%

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

      3. associate-*r* 67.7%

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

      4. sub-neg 67.7%

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

      5. distribute-rgt-in 67.7%

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

      6. metadata-eval 67.7%

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

      7. neg-mul-1 67.7%

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

      8. associate-*r* 67.7%

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

      9. *-commutative 67.7%

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

      10. metadata-eval 67.7%

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

      11. distribute-lft-in 67.7%

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

      12. distribute-rgt-in 67.7%

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

      13. distribute-lft-in 67.7%

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

      14. metadata-eval 67.7%

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

      15. associate-+r+ 67.7%

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

      16. metadata-eval 67.7%

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

      17. associate-*r* 67.7%

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

      18. metadata-eval 67.7%

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

   7. Simplified 67.7%

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

4. Final simplification 62.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+106} \lor \neg \left(y \leq 1.7 \cdot 10^{+41}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+104} \lor \neg \left(y \leq 1.5 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -2.5e+104) (not (<= y 1.5e+32))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e+104) || !(y <= 1.5e+32)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	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 <= (-2.5d+104)) .or. (.not. (y <= 1.5d+32))) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -2.5e+104) || !(y <= 1.5e+32)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -2.5e+104) or not (y <= 1.5e+32):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -2.5e+104) || !(y <= 1.5e+32))
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -2.5e+104) || ~((y <= 1.5e+32)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -2.5e+104], N[Not[LessEqual[y, 1.5e+32]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.4999999999999998e104 or 1.5e32 < y

   1. Initial program 98.8%

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

      1. +-commutative 98.8%

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

      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-define 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around -inf 98.9%

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

   7. Simplified 97.9%

      \[\leadsto \color{blue}{y \cdot \left(-\left(\left(-4 + 6 \cdot z\right) - \frac{x \cdot \left(-3 + 6 \cdot z\right)}{y}\right)\right)} \]

   8. Taylor expanded in y around inf 88.2%

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

   9. Taylor expanded in z around 0 53.3%

      \[\leadsto \color{blue}{4 \cdot y} \]
   10. Step-by-step derivation

       1. *-commutative 53.3%

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

   11. Simplified 53.3%

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

   if -2.4999999999999998e104 < y < 1.5e32

   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. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 67.8%

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

      1. *-lft-identity 67.8%

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

      2. *-commutative 67.8%

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

      3. associate-*r* 68.0%

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

      4. sub-neg 68.0%

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

      5. distribute-rgt-in 68.0%

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

      6. metadata-eval 68.0%

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

      7. neg-mul-1 68.0%

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

      8. associate-*r* 68.0%

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

      9. *-commutative 68.0%

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

      10. metadata-eval 68.0%

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

      11. distribute-lft-in 68.0%

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

      12. distribute-rgt-in 68.1%

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

      13. distribute-lft-in 68.1%

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

      14. metadata-eval 68.1%

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

      15. associate-+r+ 68.1%

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

      16. metadata-eval 68.1%

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

      17. associate-*r* 68.1%

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

      18. metadata-eval 68.1%

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

   7. Simplified 68.1%

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

   8. Taylor expanded in z around 0 38.6%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   9. Step-by-step derivation

      1. *-commutative 38.6%

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

   10. Simplified 38.6%

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

4. Final simplification 44.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.5 \cdot 10^{+104} \lor \neg \left(y \leq 1.5 \cdot 10^{+32}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.8% accurate, 1.2× speedup

Math

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

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(y - x) * Float64(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[(y - x), $MachinePrecision] * N[(6.0 * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

   1. +-commutative 99.2%

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

   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-define 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. fma-undefine 99.8%

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

6. Applied egg-rr 99.8%

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

7. Final simplification 99.8%

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

Alternative 14: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((0.6666666666666666d0 - z) * ((y - x) * 6.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 15: 26.0% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (-3.0d0)
end function

Java

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

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.2%

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

   1. +-commutative 99.2%

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

   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-define 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around 0 46.8%

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

   1. *-lft-identity 46.8%

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

   2. *-commutative 46.8%

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

   3. associate-*r* 47.0%

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

   4. sub-neg 47.0%

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

   5. distribute-rgt-in 47.0%

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

   6. metadata-eval 47.0%

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

   7. neg-mul-1 47.0%

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

   8. associate-*r* 47.0%

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

   9. *-commutative 47.0%

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

   10. metadata-eval 47.0%

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

   11. distribute-lft-in 47.0%

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

   12. distribute-rgt-in 47.0%

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

   13. distribute-lft-in 47.0%

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

   14. metadata-eval 47.0%

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

   15. associate-+r+ 47.0%

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

   16. metadata-eval 47.0%

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

   17. associate-*r* 47.0%

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

   18. metadata-eval 47.0%

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

7. Simplified 47.0%

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

8. Taylor expanded in z around 0 25.6%

   \[\leadsto \color{blue}{-3 \cdot x} \]
9. Step-by-step derivation

   1. *-commutative 25.6%

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

10. Simplified 25.6%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

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 99.2%

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

   1. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in y around inf 54.1%

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

6. Taylor expanded in x around inf 2.5%

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

Reproduce

herbie shell --seed 2024152 
(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))))