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

Percentage Accurate: 99.5% → 99.8%

Time: 18.1s

Alternatives: 17

Speedup: 1.2×

• 21.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. sub-neg 99.7%

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

   5. +-commutative 99.7%

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

   6. distribute-lft-in 99.7%

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

   7. distribute-rgt-neg-out 99.7%

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

   8. *-commutative 99.7%

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

   9. distribute-rgt-neg-in 99.7%

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

   10. fma-define 99.7%

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

   11. metadata-eval 99.7%

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

   12. metadata-eval 99.7%

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

   13. metadata-eval 99.7%

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

3. Simplified 99.7%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

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 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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. sub-neg 99.7%

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

   5. distribute-rgt-in 99.7%

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

   6. metadata-eval 99.7%

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

   7. metadata-eval 99.7%

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

   8. distribute-lft-neg-out 99.7%

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

   9. distribute-rgt-neg-in 99.7%

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

   10. metadata-eval 99.7%

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

3. Simplified 99.7%

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

Alternative 3: 51.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.118:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+182}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.85e+194)
   (* z (* x 6.0))
   (if (<= z -0.118)
     (* z (* y -6.0))
     (if (<= z -4e-299)
       (* x -3.0)
       (if (<= z 6.4e-125)
         (* y 4.0)
         (if (<= z 1.4e-6)
           (* x -3.0)
           (if (<= z 4.5e+182) (* 6.0 (* x z)) (* -6.0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.85e+194) {
		tmp = z * (x * 6.0);
	} else if (z <= -0.118) {
		tmp = z * (y * -6.0);
	} else if (z <= -4e-299) {
		tmp = x * -3.0;
	} else if (z <= 6.4e-125) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-6) {
		tmp = x * -3.0;
	} else if (z <= 4.5e+182) {
		tmp = 6.0 * (x * z);
	} 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 <= (-1.85d+194)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-0.118d0)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-4d-299)) then
        tmp = x * (-3.0d0)
    else if (z <= 6.4d-125) then
        tmp = y * 4.0d0
    else if (z <= 1.4d-6) then
        tmp = x * (-3.0d0)
    else if (z <= 4.5d+182) then
        tmp = 6.0d0 * (x * z)
    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 <= -1.85e+194) {
		tmp = z * (x * 6.0);
	} else if (z <= -0.118) {
		tmp = z * (y * -6.0);
	} else if (z <= -4e-299) {
		tmp = x * -3.0;
	} else if (z <= 6.4e-125) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-6) {
		tmp = x * -3.0;
	} else if (z <= 4.5e+182) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.85e+194:
		tmp = z * (x * 6.0)
	elif z <= -0.118:
		tmp = z * (y * -6.0)
	elif z <= -4e-299:
		tmp = x * -3.0
	elif z <= 6.4e-125:
		tmp = y * 4.0
	elif z <= 1.4e-6:
		tmp = x * -3.0
	elif z <= 4.5e+182:
		tmp = 6.0 * (x * z)
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.85e+194)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -0.118)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -4e-299)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.4e-125)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.4e-6)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.5e+182)
		tmp = Float64(6.0 * Float64(x * z));
	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 <= -1.85e+194)
		tmp = z * (x * 6.0);
	elseif (z <= -0.118)
		tmp = z * (y * -6.0);
	elseif (z <= -4e-299)
		tmp = x * -3.0;
	elseif (z <= 6.4e-125)
		tmp = y * 4.0;
	elseif (z <= 1.4e-6)
		tmp = x * -3.0;
	elseif (z <= 4.5e+182)
		tmp = 6.0 * (x * z);
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.85e+194], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.118], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4e-299], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.4e-125], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.4e-6], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.5e+182], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.8500000000000001e194

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      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. Taylor expanded in y around 0 63.2%

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

      1. *-lft-identity 63.2%

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

      2. *-commutative 63.2%

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

      3. +-commutative 63.2%

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

      4. *-commutative 63.2%

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

      5. fma-define 63.3%

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

      6. associate-*r* 63.3%

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

      7. neg-mul-1 63.3%

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

      8. fma-define 63.2%

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

      9. distribute-neg-in 63.2%

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

      10. distribute-lft-neg-in 63.2%

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

      11. metadata-eval 63.2%

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

      12. metadata-eval 63.2%

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

      13. distribute-rgt-in 63.2%

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

      14. +-commutative 63.2%

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

      15. sub-neg 63.2%

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

      16. distribute-rgt-in 63.2%

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

      17. sub-neg 63.2%

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

      18. distribute-rgt-in 63.2%

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

      19. metadata-eval 63.2%

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

      20. distribute-lft-neg-in 63.2%

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

      21. associate-+r+ 63.2%

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

   7. Simplified 63.2%

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

   8. Taylor expanded in z around inf 63.4%

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

   9. Taylor expanded in z around inf 63.4%

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

       1. *-commutative 63.4%

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

   11. Simplified 63.4%

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

   if -1.8500000000000001e194 < z < -0.11799999999999999

   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. Step-by-step derivation

      1. add-sqr-sqrt 47.4%

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

      2. fma-define 47.4%

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

      3. associate-*l* 47.3%

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

   6. Applied egg-rr 47.3%

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

   7. Taylor expanded in z around inf 96.2%

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

   8. Taylor expanded in y around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-*r* 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*r* 58.9%

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

   10. Simplified 58.9%

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

   if -0.11799999999999999 < z < -3.99999999999999997e-299 or 6.3999999999999997e-125 < z < 1.39999999999999994e-6

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 57.6%

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

      1. *-lft-identity 57.6%

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

      2. *-commutative 57.6%

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

      3. +-commutative 57.6%

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

      4. *-commutative 57.6%

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

      5. fma-define 57.6%

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

      6. associate-*r* 57.6%

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

      7. neg-mul-1 57.6%

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

      8. fma-define 57.6%

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

      9. distribute-neg-in 57.6%

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

      10. distribute-lft-neg-in 57.6%

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

      11. metadata-eval 57.6%

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

      12. metadata-eval 57.6%

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

      13. distribute-rgt-in 57.5%

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

      14. +-commutative 57.5%

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

      15. sub-neg 57.5%

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

      16. distribute-rgt-in 57.5%

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

      17. sub-neg 57.5%

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

      18. distribute-rgt-in 57.6%

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

      19. metadata-eval 57.6%

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

      20. distribute-lft-neg-in 57.6%

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

      21. associate-+r+ 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in z around 0 57.3%

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

      1. *-commutative 57.3%

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

   10. Simplified 57.3%

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

   if -3.99999999999999997e-299 < z < 6.3999999999999997e-125

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 65.1%

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

   if 1.39999999999999994e-6 < z < 4.50000000000000029e182

   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* 99.5%

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

      3. fma-define 99.6%

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

      4. sub-neg 99.6%

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

      5. distribute-rgt-in 99.5%

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

      6. metadata-eval 99.5%

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

      7. metadata-eval 99.5%

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

      8. distribute-lft-neg-out 99.5%

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

      9. distribute-rgt-neg-in 99.5%

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

      10. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 57.5%

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

      1. *-lft-identity 57.5%

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

      2. *-commutative 57.5%

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

      3. +-commutative 57.5%

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

      4. *-commutative 57.5%

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

      5. fma-define 57.5%

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

      6. associate-*r* 57.5%

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

      7. neg-mul-1 57.5%

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

      8. fma-define 57.5%

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

      9. distribute-neg-in 57.5%

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

      10. distribute-lft-neg-in 57.5%

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

      11. metadata-eval 57.5%

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

      12. metadata-eval 57.5%

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

      13. distribute-rgt-in 57.5%

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

      14. +-commutative 57.5%

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

      15. sub-neg 57.5%

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

      16. distribute-rgt-in 57.6%

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

      17. sub-neg 57.6%

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

      18. distribute-rgt-in 57.5%

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

      19. metadata-eval 57.5%

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

      20. distribute-lft-neg-in 57.5%

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

      21. associate-+r+ 57.5%

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

   7. Simplified 57.5%

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

   8. Taylor expanded in z around inf 57.5%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(6 - 3 \cdot \frac{1}{z}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 57.5%

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

      2. metadata-eval 57.5%

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

   10. Simplified 57.5%

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

   11. Taylor expanded in z around inf 56.0%

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

   if 4.50000000000000029e182 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. add-sqr-sqrt 39.9%

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

      2. fma-define 39.9%

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

      3. associate-*l* 40.0%

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

   6. Applied egg-rr 40.0%

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

   7. Taylor expanded in z around inf 99.9%

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

   8. Taylor expanded in y around inf 64.9%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.85 \cdot 10^{+194}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.118:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-299}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+182}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -5.1 \cdot 10^{+199}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.22:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+184}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -5.1e+199)
     t_0
     (if (<= z -0.22)
       (* z (* y -6.0))
       (if (<= z -6.6e-298)
         (* x -3.0)
         (if (<= z 5e-125)
           (* y 4.0)
           (if (<= z 1.4e-6)
             (* x -3.0)
             (if (<= z 2e+184) t_0 (* -6.0 (* y z))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -5.1e+199) {
		tmp = t_0;
	} else if (z <= -0.22) {
		tmp = z * (y * -6.0);
	} else if (z <= -6.6e-298) {
		tmp = x * -3.0;
	} else if (z <= 5e-125) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-6) {
		tmp = x * -3.0;
	} else if (z <= 2e+184) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-5.1d+199)) then
        tmp = t_0
    else if (z <= (-0.22d0)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-6.6d-298)) then
        tmp = x * (-3.0d0)
    else if (z <= 5d-125) then
        tmp = y * 4.0d0
    else if (z <= 1.4d-6) then
        tmp = x * (-3.0d0)
    else if (z <= 2d+184) then
        tmp = t_0
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -5.1e+199) {
		tmp = t_0;
	} else if (z <= -0.22) {
		tmp = z * (y * -6.0);
	} else if (z <= -6.6e-298) {
		tmp = x * -3.0;
	} else if (z <= 5e-125) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-6) {
		tmp = x * -3.0;
	} else if (z <= 2e+184) {
		tmp = t_0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -5.1e+199:
		tmp = t_0
	elif z <= -0.22:
		tmp = z * (y * -6.0)
	elif z <= -6.6e-298:
		tmp = x * -3.0
	elif z <= 5e-125:
		tmp = y * 4.0
	elif z <= 1.4e-6:
		tmp = x * -3.0
	elif z <= 2e+184:
		tmp = t_0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -5.1e+199)
		tmp = t_0;
	elseif (z <= -0.22)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -6.6e-298)
		tmp = Float64(x * -3.0);
	elseif (z <= 5e-125)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.4e-6)
		tmp = Float64(x * -3.0);
	elseif (z <= 2e+184)
		tmp = t_0;
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -5.1e+199)
		tmp = t_0;
	elseif (z <= -0.22)
		tmp = z * (y * -6.0);
	elseif (z <= -6.6e-298)
		tmp = x * -3.0;
	elseif (z <= 5e-125)
		tmp = y * 4.0;
	elseif (z <= 1.4e-6)
		tmp = x * -3.0;
	elseif (z <= 2e+184)
		tmp = t_0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.1e+199], t$95$0, If[LessEqual[z, -0.22], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.6e-298], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5e-125], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.4e-6], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2e+184], t$95$0, N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.10000000000000005e199 or 1.39999999999999994e-6 < z < 2.00000000000000003e184

   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. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 59.8%

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

      1. *-lft-identity 59.8%

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

      2. *-commutative 59.8%

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

      3. +-commutative 59.8%

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

      4. *-commutative 59.8%

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

      5. fma-define 59.8%

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

      6. associate-*r* 59.8%

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

      7. neg-mul-1 59.8%

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

      8. fma-define 59.8%

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

      9. distribute-neg-in 59.8%

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

      10. distribute-lft-neg-in 59.8%

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

      11. metadata-eval 59.8%

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

      12. metadata-eval 59.8%

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

      13. distribute-rgt-in 59.8%

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

      14. +-commutative 59.8%

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

      15. sub-neg 59.8%

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

      16. distribute-rgt-in 59.8%

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

      17. sub-neg 59.8%

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

      18. distribute-rgt-in 59.8%

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

      19. metadata-eval 59.8%

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

      20. distribute-lft-neg-in 59.8%

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

      21. associate-+r+ 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in z around inf 59.8%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(6 - 3 \cdot \frac{1}{z}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 59.8%

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

      2. metadata-eval 59.8%

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

   10. Simplified 59.8%

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

   11. Taylor expanded in z around inf 58.9%

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

   if -5.10000000000000005e199 < z < -0.220000000000000001

   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. Step-by-step derivation

      1. add-sqr-sqrt 47.4%

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

      2. fma-define 47.4%

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

      3. associate-*l* 47.3%

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

   6. Applied egg-rr 47.3%

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

   7. Taylor expanded in z around inf 96.2%

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

   8. Taylor expanded in y around inf 58.8%

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

      1. *-commutative 58.8%

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

      2. associate-*r* 58.8%

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

      3. *-commutative 58.8%

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

      4. associate-*r* 58.9%

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

   10. Simplified 58.9%

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

   if -0.220000000000000001 < z < -6.6000000000000004e-298 or 4.99999999999999967e-125 < z < 1.39999999999999994e-6

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 57.6%

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

      1. *-lft-identity 57.6%

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

      2. *-commutative 57.6%

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

      3. +-commutative 57.6%

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

      4. *-commutative 57.6%

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

      5. fma-define 57.6%

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

      6. associate-*r* 57.6%

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

      7. neg-mul-1 57.6%

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

      8. fma-define 57.6%

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

      9. distribute-neg-in 57.6%

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

      10. distribute-lft-neg-in 57.6%

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

      11. metadata-eval 57.6%

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

      12. metadata-eval 57.6%

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

      13. distribute-rgt-in 57.5%

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

      14. +-commutative 57.5%

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

      15. sub-neg 57.5%

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

      16. distribute-rgt-in 57.5%

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

      17. sub-neg 57.5%

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

      18. distribute-rgt-in 57.6%

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

      19. metadata-eval 57.6%

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

      20. distribute-lft-neg-in 57.6%

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

      21. associate-+r+ 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in z around 0 57.3%

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

      1. *-commutative 57.3%

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

   10. Simplified 57.3%

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

   if -6.6000000000000004e-298 < z < 4.99999999999999967e-125

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 65.1%

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

   if 2.00000000000000003e184 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. add-sqr-sqrt 39.9%

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

      2. fma-define 39.9%

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

      3. associate-*l* 40.0%

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

   6. Applied egg-rr 40.0%

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

   7. Taylor expanded in z around inf 99.9%

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

   8. Taylor expanded in y around inf 64.9%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.1 \cdot 10^{+199}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.22:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-298}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+184}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+192}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.048:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+183}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -4.6e+192)
     t_0
     (if (<= z -0.048)
       t_1
       (if (<= z -2.4e-296)
         (* x -3.0)
         (if (<= z 3.3e-125)
           (* y 4.0)
           (if (<= z 1.4e-6) (* x -3.0) (if (<= z 2.1e+183) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -4.6e+192) {
		tmp = t_0;
	} else if (z <= -0.048) {
		tmp = t_1;
	} else if (z <= -2.4e-296) {
		tmp = x * -3.0;
	} else if (z <= 3.3e-125) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-6) {
		tmp = x * -3.0;
	} else if (z <= 2.1e+183) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-4.6d+192)) then
        tmp = t_0
    else if (z <= (-0.048d0)) then
        tmp = t_1
    else if (z <= (-2.4d-296)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.3d-125) then
        tmp = y * 4.0d0
    else if (z <= 1.4d-6) then
        tmp = x * (-3.0d0)
    else if (z <= 2.1d+183) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -4.6e+192) {
		tmp = t_0;
	} else if (z <= -0.048) {
		tmp = t_1;
	} else if (z <= -2.4e-296) {
		tmp = x * -3.0;
	} else if (z <= 3.3e-125) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-6) {
		tmp = x * -3.0;
	} else if (z <= 2.1e+183) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -4.6e+192:
		tmp = t_0
	elif z <= -0.048:
		tmp = t_1
	elif z <= -2.4e-296:
		tmp = x * -3.0
	elif z <= 3.3e-125:
		tmp = y * 4.0
	elif z <= 1.4e-6:
		tmp = x * -3.0
	elif z <= 2.1e+183:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -4.6e+192)
		tmp = t_0;
	elseif (z <= -0.048)
		tmp = t_1;
	elseif (z <= -2.4e-296)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.3e-125)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.4e-6)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.1e+183)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -4.6e+192)
		tmp = t_0;
	elseif (z <= -0.048)
		tmp = t_1;
	elseif (z <= -2.4e-296)
		tmp = x * -3.0;
	elseif (z <= 3.3e-125)
		tmp = y * 4.0;
	elseif (z <= 1.4e-6)
		tmp = x * -3.0;
	elseif (z <= 2.1e+183)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+192], t$95$0, If[LessEqual[z, -0.048], t$95$1, If[LessEqual[z, -2.4e-296], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.3e-125], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.4e-6], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.1e+183], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5999999999999999e192 or 1.39999999999999994e-6 < z < 2.1e183

   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. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 59.8%

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

      1. *-lft-identity 59.8%

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

      2. *-commutative 59.8%

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

      3. +-commutative 59.8%

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

      4. *-commutative 59.8%

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

      5. fma-define 59.8%

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

      6. associate-*r* 59.8%

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

      7. neg-mul-1 59.8%

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

      8. fma-define 59.8%

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

      9. distribute-neg-in 59.8%

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

      10. distribute-lft-neg-in 59.8%

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

      11. metadata-eval 59.8%

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

      12. metadata-eval 59.8%

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

      13. distribute-rgt-in 59.8%

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

      14. +-commutative 59.8%

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

      15. sub-neg 59.8%

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

      16. distribute-rgt-in 59.8%

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

      17. sub-neg 59.8%

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

      18. distribute-rgt-in 59.8%

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

      19. metadata-eval 59.8%

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

      20. distribute-lft-neg-in 59.8%

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

      21. associate-+r+ 59.8%

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

   7. Simplified 59.8%

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

   8. Taylor expanded in z around inf 59.8%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(6 - 3 \cdot \frac{1}{z}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 59.8%

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

      2. metadata-eval 59.8%

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

   10. Simplified 59.8%

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

   11. Taylor expanded in z around inf 58.9%

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

   if -4.5999999999999999e192 < z < -0.048000000000000001 or 2.1e183 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. add-sqr-sqrt 44.5%

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

      2. fma-define 44.5%

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

      3. associate-*l* 44.5%

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

   6. Applied egg-rr 44.5%

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

   7. Taylor expanded in z around inf 97.6%

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

   8. Taylor expanded in y around inf 61.1%

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

   if -0.048000000000000001 < z < -2.39999999999999996e-296 or 3.3000000000000001e-125 < z < 1.39999999999999994e-6

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 57.6%

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

      1. *-lft-identity 57.6%

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

      2. *-commutative 57.6%

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

      3. +-commutative 57.6%

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

      4. *-commutative 57.6%

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

      5. fma-define 57.6%

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

      6. associate-*r* 57.6%

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

      7. neg-mul-1 57.6%

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

      8. fma-define 57.6%

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

      9. distribute-neg-in 57.6%

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

      10. distribute-lft-neg-in 57.6%

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

      11. metadata-eval 57.6%

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

      12. metadata-eval 57.6%

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

      13. distribute-rgt-in 57.5%

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

      14. +-commutative 57.5%

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

      15. sub-neg 57.5%

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

      16. distribute-rgt-in 57.5%

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

      17. sub-neg 57.5%

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

      18. distribute-rgt-in 57.6%

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

      19. metadata-eval 57.6%

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

      20. distribute-lft-neg-in 57.6%

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

      21. associate-+r+ 57.6%

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

   7. Simplified 57.6%

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

   8. Taylor expanded in z around 0 57.3%

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

      1. *-commutative 57.3%

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

   10. Simplified 57.3%

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

   if -2.39999999999999996e-296 < z < 3.3000000000000001e-125

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 65.1%

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

4. Final simplification 59.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+192}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.048:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-296}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-6}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+183}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -82000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-295}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 15600:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -82000000.0)
     t_1
     (if (<= z -1.9e-295)
       t_0
       (if (<= z 2.05e-125) (* y 4.0) (if (<= z 15600.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -82000000.0) {
		tmp = t_1;
	} else if (z <= -1.9e-295) {
		tmp = t_0;
	} else if (z <= 2.05e-125) {
		tmp = y * 4.0;
	} else if (z <= 15600.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-82000000.0d0)) then
        tmp = t_1
    else if (z <= (-1.9d-295)) then
        tmp = t_0
    else if (z <= 2.05d-125) then
        tmp = y * 4.0d0
    else if (z <= 15600.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -82000000.0) {
		tmp = t_1;
	} else if (z <= -1.9e-295) {
		tmp = t_0;
	} else if (z <= 2.05e-125) {
		tmp = y * 4.0;
	} else if (z <= 15600.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -82000000.0:
		tmp = t_1
	elif z <= -1.9e-295:
		tmp = t_0
	elif z <= 2.05e-125:
		tmp = y * 4.0
	elif z <= 15600.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -82000000.0)
		tmp = t_1;
	elseif (z <= -1.9e-295)
		tmp = t_0;
	elseif (z <= 2.05e-125)
		tmp = Float64(y * 4.0);
	elseif (z <= 15600.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -82000000.0)
		tmp = t_1;
	elseif (z <= -1.9e-295)
		tmp = t_0;
	elseif (z <= 2.05e-125)
		tmp = y * 4.0;
	elseif (z <= 15600.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -82000000.0], t$95$1, If[LessEqual[z, -1.9e-295], t$95$0, If[LessEqual[z, 2.05e-125], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 15600.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -8.2e7 or 15600 < 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. Step-by-step derivation

      1. add-sqr-sqrt 52.6%

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

      2. fma-define 52.6%

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

      3. associate-*l* 52.5%

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

   6. Applied egg-rr 52.5%

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

   7. Taylor expanded in z around inf 99.6%

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

   if -8.2e7 < z < -1.90000000000000009e-295 or 2.0499999999999999e-125 < z < 15600

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 57.2%

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

      1. *-lft-identity 57.2%

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

      2. *-commutative 57.2%

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

      3. +-commutative 57.2%

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

      4. *-commutative 57.2%

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

      5. fma-define 57.2%

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

      6. associate-*r* 57.2%

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

      7. neg-mul-1 57.2%

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

      8. fma-define 57.2%

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

      9. distribute-neg-in 57.2%

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

      10. distribute-lft-neg-in 57.2%

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

      11. metadata-eval 57.2%

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

      12. metadata-eval 57.2%

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

      13. distribute-rgt-in 57.2%

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

      14. +-commutative 57.2%

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

      15. sub-neg 57.2%

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

      16. distribute-rgt-in 57.2%

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

      17. sub-neg 57.2%

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

      18. distribute-rgt-in 57.2%

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

      19. metadata-eval 57.2%

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

      20. distribute-lft-neg-in 57.2%

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

      21. associate-+r+ 57.2%

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

   7. Simplified 57.2%

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

   if -1.90000000000000009e-295 < z < 2.0499999999999999e-125

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 65.1%

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

4. Final simplification 79.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -82000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 2.05 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 15600:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.011:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{-3}{z}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.011)
     t_0
     (if (<= z -7.8e-299)
       (* x (* z (/ -3.0 z)))
       (if (<= z 4.1e-125) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.011) {
		tmp = t_0;
	} else if (z <= -7.8e-299) {
		tmp = x * (z * (-3.0 / z));
	} else if (z <= 4.1e-125) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		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 - x) * z)
    if (z <= (-0.011d0)) then
        tmp = t_0
    else if (z <= (-7.8d-299)) then
        tmp = x * (z * ((-3.0d0) / z))
    else if (z <= 4.1d-125) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) 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 - x) * z);
	double tmp;
	if (z <= -0.011) {
		tmp = t_0;
	} else if (z <= -7.8e-299) {
		tmp = x * (z * (-3.0 / z));
	} else if (z <= 4.1e-125) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.011:
		tmp = t_0
	elif z <= -7.8e-299:
		tmp = x * (z * (-3.0 / z))
	elif z <= 4.1e-125:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.011)
		tmp = t_0;
	elseif (z <= -7.8e-299)
		tmp = Float64(x * Float64(z * Float64(-3.0 / z)));
	elseif (z <= 4.1e-125)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		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 - x) * z);
	tmp = 0.0;
	if (z <= -0.011)
		tmp = t_0;
	elseif (z <= -7.8e-299)
		tmp = x * (z * (-3.0 / z));
	elseif (z <= 4.1e-125)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.011], t$95$0, If[LessEqual[z, -7.8e-299], N[(x * N[(z * N[(-3.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.1e-125], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.010999999999999999 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. add-sqr-sqrt 52.9%

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

      2. fma-define 52.9%

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

      3. associate-*l* 52.9%

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

   6. Applied egg-rr 52.9%

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

   7. Taylor expanded in z around inf 98.0%

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

   if -0.010999999999999999 < z < -7.7999999999999997e-299

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      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. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 53.9%

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

      1. *-lft-identity 53.9%

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

      2. *-commutative 53.9%

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

      3. +-commutative 53.9%

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

      4. *-commutative 53.9%

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

      5. fma-define 53.9%

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

      6. associate-*r* 53.9%

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

      7. neg-mul-1 53.9%

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

      8. fma-define 53.9%

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

      9. distribute-neg-in 53.9%

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

      10. distribute-lft-neg-in 53.9%

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

      11. metadata-eval 53.9%

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

      12. metadata-eval 53.9%

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

      13. distribute-rgt-in 53.9%

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

      14. +-commutative 53.9%

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

      15. sub-neg 53.9%

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

      16. distribute-rgt-in 53.9%

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

      17. sub-neg 53.9%

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

      18. distribute-rgt-in 53.9%

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

      19. metadata-eval 53.9%

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

      20. distribute-lft-neg-in 53.9%

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

      21. associate-+r+ 53.9%

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

   7. Simplified 53.9%

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

   8. Taylor expanded in z around inf 53.7%

      \[\leadsto x \cdot \color{blue}{\left(z \cdot \left(6 - 3 \cdot \frac{1}{z}\right)\right)} \]
   9. Step-by-step derivation

      1. associate-*r/ 53.9%

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

      2. metadata-eval 53.9%

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

   10. Simplified 53.9%

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

   11. Taylor expanded in z around 0 53.9%

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

   if -7.7999999999999997e-299 < z < 4.0999999999999997e-125

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 65.1%

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

   if 4.0999999999999997e-125 < z < 0.5

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      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. Taylor expanded in y around 0 62.1%

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

      1. *-lft-identity 62.1%

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

      2. *-commutative 62.1%

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

      3. +-commutative 62.1%

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

      4. *-commutative 62.1%

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

      5. fma-define 62.1%

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

      6. associate-*r* 62.1%

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

      7. neg-mul-1 62.1%

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

      8. fma-define 62.1%

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

      9. distribute-neg-in 62.1%

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

      10. distribute-lft-neg-in 62.1%

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

      11. metadata-eval 62.1%

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

      12. metadata-eval 62.1%

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

      13. distribute-rgt-in 62.0%

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

      14. +-commutative 62.0%

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

      15. sub-neg 62.0%

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

      16. distribute-rgt-in 62.0%

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

      17. sub-neg 62.0%

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

      18. distribute-rgt-in 62.1%

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

      19. metadata-eval 62.1%

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

      20. distribute-lft-neg-in 62.1%

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

      21. associate-+r+ 62.1%

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

   7. Simplified 62.1%

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

   8. Taylor expanded in z around 0 61.3%

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

      1. *-commutative 61.3%

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

   10. Simplified 61.3%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.011:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-299}:\\ \;\;\;\;x \cdot \left(z \cdot \frac{-3}{z}\right)\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.018:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.018)
     t_0
     (if (<= z -3.8e-294)
       (* x -3.0)
       (if (<= z 6.2e-125) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.018) {
		tmp = t_0;
	} else if (z <= -3.8e-294) {
		tmp = x * -3.0;
	} else if (z <= 6.2e-125) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		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 - x) * z)
    if (z <= (-0.018d0)) then
        tmp = t_0
    else if (z <= (-3.8d-294)) then
        tmp = x * (-3.0d0)
    else if (z <= 6.2d-125) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) 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 - x) * z);
	double tmp;
	if (z <= -0.018) {
		tmp = t_0;
	} else if (z <= -3.8e-294) {
		tmp = x * -3.0;
	} else if (z <= 6.2e-125) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.018:
		tmp = t_0
	elif z <= -3.8e-294:
		tmp = x * -3.0
	elif z <= 6.2e-125:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.018)
		tmp = t_0;
	elseif (z <= -3.8e-294)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.2e-125)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		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 - x) * z);
	tmp = 0.0;
	if (z <= -0.018)
		tmp = t_0;
	elseif (z <= -3.8e-294)
		tmp = x * -3.0;
	elseif (z <= 6.2e-125)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.018], t$95$0, If[LessEqual[z, -3.8e-294], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.2e-125], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0179999999999999986 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. add-sqr-sqrt 52.9%

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

      2. fma-define 52.9%

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

      3. associate-*l* 52.9%

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

   6. Applied egg-rr 52.9%

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

   7. Taylor expanded in z around inf 98.0%

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

   if -0.0179999999999999986 < z < -3.8e-294 or 6.20000000000000026e-125 < z < 0.5

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 56.9%

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

      1. *-lft-identity 56.9%

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

      2. *-commutative 56.9%

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

      3. +-commutative 56.9%

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

      4. *-commutative 56.9%

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

      5. fma-define 56.9%

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

      6. associate-*r* 56.9%

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

      7. neg-mul-1 56.9%

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

      8. fma-define 56.9%

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

      9. distribute-neg-in 56.9%

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

      10. distribute-lft-neg-in 56.9%

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

      11. metadata-eval 56.9%

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

      12. metadata-eval 56.9%

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

      13. distribute-rgt-in 56.9%

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

      14. +-commutative 56.9%

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

      15. sub-neg 56.9%

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

      16. distribute-rgt-in 56.9%

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

      17. sub-neg 56.9%

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

      18. distribute-rgt-in 56.9%

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

      19. metadata-eval 56.9%

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

      20. distribute-lft-neg-in 56.9%

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

      21. associate-+r+ 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in z around 0 56.6%

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

      1. *-commutative 56.6%

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

   10. Simplified 56.6%

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

   if -3.8e-294 < z < 6.20000000000000026e-125

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 65.1%

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

4. Final simplification 79.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.018:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 52.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-296}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.5)
     t_0
     (if (<= z -3.8e-296)
       (* x -3.0)
       (if (<= z 4.3e-125) (* y 4.0) (if (<= z 0.52) (* 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 <= -3.8e-296) {
		tmp = x * -3.0;
	} else if (z <= 4.3e-125) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		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 <= (-3.8d-296)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.3d-125) then
        tmp = y * 4.0d0
    else if (z <= 0.52d0) 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 <= -3.8e-296) {
		tmp = x * -3.0;
	} else if (z <= 4.3e-125) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		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 <= -3.8e-296:
		tmp = x * -3.0
	elif z <= 4.3e-125:
		tmp = y * 4.0
	elif z <= 0.52:
		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 <= -3.8e-296)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.3e-125)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.52)
		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 <= -3.8e-296)
		tmp = x * -3.0;
	elseif (z <= 4.3e-125)
		tmp = y * 4.0;
	elseif (z <= 0.52)
		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, -3.8e-296], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.3e-125], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.5 or 0.52000000000000002 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. add-sqr-sqrt 52.9%

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

      2. fma-define 52.9%

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

      3. associate-*l* 52.9%

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

   6. Applied egg-rr 52.9%

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

   7. Taylor expanded in z around inf 98.0%

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

   8. Taylor expanded in y around inf 52.1%

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

   if -0.5 < z < -3.8000000000000002e-296 or 4.3000000000000002e-125 < z < 0.52000000000000002

   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* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 56.9%

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

      1. *-lft-identity 56.9%

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

      2. *-commutative 56.9%

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

      3. +-commutative 56.9%

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

      4. *-commutative 56.9%

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

      5. fma-define 56.9%

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

      6. associate-*r* 56.9%

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

      7. neg-mul-1 56.9%

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

      8. fma-define 56.9%

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

      9. distribute-neg-in 56.9%

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

      10. distribute-lft-neg-in 56.9%

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

      11. metadata-eval 56.9%

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

      12. metadata-eval 56.9%

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

      13. distribute-rgt-in 56.9%

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

      14. +-commutative 56.9%

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

      15. sub-neg 56.9%

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

      16. distribute-rgt-in 56.9%

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

      17. sub-neg 56.9%

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

      18. distribute-rgt-in 56.9%

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

      19. metadata-eval 56.9%

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

      20. distribute-lft-neg-in 56.9%

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

      21. associate-+r+ 56.9%

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

   7. Simplified 56.9%

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

   8. Taylor expanded in z around 0 56.6%

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

      1. *-commutative 56.6%

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

   10. Simplified 56.6%

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

   if -3.8000000000000002e-296 < z < 4.3000000000000002e-125

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 99.9%

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

   6. Taylor expanded in x around 0 65.1%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.5:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.8 \cdot 10^{-296}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-125}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-24} \lor \neg \left(x \leq 9.5 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -8.5e-24) (not (<= x 9.5e+26)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-24) || !(x <= 9.5e+26)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (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 ((x <= (-8.5d-24)) .or. (.not. (x <= 9.5d+26))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -8.5e-24) || !(x <= 9.5e+26)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -8.5e-24) or not (x <= 9.5e+26):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -8.5e-24) || !(x <= 9.5e+26))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -8.5e-24) || ~((x <= 9.5e+26)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -8.5e-24], N[Not[LessEqual[x, 9.5e+26]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8.5000000000000002e-24 or 9.50000000000000054e26 < x

   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. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 79.5%

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

      1. *-lft-identity 79.5%

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

      2. *-commutative 79.5%

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

      3. +-commutative 79.5%

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

      4. *-commutative 79.5%

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

      5. fma-define 79.5%

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

      6. associate-*r* 79.5%

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

      7. neg-mul-1 79.5%

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

      8. fma-define 79.5%

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

      9. distribute-neg-in 79.5%

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

      10. distribute-lft-neg-in 79.5%

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

      11. metadata-eval 79.5%

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

      12. metadata-eval 79.5%

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

      13. distribute-rgt-in 79.5%

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

      14. +-commutative 79.5%

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

      15. sub-neg 79.5%

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

      16. distribute-rgt-in 79.6%

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

      17. sub-neg 79.6%

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

      18. distribute-rgt-in 79.5%

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

      19. metadata-eval 79.5%

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

      20. distribute-lft-neg-in 79.5%

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

      21. associate-+r+ 79.5%

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

   7. Simplified 79.5%

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

   if -8.5000000000000002e-24 < x < 9.50000000000000054e26

   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* 99.8%

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

      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. Taylor expanded in y around inf 78.2%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.5 \cdot 10^{-24} \lor \neg \left(x \leq 9.5 \cdot 10^{+26}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.0% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* z (* (- y x) -6.0))
   (if (<= z 0.6) (+ (* y 4.0) (* x -3.0)) (* -6.0 (* (- y x) z)))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.6d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.6d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.6:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.6], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. add-sqr-sqrt 52.9%

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

      2. fma-define 52.9%

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

      3. associate-*l* 52.9%

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

   6. Applied egg-rr 52.9%

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

   7. Taylor expanded in z around inf 98.9%

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

      1. associate-*r* 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-*r* 99.0%

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

   9. Simplified 99.0%

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

   if -0.599999999999999978 < z < 0.599999999999999978

   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 z around 0 97.9%

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

   6. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 0.599999999999999978 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. add-sqr-sqrt 52.1%

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

      2. fma-define 52.1%

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

      3. associate-*l* 52.1%

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

   6. Applied egg-rr 52.1%

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

   7. Taylor expanded in z around inf 98.3%

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

4. Final simplification 98.3%

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

Alternative 12: 98.0% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.58d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = (-6.0d0) * ((y - x) * z)
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. add-sqr-sqrt 52.9%

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

      2. fma-define 52.9%

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

      3. associate-*l* 52.9%

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

   6. Applied egg-rr 52.9%

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

   7. Taylor expanded in z around inf 98.9%

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

      1. associate-*r* 98.9%

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

      2. *-commutative 98.9%

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

      3. associate-*r* 99.0%

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

   9. Simplified 99.0%

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

   if -0.57999999999999996 < z < 0.57999999999999996

   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 z around 0 97.9%

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

   if 0.57999999999999996 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. add-sqr-sqrt 52.1%

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

      2. fma-define 52.1%

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

      3. associate-*l* 52.1%

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

   6. Applied egg-rr 52.1%

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

   7. Taylor expanded in z around inf 98.3%

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

4. Final simplification 98.3%

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

Alternative 13: 36.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+105} \lor \neg \left(x \leq 4.8 \cdot 10^{-86}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e+105) (not (<= x 4.8e-86))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e+105) || !(x <= 4.8e-86)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-3d+105)) .or. (.not. (x <= 4.8d-86))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e+105) || !(x <= 4.8e-86)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e+105) or not (x <= 4.8e-86):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e+105) || !(x <= 4.8e-86))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3e+105) || ~((x <= 4.8e-86)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e+105], N[Not[LessEqual[x, 4.8e-86]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.0000000000000001e105 or 4.80000000000000026e-86 < x

   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. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. *-lft-identity 77.8%

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

      2. *-commutative 77.8%

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

      3. +-commutative 77.8%

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

      4. *-commutative 77.8%

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

      5. fma-define 77.8%

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

      6. associate-*r* 77.8%

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

      7. neg-mul-1 77.8%

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

      8. fma-define 77.8%

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

      9. distribute-neg-in 77.8%

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

      10. distribute-lft-neg-in 77.8%

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

      11. metadata-eval 77.8%

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

      12. metadata-eval 77.8%

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

      13. distribute-rgt-in 77.8%

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

      14. +-commutative 77.8%

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

      15. sub-neg 77.8%

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

      16. distribute-rgt-in 77.9%

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

      17. sub-neg 77.9%

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

      18. distribute-rgt-in 77.9%

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

      19. metadata-eval 77.9%

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

      20. distribute-lft-neg-in 77.9%

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

      21. associate-+r+ 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in z around 0 40.9%

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

      1. *-commutative 40.9%

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

   10. Simplified 40.9%

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

   if -3.0000000000000001e105 < x < 4.80000000000000026e-86

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 49.1%

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

   6. Taylor expanded in x around 0 40.4%

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

4. Final simplification 40.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+105} \lor \neg \left(x \leq 4.8 \cdot 10^{-86}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((y - x) * (4.0 + (z * -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 + ((y - x) * (4.0d0 + (z * (-6.0d0))))
end function

Java

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

Python

def code(x, y, z):
	return x + ((y - x) * (4.0 + (z * -6.0)))

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (4.0 + (z * -6.0)));
end

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. +-commutative 99.5%

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

   2. *-commutative 99.5%

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

   3. associate-*r* 99.5%

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

   4. fma-define 99.5%

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

6. Applied egg-rr 99.5%

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

7. Taylor expanded in z around 0 99.7%

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

   1. +-commutative 99.7%

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

   2. associate-*r* 99.7%

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

   3. distribute-rgt-out 99.7%

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

9. Simplified 99.7%

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

10. Final simplification 99.7%

    \[\leadsto x + \left(y - x\right) \cdot \left(4 + z \cdot -6\right) \]
11. Add Preprocessing

Alternative 15: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

Alternative 16: 25.5% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in z around 0 49.5%

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

6. Taylor expanded in x around 0 25.5%

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

7. Final simplification 25.5%

   \[\leadsto y \cdot 4 \]
8. Add Preprocessing

Alternative 17: 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 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in y around inf 50.9%

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

6. Taylor expanded in x around inf 2.7%

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

Reproduce

herbie shell --seed 2024150 
(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))))