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

Percentage Accurate: 99.5% → 99.7%

Time: 12.9s

Alternatives: 16

Speedup: 1.2×

• 20.6% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * ((2.0d0 / 3.0d0) - z))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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-def 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. Final simplification 99.8%

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

Alternative 2: 49.9% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.12 \cdot 10^{+231}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+183}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+128}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+57}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-111}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-77}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+104}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -1.12e+231)
     t_0
     (if (<= z -4e+183)
       t_1
       (if (<= z -2.05e+128)
         t_0
         (if (<= z -1e+57)
           t_1
           (if (<= z -0.65)
             t_0
             (if (<= z -2.5e-82)
               (* y 4.0)
               (if (<= z -2.6e-111)
                 (* x -3.0)
                 (if (<= z -5.2e-145)
                   (* y 4.0)
                   (if (<= z -6.4e-307)
                     (* x -3.0)
                     (if (<= z 2e-176)
                       (* y 4.0)
                       (if (<= z 6e-77)
                         (* x -3.0)
                         (if (<= z 2550.0)
                           (* y 4.0)
                           (if (<= z 1.5e+104) t_0 t_1)))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.12e+231) {
		tmp = t_0;
	} else if (z <= -4e+183) {
		tmp = t_1;
	} else if (z <= -2.05e+128) {
		tmp = t_0;
	} else if (z <= -1e+57) {
		tmp = t_1;
	} else if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -2.5e-82) {
		tmp = y * 4.0;
	} else if (z <= -2.6e-111) {
		tmp = x * -3.0;
	} else if (z <= -5.2e-145) {
		tmp = y * 4.0;
	} else if (z <= -6.4e-307) {
		tmp = x * -3.0;
	} else if (z <= 2e-176) {
		tmp = y * 4.0;
	} else if (z <= 6e-77) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else if (z <= 1.5e+104) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-1.12d+231)) then
        tmp = t_0
    else if (z <= (-4d+183)) then
        tmp = t_1
    else if (z <= (-2.05d+128)) then
        tmp = t_0
    else if (z <= (-1d+57)) then
        tmp = t_1
    else if (z <= (-0.65d0)) then
        tmp = t_0
    else if (z <= (-2.5d-82)) then
        tmp = y * 4.0d0
    else if (z <= (-2.6d-111)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5.2d-145)) then
        tmp = y * 4.0d0
    else if (z <= (-6.4d-307)) then
        tmp = x * (-3.0d0)
    else if (z <= 2d-176) then
        tmp = y * 4.0d0
    else if (z <= 6d-77) then
        tmp = x * (-3.0d0)
    else if (z <= 2550.0d0) then
        tmp = y * 4.0d0
    else if (z <= 1.5d+104) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.12e+231) {
		tmp = t_0;
	} else if (z <= -4e+183) {
		tmp = t_1;
	} else if (z <= -2.05e+128) {
		tmp = t_0;
	} else if (z <= -1e+57) {
		tmp = t_1;
	} else if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -2.5e-82) {
		tmp = y * 4.0;
	} else if (z <= -2.6e-111) {
		tmp = x * -3.0;
	} else if (z <= -5.2e-145) {
		tmp = y * 4.0;
	} else if (z <= -6.4e-307) {
		tmp = x * -3.0;
	} else if (z <= 2e-176) {
		tmp = y * 4.0;
	} else if (z <= 6e-77) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else if (z <= 1.5e+104) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -1.12e+231:
		tmp = t_0
	elif z <= -4e+183:
		tmp = t_1
	elif z <= -2.05e+128:
		tmp = t_0
	elif z <= -1e+57:
		tmp = t_1
	elif z <= -0.65:
		tmp = t_0
	elif z <= -2.5e-82:
		tmp = y * 4.0
	elif z <= -2.6e-111:
		tmp = x * -3.0
	elif z <= -5.2e-145:
		tmp = y * 4.0
	elif z <= -6.4e-307:
		tmp = x * -3.0
	elif z <= 2e-176:
		tmp = y * 4.0
	elif z <= 6e-77:
		tmp = x * -3.0
	elif z <= 2550.0:
		tmp = y * 4.0
	elif z <= 1.5e+104:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.12e+231)
		tmp = t_0;
	elseif (z <= -4e+183)
		tmp = t_1;
	elseif (z <= -2.05e+128)
		tmp = t_0;
	elseif (z <= -1e+57)
		tmp = t_1;
	elseif (z <= -0.65)
		tmp = t_0;
	elseif (z <= -2.5e-82)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.6e-111)
		tmp = Float64(x * -3.0);
	elseif (z <= -5.2e-145)
		tmp = Float64(y * 4.0);
	elseif (z <= -6.4e-307)
		tmp = Float64(x * -3.0);
	elseif (z <= 2e-176)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e-77)
		tmp = Float64(x * -3.0);
	elseif (z <= 2550.0)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.5e+104)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.12e+231)
		tmp = t_0;
	elseif (z <= -4e+183)
		tmp = t_1;
	elseif (z <= -2.05e+128)
		tmp = t_0;
	elseif (z <= -1e+57)
		tmp = t_1;
	elseif (z <= -0.65)
		tmp = t_0;
	elseif (z <= -2.5e-82)
		tmp = y * 4.0;
	elseif (z <= -2.6e-111)
		tmp = x * -3.0;
	elseif (z <= -5.2e-145)
		tmp = y * 4.0;
	elseif (z <= -6.4e-307)
		tmp = x * -3.0;
	elseif (z <= 2e-176)
		tmp = y * 4.0;
	elseif (z <= 6e-77)
		tmp = x * -3.0;
	elseif (z <= 2550.0)
		tmp = y * 4.0;
	elseif (z <= 1.5e+104)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.12e+231], t$95$0, If[LessEqual[z, -4e+183], t$95$1, If[LessEqual[z, -2.05e+128], t$95$0, If[LessEqual[z, -1e+57], t$95$1, If[LessEqual[z, -0.65], t$95$0, If[LessEqual[z, -2.5e-82], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.6e-111], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5.2e-145], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -6.4e-307], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2e-176], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e-77], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2550.0], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.5e+104], t$95$0, t$95$1]]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1200000000000001e231 or -3.99999999999999979e183 < z < -2.05000000000000006e128 or -1.00000000000000005e57 < z < -0.650000000000000022 or 2550 < z < 1.49999999999999984e104

   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 x around 0 98.2%

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

   6. Taylor expanded in y around inf 69.6%

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

      1. *-commutative 69.6%

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

   8. Simplified 69.6%

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

   9. Taylor expanded in z around inf 68.0%

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

   if -1.1200000000000001e231 < z < -3.99999999999999979e183 or -2.05000000000000006e128 < z < -1.00000000000000005e57 or 1.49999999999999984e104 < 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. Taylor expanded in x around inf 67.5%

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

      1. sub-neg 67.5%

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

      2. distribute-rgt-in 67.5%

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

      3. metadata-eval 67.5%

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

      4. metadata-eval 67.5%

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

      5. neg-mul-1 67.5%

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

      6. associate-*r* 67.5%

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

      7. *-commutative 67.5%

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

      8. associate-+r+ 67.5%

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

      9. metadata-eval 67.5%

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

      10. metadata-eval 67.5%

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

      11. associate-*r* 67.5%

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

      12. metadata-eval 67.5%

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

      13. *-commutative 67.5%

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

   7. Simplified 67.5%

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

   8. Taylor expanded in z around inf 67.6%

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

   if -0.650000000000000022 < z < -2.4999999999999999e-82 or -2.59999999999999982e-111 < z < -5.1999999999999999e-145 or -6.40000000000000021e-307 < z < 2e-176 or 6.00000000000000033e-77 < z < 2550

   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 x around 0 99.5%

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

      1. fma-def 99.5%

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

      2. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around 0 93.6%

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

   9. Taylor expanded in x around 0 64.9%

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

       1. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if -2.4999999999999999e-82 < z < -2.59999999999999982e-111 or -5.1999999999999999e-145 < z < -6.40000000000000021e-307 or 2e-176 < z < 6.00000000000000033e-77

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. associate-+r+ 67.2%

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

      9. metadata-eval 67.2%

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

      10. metadata-eval 67.2%

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

      11. associate-*r* 67.2%

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

      12. metadata-eval 67.2%

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

      13. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   10. Simplified 67.2%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.12 \cdot 10^{+231}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{+183}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{+128}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1 \cdot 10^{+57}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-111}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-77}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{+104}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-81}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-110}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-77}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -2.4e+60)
     (* x (* z 6.0))
     (if (<= z -0.65)
       t_0
       (if (<= z -3.5e-81)
         (* y 4.0)
         (if (<= z -3.3e-110)
           (* x -3.0)
           (if (<= z -2.8e-145)
             (* y 4.0)
             (if (<= z -9.6e-307)
               (* x -3.0)
               (if (<= z 5.8e-176)
                 (* y 4.0)
                 (if (<= z 1.15e-77)
                   (* x -3.0)
                   (if (<= z 2550.0)
                     (* y 4.0)
                     (if (<= z 4.5e+106) t_0 (* 6.0 (* x z))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.4e+60) {
		tmp = x * (z * 6.0);
	} else if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -3.5e-81) {
		tmp = y * 4.0;
	} else if (z <= -3.3e-110) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-145) {
		tmp = y * 4.0;
	} else if (z <= -9.6e-307) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-176) {
		tmp = y * 4.0;
	} else if (z <= 1.15e-77) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else if (z <= 4.5e+106) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-2.4d+60)) then
        tmp = x * (z * 6.0d0)
    else if (z <= (-0.65d0)) then
        tmp = t_0
    else if (z <= (-3.5d-81)) then
        tmp = y * 4.0d0
    else if (z <= (-3.3d-110)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.8d-145)) then
        tmp = y * 4.0d0
    else if (z <= (-9.6d-307)) then
        tmp = x * (-3.0d0)
    else if (z <= 5.8d-176) then
        tmp = y * 4.0d0
    else if (z <= 1.15d-77) then
        tmp = x * (-3.0d0)
    else if (z <= 2550.0d0) then
        tmp = y * 4.0d0
    else if (z <= 4.5d+106) then
        tmp = t_0
    else
        tmp = 6.0d0 * (x * z)
    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 <= -2.4e+60) {
		tmp = x * (z * 6.0);
	} else if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -3.5e-81) {
		tmp = y * 4.0;
	} else if (z <= -3.3e-110) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-145) {
		tmp = y * 4.0;
	} else if (z <= -9.6e-307) {
		tmp = x * -3.0;
	} else if (z <= 5.8e-176) {
		tmp = y * 4.0;
	} else if (z <= 1.15e-77) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else if (z <= 4.5e+106) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.4e+60:
		tmp = x * (z * 6.0)
	elif z <= -0.65:
		tmp = t_0
	elif z <= -3.5e-81:
		tmp = y * 4.0
	elif z <= -3.3e-110:
		tmp = x * -3.0
	elif z <= -2.8e-145:
		tmp = y * 4.0
	elif z <= -9.6e-307:
		tmp = x * -3.0
	elif z <= 5.8e-176:
		tmp = y * 4.0
	elif z <= 1.15e-77:
		tmp = x * -3.0
	elif z <= 2550.0:
		tmp = y * 4.0
	elif z <= 4.5e+106:
		tmp = t_0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.4e+60)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= -0.65)
		tmp = t_0;
	elseif (z <= -3.5e-81)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.3e-110)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.8e-145)
		tmp = Float64(y * 4.0);
	elseif (z <= -9.6e-307)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.8e-176)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.15e-77)
		tmp = Float64(x * -3.0);
	elseif (z <= 2550.0)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.5e+106)
		tmp = t_0;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.4e+60)
		tmp = x * (z * 6.0);
	elseif (z <= -0.65)
		tmp = t_0;
	elseif (z <= -3.5e-81)
		tmp = y * 4.0;
	elseif (z <= -3.3e-110)
		tmp = x * -3.0;
	elseif (z <= -2.8e-145)
		tmp = y * 4.0;
	elseif (z <= -9.6e-307)
		tmp = x * -3.0;
	elseif (z <= 5.8e-176)
		tmp = y * 4.0;
	elseif (z <= 1.15e-77)
		tmp = x * -3.0;
	elseif (z <= 2550.0)
		tmp = y * 4.0;
	elseif (z <= 4.5e+106)
		tmp = t_0;
	else
		tmp = 6.0 * (x * z);
	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, -2.4e+60], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.65], t$95$0, If[LessEqual[z, -3.5e-81], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.3e-110], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.8e-145], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -9.6e-307], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.8e-176], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.15e-77], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2550.0], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.5e+106], t$95$0, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.4e60

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 57.9%

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

      1. sub-neg 57.9%

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

      2. distribute-rgt-in 57.9%

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

      3. metadata-eval 57.9%

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

      4. metadata-eval 57.9%

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

      5. neg-mul-1 57.9%

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

      6. associate-*r* 57.9%

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

      7. *-commutative 57.9%

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

      8. associate-+r+ 57.9%

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

      9. metadata-eval 57.9%

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

      10. metadata-eval 57.9%

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

      11. associate-*r* 57.9%

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

      12. metadata-eval 57.9%

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

      13. *-commutative 57.9%

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

   7. Simplified 57.9%

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

   8. Taylor expanded in z around inf 57.8%

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

      1. associate-*r* 57.9%

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

      2. *-commutative 57.9%

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

      3. associate-*l* 57.9%

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

      4. *-commutative 57.9%

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

   10. Simplified 57.9%

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

   if -2.4e60 < z < -0.650000000000000022 or 2550 < z < 4.4999999999999997e106

   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 x around 0 99.6%

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

   6. Taylor expanded in y around inf 67.1%

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

      1. *-commutative 67.1%

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

   8. Simplified 67.1%

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

   9. Taylor expanded in z around inf 64.4%

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

   if -0.650000000000000022 < z < -3.49999999999999986e-81 or -3.2999999999999999e-110 < z < -2.8000000000000001e-145 or -9.60000000000000071e-307 < z < 5.80000000000000012e-176 or 1.14999999999999999e-77 < z < 2550

   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 x around 0 99.5%

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

      1. fma-def 99.5%

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

      2. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around 0 93.6%

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

   9. Taylor expanded in x around 0 64.9%

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

       1. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if -3.49999999999999986e-81 < z < -3.2999999999999999e-110 or -2.8000000000000001e-145 < z < -9.60000000000000071e-307 or 5.80000000000000012e-176 < z < 1.14999999999999999e-77

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. associate-+r+ 67.2%

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

      9. metadata-eval 67.2%

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

      10. metadata-eval 67.2%

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

      11. associate-*r* 67.2%

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

      12. metadata-eval 67.2%

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

      13. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   10. Simplified 67.2%

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

   if 4.4999999999999997e106 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 64.2%

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

      1. sub-neg 64.2%

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

      2. distribute-rgt-in 64.2%

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

      3. metadata-eval 64.2%

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

      4. metadata-eval 64.2%

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

      5. neg-mul-1 64.2%

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

      6. associate-*r* 64.2%

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

      7. *-commutative 64.2%

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

      8. associate-+r+ 64.2%

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

      9. metadata-eval 64.2%

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

      10. metadata-eval 64.2%

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

      11. associate-*r* 64.2%

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

      12. metadata-eval 64.2%

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

      13. *-commutative 64.2%

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

   7. Simplified 64.2%

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

   8. Taylor expanded in z around inf 64.4%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{+60}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-81}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-110}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-77}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+106}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -6.2 \cdot 10^{+61}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-81}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-113}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-77}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+105}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))) (t_1 (* -6.0 (* y z))))
   (if (<= z -6.2e+61)
     t_0
     (if (<= z -0.65)
       t_1
       (if (<= z -7.2e-81)
         (* y 4.0)
         (if (<= z -1.4e-113)
           (* x -3.0)
           (if (<= z -7.2e-145)
             (* y 4.0)
             (if (<= z -5e-306)
               (* x -3.0)
               (if (<= z 3.1e-175)
                 (* y 4.0)
                 (if (<= z 5.1e-77)
                   (* x -3.0)
                   (if (<= z 2550.0)
                     (* y 4.0)
                     (if (<= z 1.42e+105) t_1 t_0))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -6.2e+61) {
		tmp = t_0;
	} else if (z <= -0.65) {
		tmp = t_1;
	} else if (z <= -7.2e-81) {
		tmp = y * 4.0;
	} else if (z <= -1.4e-113) {
		tmp = x * -3.0;
	} else if (z <= -7.2e-145) {
		tmp = y * 4.0;
	} else if (z <= -5e-306) {
		tmp = x * -3.0;
	} else if (z <= 3.1e-175) {
		tmp = y * 4.0;
	} else if (z <= 5.1e-77) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else if (z <= 1.42e+105) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = z * (x * 6.0d0)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-6.2d+61)) then
        tmp = t_0
    else if (z <= (-0.65d0)) then
        tmp = t_1
    else if (z <= (-7.2d-81)) then
        tmp = y * 4.0d0
    else if (z <= (-1.4d-113)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7.2d-145)) then
        tmp = y * 4.0d0
    else if (z <= (-5d-306)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.1d-175) then
        tmp = y * 4.0d0
    else if (z <= 5.1d-77) then
        tmp = x * (-3.0d0)
    else if (z <= 2550.0d0) then
        tmp = y * 4.0d0
    else if (z <= 1.42d+105) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -6.2e+61) {
		tmp = t_0;
	} else if (z <= -0.65) {
		tmp = t_1;
	} else if (z <= -7.2e-81) {
		tmp = y * 4.0;
	} else if (z <= -1.4e-113) {
		tmp = x * -3.0;
	} else if (z <= -7.2e-145) {
		tmp = y * 4.0;
	} else if (z <= -5e-306) {
		tmp = x * -3.0;
	} else if (z <= 3.1e-175) {
		tmp = y * 4.0;
	} else if (z <= 5.1e-77) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else if (z <= 1.42e+105) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -6.2e+61:
		tmp = t_0
	elif z <= -0.65:
		tmp = t_1
	elif z <= -7.2e-81:
		tmp = y * 4.0
	elif z <= -1.4e-113:
		tmp = x * -3.0
	elif z <= -7.2e-145:
		tmp = y * 4.0
	elif z <= -5e-306:
		tmp = x * -3.0
	elif z <= 3.1e-175:
		tmp = y * 4.0
	elif z <= 5.1e-77:
		tmp = x * -3.0
	elif z <= 2550.0:
		tmp = y * 4.0
	elif z <= 1.42e+105:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -6.2e+61)
		tmp = t_0;
	elseif (z <= -0.65)
		tmp = t_1;
	elseif (z <= -7.2e-81)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.4e-113)
		tmp = Float64(x * -3.0);
	elseif (z <= -7.2e-145)
		tmp = Float64(y * 4.0);
	elseif (z <= -5e-306)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.1e-175)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.1e-77)
		tmp = Float64(x * -3.0);
	elseif (z <= 2550.0)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.42e+105)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -6.2e+61)
		tmp = t_0;
	elseif (z <= -0.65)
		tmp = t_1;
	elseif (z <= -7.2e-81)
		tmp = y * 4.0;
	elseif (z <= -1.4e-113)
		tmp = x * -3.0;
	elseif (z <= -7.2e-145)
		tmp = y * 4.0;
	elseif (z <= -5e-306)
		tmp = x * -3.0;
	elseif (z <= 3.1e-175)
		tmp = y * 4.0;
	elseif (z <= 5.1e-77)
		tmp = x * -3.0;
	elseif (z <= 2550.0)
		tmp = y * 4.0;
	elseif (z <= 1.42e+105)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6.2e+61], t$95$0, If[LessEqual[z, -0.65], t$95$1, If[LessEqual[z, -7.2e-81], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.4e-113], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7.2e-145], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5e-306], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.1e-175], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.1e-77], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2550.0], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.42e+105], t$95$1, t$95$0]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.1999999999999998e61 or 1.41999999999999991e105 < 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. Taylor expanded in x around 0 96.5%

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

      1. fma-def 96.5%

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

      2. *-commutative 96.5%

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

   7. Simplified 96.5%

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

   8. Taylor expanded in z around inf 99.8%

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

   9. Taylor expanded in y around 0 60.3%

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

   if -6.1999999999999998e61 < z < -0.650000000000000022 or 2550 < z < 1.41999999999999991e105

   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 x around 0 99.6%

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

   6. Taylor expanded in y around inf 67.1%

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

      1. *-commutative 67.1%

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

   8. Simplified 67.1%

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

   9. Taylor expanded in z around inf 64.4%

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

   if -0.650000000000000022 < z < -7.1999999999999997e-81 or -1.4e-113 < z < -7.2000000000000001e-145 or -4.99999999999999998e-306 < z < 3.09999999999999999e-175 or 5.10000000000000032e-77 < z < 2550

   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 x around 0 99.5%

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

      1. fma-def 99.5%

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

      2. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around 0 93.6%

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

   9. Taylor expanded in x around 0 64.9%

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

       1. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if -7.1999999999999997e-81 < z < -1.4e-113 or -7.2000000000000001e-145 < z < -4.99999999999999998e-306 or 3.09999999999999999e-175 < z < 5.10000000000000032e-77

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. associate-+r+ 67.2%

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

      9. metadata-eval 67.2%

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

      10. metadata-eval 67.2%

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

      11. associate-*r* 67.2%

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

      12. metadata-eval 67.2%

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

      13. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   10. Simplified 67.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6.2 \cdot 10^{+61}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-81}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-113}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-77}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{+105}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+62}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-83}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-110}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+105}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))))
   (if (<= z -1.95e+62)
     t_0
     (if (<= z -0.65)
       (* z (* y -6.0))
       (if (<= z -2.55e-83)
         (* y 4.0)
         (if (<= z -2.1e-110)
           (* x -3.0)
           (if (<= z -2.95e-145)
             (* y 4.0)
             (if (<= z -1.65e-305)
               (* x -3.0)
               (if (<= z 4.5e-175)
                 (* y 4.0)
                 (if (<= z 1.95e-82)
                   (* x -3.0)
                   (if (<= z 2550.0)
                     (* y 4.0)
                     (if (<= z 3.15e+105) (* -6.0 (* y z)) t_0))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (z <= -1.95e+62) {
		tmp = t_0;
	} else if (z <= -0.65) {
		tmp = z * (y * -6.0);
	} else if (z <= -2.55e-83) {
		tmp = y * 4.0;
	} else if (z <= -2.1e-110) {
		tmp = x * -3.0;
	} else if (z <= -2.95e-145) {
		tmp = y * 4.0;
	} else if (z <= -1.65e-305) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-175) {
		tmp = y * 4.0;
	} else if (z <= 1.95e-82) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else if (z <= 3.15e+105) {
		tmp = -6.0 * (y * z);
	} 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 = z * (x * 6.0d0)
    if (z <= (-1.95d+62)) then
        tmp = t_0
    else if (z <= (-0.65d0)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-2.55d-83)) then
        tmp = y * 4.0d0
    else if (z <= (-2.1d-110)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.95d-145)) then
        tmp = y * 4.0d0
    else if (z <= (-1.65d-305)) then
        tmp = x * (-3.0d0)
    else if (z <= 4.5d-175) then
        tmp = y * 4.0d0
    else if (z <= 1.95d-82) then
        tmp = x * (-3.0d0)
    else if (z <= 2550.0d0) then
        tmp = y * 4.0d0
    else if (z <= 3.15d+105) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (z <= -1.95e+62) {
		tmp = t_0;
	} else if (z <= -0.65) {
		tmp = z * (y * -6.0);
	} else if (z <= -2.55e-83) {
		tmp = y * 4.0;
	} else if (z <= -2.1e-110) {
		tmp = x * -3.0;
	} else if (z <= -2.95e-145) {
		tmp = y * 4.0;
	} else if (z <= -1.65e-305) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-175) {
		tmp = y * 4.0;
	} else if (z <= 1.95e-82) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else if (z <= 3.15e+105) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	tmp = 0
	if z <= -1.95e+62:
		tmp = t_0
	elif z <= -0.65:
		tmp = z * (y * -6.0)
	elif z <= -2.55e-83:
		tmp = y * 4.0
	elif z <= -2.1e-110:
		tmp = x * -3.0
	elif z <= -2.95e-145:
		tmp = y * 4.0
	elif z <= -1.65e-305:
		tmp = x * -3.0
	elif z <= 4.5e-175:
		tmp = y * 4.0
	elif z <= 1.95e-82:
		tmp = x * -3.0
	elif z <= 2550.0:
		tmp = y * 4.0
	elif z <= 3.15e+105:
		tmp = -6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -1.95e+62)
		tmp = t_0;
	elseif (z <= -0.65)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -2.55e-83)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.1e-110)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.95e-145)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.65e-305)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.5e-175)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.95e-82)
		tmp = Float64(x * -3.0);
	elseif (z <= 2550.0)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.15e+105)
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -1.95e+62)
		tmp = t_0;
	elseif (z <= -0.65)
		tmp = z * (y * -6.0);
	elseif (z <= -2.55e-83)
		tmp = y * 4.0;
	elseif (z <= -2.1e-110)
		tmp = x * -3.0;
	elseif (z <= -2.95e-145)
		tmp = y * 4.0;
	elseif (z <= -1.65e-305)
		tmp = x * -3.0;
	elseif (z <= 4.5e-175)
		tmp = y * 4.0;
	elseif (z <= 1.95e-82)
		tmp = x * -3.0;
	elseif (z <= 2550.0)
		tmp = y * 4.0;
	elseif (z <= 3.15e+105)
		tmp = -6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+62], t$95$0, If[LessEqual[z, -0.65], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.55e-83], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.1e-110], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.95e-145], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.65e-305], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.5e-175], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.95e-82], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2550.0], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.15e+105], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.95e62 or 3.14999999999999977e105 < 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. Taylor expanded in x around 0 96.5%

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

      1. fma-def 96.5%

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

      2. *-commutative 96.5%

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

   7. Simplified 96.5%

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

   8. Taylor expanded in z around inf 99.8%

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

   9. Taylor expanded in y around 0 60.3%

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

   if -1.95e62 < z < -0.650000000000000022

   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 x around 0 99.6%

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

   6. Taylor expanded in y around inf 70.9%

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

      1. *-commutative 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in z around inf 66.9%

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

       1. *-commutative 66.9%

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

       2. *-commutative 66.9%

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

       3. associate-*r* 67.1%

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

   11. Simplified 67.1%

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

   if -0.650000000000000022 < z < -2.55000000000000018e-83 or -2.10000000000000002e-110 < z < -2.9499999999999999e-145 or -1.64999999999999991e-305 < z < 4.49999999999999998e-175 or 1.94999999999999987e-82 < z < 2550

   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 x around 0 99.5%

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

      1. fma-def 99.5%

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

      2. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around 0 93.6%

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

   9. Taylor expanded in x around 0 64.9%

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

       1. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if -2.55000000000000018e-83 < z < -2.10000000000000002e-110 or -2.9499999999999999e-145 < z < -1.64999999999999991e-305 or 4.49999999999999998e-175 < z < 1.94999999999999987e-82

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. associate-+r+ 67.2%

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

      9. metadata-eval 67.2%

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

      10. metadata-eval 67.2%

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

      11. associate-*r* 67.2%

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

      12. metadata-eval 67.2%

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

      13. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   10. Simplified 67.2%

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

   if 2550 < z < 3.14999999999999977e105

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 65.4%

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

      1. *-commutative 65.4%

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

   8. Simplified 65.4%

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

   9. Taylor expanded in z around inf 63.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+62}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.55 \cdot 10^{-83}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-110}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.95 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{-82}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.15 \cdot 10^{+105}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -8.5 \cdot 10^{+60}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-80}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-109}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-79}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2800:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+105}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))))
   (if (<= z -8.5e+60)
     t_0
     (if (<= z -0.65)
       (* z (* y -6.0))
       (if (<= z -4.4e-80)
         (* y 4.0)
         (if (<= z -7.2e-109)
           (* x -3.0)
           (if (<= z -5.6e-145)
             (* y 4.0)
             (if (<= z -5.2e-306)
               (* x -3.0)
               (if (<= z 7e-175)
                 (* y 4.0)
                 (if (<= z 4.3e-79)
                   (* x -3.0)
                   (if (<= z 2800.0)
                     (+ x (* y 4.0))
                     (if (<= z 1.9e+105) (* -6.0 (* y z)) t_0))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (z <= -8.5e+60) {
		tmp = t_0;
	} else if (z <= -0.65) {
		tmp = z * (y * -6.0);
	} else if (z <= -4.4e-80) {
		tmp = y * 4.0;
	} else if (z <= -7.2e-109) {
		tmp = x * -3.0;
	} else if (z <= -5.6e-145) {
		tmp = y * 4.0;
	} else if (z <= -5.2e-306) {
		tmp = x * -3.0;
	} else if (z <= 7e-175) {
		tmp = y * 4.0;
	} else if (z <= 4.3e-79) {
		tmp = x * -3.0;
	} else if (z <= 2800.0) {
		tmp = x + (y * 4.0);
	} else if (z <= 1.9e+105) {
		tmp = -6.0 * (y * z);
	} 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 = z * (x * 6.0d0)
    if (z <= (-8.5d+60)) then
        tmp = t_0
    else if (z <= (-0.65d0)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-4.4d-80)) then
        tmp = y * 4.0d0
    else if (z <= (-7.2d-109)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5.6d-145)) then
        tmp = y * 4.0d0
    else if (z <= (-5.2d-306)) then
        tmp = x * (-3.0d0)
    else if (z <= 7d-175) then
        tmp = y * 4.0d0
    else if (z <= 4.3d-79) then
        tmp = x * (-3.0d0)
    else if (z <= 2800.0d0) then
        tmp = x + (y * 4.0d0)
    else if (z <= 1.9d+105) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double tmp;
	if (z <= -8.5e+60) {
		tmp = t_0;
	} else if (z <= -0.65) {
		tmp = z * (y * -6.0);
	} else if (z <= -4.4e-80) {
		tmp = y * 4.0;
	} else if (z <= -7.2e-109) {
		tmp = x * -3.0;
	} else if (z <= -5.6e-145) {
		tmp = y * 4.0;
	} else if (z <= -5.2e-306) {
		tmp = x * -3.0;
	} else if (z <= 7e-175) {
		tmp = y * 4.0;
	} else if (z <= 4.3e-79) {
		tmp = x * -3.0;
	} else if (z <= 2800.0) {
		tmp = x + (y * 4.0);
	} else if (z <= 1.9e+105) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	tmp = 0
	if z <= -8.5e+60:
		tmp = t_0
	elif z <= -0.65:
		tmp = z * (y * -6.0)
	elif z <= -4.4e-80:
		tmp = y * 4.0
	elif z <= -7.2e-109:
		tmp = x * -3.0
	elif z <= -5.6e-145:
		tmp = y * 4.0
	elif z <= -5.2e-306:
		tmp = x * -3.0
	elif z <= 7e-175:
		tmp = y * 4.0
	elif z <= 4.3e-79:
		tmp = x * -3.0
	elif z <= 2800.0:
		tmp = x + (y * 4.0)
	elif z <= 1.9e+105:
		tmp = -6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -8.5e+60)
		tmp = t_0;
	elseif (z <= -0.65)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -4.4e-80)
		tmp = Float64(y * 4.0);
	elseif (z <= -7.2e-109)
		tmp = Float64(x * -3.0);
	elseif (z <= -5.6e-145)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.2e-306)
		tmp = Float64(x * -3.0);
	elseif (z <= 7e-175)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.3e-79)
		tmp = Float64(x * -3.0);
	elseif (z <= 2800.0)
		tmp = Float64(x + Float64(y * 4.0));
	elseif (z <= 1.9e+105)
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -8.5e+60)
		tmp = t_0;
	elseif (z <= -0.65)
		tmp = z * (y * -6.0);
	elseif (z <= -4.4e-80)
		tmp = y * 4.0;
	elseif (z <= -7.2e-109)
		tmp = x * -3.0;
	elseif (z <= -5.6e-145)
		tmp = y * 4.0;
	elseif (z <= -5.2e-306)
		tmp = x * -3.0;
	elseif (z <= 7e-175)
		tmp = y * 4.0;
	elseif (z <= 4.3e-79)
		tmp = x * -3.0;
	elseif (z <= 2800.0)
		tmp = x + (y * 4.0);
	elseif (z <= 1.9e+105)
		tmp = -6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.5e+60], t$95$0, If[LessEqual[z, -0.65], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.4e-80], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -7.2e-109], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5.6e-145], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.2e-306], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7e-175], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.3e-79], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2800.0], N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.9e+105], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8.50000000000000064e60 or 1.9e105 < 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. Taylor expanded in x around 0 96.5%

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

      1. fma-def 96.5%

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

      2. *-commutative 96.5%

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

   7. Simplified 96.5%

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

   8. Taylor expanded in z around inf 99.8%

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

   9. Taylor expanded in y around 0 60.3%

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

   if -8.50000000000000064e60 < z < -0.650000000000000022

   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 x around 0 99.6%

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

   6. Taylor expanded in y around inf 70.9%

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

      1. *-commutative 70.9%

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

   8. Simplified 70.9%

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

   9. Taylor expanded in z around inf 66.9%

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

       1. *-commutative 66.9%

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

       2. *-commutative 66.9%

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

       3. associate-*r* 67.1%

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

   11. Simplified 67.1%

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

   if -0.650000000000000022 < z < -4.4000000000000002e-80 or -7.2000000000000001e-109 < z < -5.6000000000000002e-145 or -5.2000000000000001e-306 < z < 6.99999999999999997e-175

   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 x around 0 99.6%

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

      1. fma-def 99.5%

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

      2. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around 0 97.3%

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

   9. Taylor expanded in x around 0 68.8%

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

       1. *-commutative 68.8%

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

   11. Simplified 68.8%

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

   if -4.4000000000000002e-80 < z < -7.2000000000000001e-109 or -5.6000000000000002e-145 < z < -5.2000000000000001e-306 or 6.99999999999999997e-175 < z < 4.29999999999999982e-79

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. associate-+r+ 67.2%

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

      9. metadata-eval 67.2%

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

      10. metadata-eval 67.2%

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

      11. associate-*r* 67.2%

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

      12. metadata-eval 67.2%

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

      13. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   10. Simplified 67.2%

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

   if 4.29999999999999982e-79 < z < 2800

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around inf 51.1%

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

   6. Taylor expanded in z around 0 50.8%

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

      1. *-commutative 50.8%

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

   8. Simplified 50.8%

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

   if 2800 < z < 1.9e105

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around 0 99.5%

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

   6. Taylor expanded in y around inf 65.4%

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

      1. *-commutative 65.4%

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

   8. Simplified 65.4%

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

   9. Taylor expanded in z around inf 63.2%

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

4. Final simplification 63.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.5 \cdot 10^{+60}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.65:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.4 \cdot 10^{-80}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-109}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-79}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2800:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+105}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-110}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-80}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.65)
     t_0
     (if (<= z -1.5e-82)
       (* y 4.0)
       (if (<= z -1.1e-110)
         (* x -3.0)
         (if (<= z -6.1e-145)
           (* y 4.0)
           (if (<= z -6.8e-306)
             (* x -3.0)
             (if (<= z 2.3e-175)
               (* y 4.0)
               (if (<= z 7.8e-80)
                 (* x -3.0)
                 (if (<= z 2550.0) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -1.5e-82) {
		tmp = y * 4.0;
	} else if (z <= -1.1e-110) {
		tmp = x * -3.0;
	} else if (z <= -6.1e-145) {
		tmp = y * 4.0;
	} else if (z <= -6.8e-306) {
		tmp = x * -3.0;
	} else if (z <= 2.3e-175) {
		tmp = y * 4.0;
	} else if (z <= 7.8e-80) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.65d0)) then
        tmp = t_0
    else if (z <= (-1.5d-82)) then
        tmp = y * 4.0d0
    else if (z <= (-1.1d-110)) then
        tmp = x * (-3.0d0)
    else if (z <= (-6.1d-145)) then
        tmp = y * 4.0d0
    else if (z <= (-6.8d-306)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.3d-175) then
        tmp = y * 4.0d0
    else if (z <= 7.8d-80) then
        tmp = x * (-3.0d0)
    else if (z <= 2550.0d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -1.5e-82) {
		tmp = y * 4.0;
	} else if (z <= -1.1e-110) {
		tmp = x * -3.0;
	} else if (z <= -6.1e-145) {
		tmp = y * 4.0;
	} else if (z <= -6.8e-306) {
		tmp = x * -3.0;
	} else if (z <= 2.3e-175) {
		tmp = y * 4.0;
	} else if (z <= 7.8e-80) {
		tmp = x * -3.0;
	} else if (z <= 2550.0) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.65:
		tmp = t_0
	elif z <= -1.5e-82:
		tmp = y * 4.0
	elif z <= -1.1e-110:
		tmp = x * -3.0
	elif z <= -6.1e-145:
		tmp = y * 4.0
	elif z <= -6.8e-306:
		tmp = x * -3.0
	elif z <= 2.3e-175:
		tmp = y * 4.0
	elif z <= 7.8e-80:
		tmp = x * -3.0
	elif z <= 2550.0:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.65)
		tmp = t_0;
	elseif (z <= -1.5e-82)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.1e-110)
		tmp = Float64(x * -3.0);
	elseif (z <= -6.1e-145)
		tmp = Float64(y * 4.0);
	elseif (z <= -6.8e-306)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.3e-175)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.8e-80)
		tmp = Float64(x * -3.0);
	elseif (z <= 2550.0)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.65)
		tmp = t_0;
	elseif (z <= -1.5e-82)
		tmp = y * 4.0;
	elseif (z <= -1.1e-110)
		tmp = x * -3.0;
	elseif (z <= -6.1e-145)
		tmp = y * 4.0;
	elseif (z <= -6.8e-306)
		tmp = x * -3.0;
	elseif (z <= 2.3e-175)
		tmp = y * 4.0;
	elseif (z <= 7.8e-80)
		tmp = x * -3.0;
	elseif (z <= 2550.0)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.65], t$95$0, If[LessEqual[z, -1.5e-82], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.1e-110], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -6.1e-145], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -6.8e-306], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.3e-175], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.8e-80], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2550.0], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022 or 2550 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 97.4%

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

   6. Taylor expanded in y around inf 51.0%

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

      1. *-commutative 51.0%

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

   8. Simplified 51.0%

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

   9. Taylor expanded in z around inf 50.2%

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

   if -0.650000000000000022 < z < -1.4999999999999999e-82 or -1.1e-110 < z < -6.1e-145 or -6.7999999999999996e-306 < z < 2.3e-175 or 7.7999999999999995e-80 < z < 2550

   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 x around 0 99.5%

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

      1. fma-def 99.5%

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

      2. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around 0 93.6%

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

   9. Taylor expanded in x around 0 64.9%

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

       1. *-commutative 64.9%

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

   11. Simplified 64.9%

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

   if -1.4999999999999999e-82 < z < -1.1e-110 or -6.1e-145 < z < -6.7999999999999996e-306 or 2.3e-175 < z < 7.7999999999999995e-80

   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 x around inf 67.2%

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

      1. sub-neg 67.2%

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

      2. distribute-rgt-in 67.2%

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

      3. metadata-eval 67.2%

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

      4. metadata-eval 67.2%

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

      5. neg-mul-1 67.2%

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

      6. associate-*r* 67.2%

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

      7. *-commutative 67.2%

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

      8. associate-+r+ 67.2%

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

      9. metadata-eval 67.2%

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

      10. metadata-eval 67.2%

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

      11. associate-*r* 67.2%

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

      12. metadata-eval 67.2%

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

      13. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   8. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   10. Simplified 67.2%

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

4. Final simplification 57.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-110}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.1 \cdot 10^{-145}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-80}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2550:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.65)))
   (* z (+ (* y -6.0) (* x 6.0)))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.65)) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else {
		tmp = (x * -3.0) + (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 ((z <= (-0.58d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = z * ((y * (-6.0d0)) + (x * 6.0d0))
    else
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.65)) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.65):
		tmp = z * ((y * -6.0) + (x * 6.0))
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.65))
		tmp = Float64(z * Float64(Float64(y * -6.0) + Float64(x * 6.0)));
	else
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.65)))
		tmp = z * ((y * -6.0) + (x * 6.0));
	else
		tmp = (x * -3.0) + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(z * N[(N[(y * -6.0), $MachinePrecision] + N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 97.4%

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

      1. fma-def 97.4%

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

      2. *-commutative 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in z around inf 97.2%

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

   if -0.57999999999999996 < z < 0.650000000000000022

   1. Initial program 99.3%

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

      1. 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 x around 0 99.6%

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

      1. fma-def 99.6%

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

      2. *-commutative 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in z around 0 98.0%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+69} \lor \neg \left(x \leq 6.5 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.9e+69) (not (<= x 6.5e-39)))
   (* x (+ -3.0 (* z 6.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.9e+69) || !(x <= 6.5e-39)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - 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 ((x <= (-5.9d+69)) .or. (.not. (x <= 6.5d-39))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.9e+69) || !(x <= 6.5e-39)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.9e+69) or not (x <= 6.5e-39):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.9e+69) || !(x <= 6.5e-39))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -5.9e+69) || ~((x <= 6.5e-39)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.9e+69], N[Not[LessEqual[x, 6.5e-39]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.90000000000000004e69 or 6.50000000000000027e-39 < x

   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 x around inf 79.8%

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

      1. sub-neg 79.8%

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

      2. distribute-rgt-in 79.8%

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

      3. metadata-eval 79.8%

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

      4. metadata-eval 79.8%

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

      5. neg-mul-1 79.8%

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

      6. associate-*r* 79.8%

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

      7. *-commutative 79.8%

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

      8. associate-+r+ 79.8%

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

      9. metadata-eval 79.8%

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

      10. metadata-eval 79.8%

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

      11. associate-*r* 79.8%

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

      12. metadata-eval 79.8%

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

      13. *-commutative 79.8%

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

   7. Simplified 79.8%

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

   if -5.90000000000000004e69 < x < 6.50000000000000027e-39

   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 x around 0 99.5%

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

   6. Taylor expanded in y around inf 74.8%

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

      1. *-commutative 74.8%

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

   8. Simplified 74.8%

      \[\leadsto \color{blue}{6 \cdot \left(\left(0.6666666666666666 - z\right) \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.9 \cdot 10^{+69} \lor \neg \left(x \leq 6.5 \cdot 10^{-39}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+69} \lor \neg \left(x \leq 2.9 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.55e+69) (not (<= x 2.9e-40)))
   (* 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 <= -2.55e+69) || !(x <= 2.9e-40)) {
		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 <= (-2.55d+69)) .or. (.not. (x <= 2.9d-40))) 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 <= -2.55e+69) || !(x <= 2.9e-40)) {
		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 <= -2.55e+69) or not (x <= 2.9e-40):
		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 <= -2.55e+69) || !(x <= 2.9e-40))
		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 <= -2.55e+69) || ~((x <= 2.9e-40)))
		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, -2.55e+69], N[Not[LessEqual[x, 2.9e-40]], $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 < -2.54999999999999999e69 or 2.8999999999999999e-40 < x

   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 x around inf 79.8%

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

      1. sub-neg 79.8%

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

      2. distribute-rgt-in 79.8%

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

      3. metadata-eval 79.8%

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

      4. metadata-eval 79.8%

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

      5. neg-mul-1 79.8%

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

      6. associate-*r* 79.8%

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

      7. *-commutative 79.8%

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

      8. associate-+r+ 79.8%

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

      9. metadata-eval 79.8%

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

      10. metadata-eval 79.8%

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

      11. associate-*r* 79.8%

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

      12. metadata-eval 79.8%

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

      13. *-commutative 79.8%

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

   7. Simplified 79.8%

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

   if -2.54999999999999999e69 < x < 2.8999999999999999e-40

   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-def 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.7%

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

      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 inf 75.1%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.55 \cdot 10^{+69} \lor \neg \left(x \leq 2.9 \cdot 10^{-40}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 57.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+135}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+153}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.22e+135)
   (* x -3.0)
   (if (<= x 1.05e+153)
     (* 6.0 (* y (- 0.6666666666666666 z)))
     (* 6.0 (* x z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.22e+135) {
		tmp = x * -3.0;
	} else if (x <= 1.05e+153) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.22d+135)) then
        tmp = x * (-3.0d0)
    else if (x <= 1.05d+153) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.22e+135) {
		tmp = x * -3.0;
	} else if (x <= 1.05e+153) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.22e+135:
		tmp = x * -3.0
	elif x <= 1.05e+153:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.22e+135)
		tmp = Float64(x * -3.0);
	elseif (x <= 1.05e+153)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.22e+135)
		tmp = x * -3.0;
	elseif (x <= 1.05e+153)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.22e+135], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 1.05e+153], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.21999999999999996e135

   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. Taylor expanded in x around inf 91.2%

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

      1. sub-neg 91.2%

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

      2. distribute-rgt-in 91.2%

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

      3. metadata-eval 91.2%

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

      4. metadata-eval 91.2%

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

      5. neg-mul-1 91.2%

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

      6. associate-*r* 91.2%

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

      7. *-commutative 91.2%

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

      8. associate-+r+ 91.2%

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

      9. metadata-eval 91.2%

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

      10. metadata-eval 91.2%

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

      11. associate-*r* 91.2%

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

      12. metadata-eval 91.2%

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

      13. *-commutative 91.2%

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

   7. Simplified 91.2%

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

   8. Taylor expanded in z around 0 53.7%

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

      1. *-commutative 53.7%

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

   10. Simplified 53.7%

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

   if -1.21999999999999996e135 < x < 1.05000000000000008e153

   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 x around 0 99.6%

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

   6. Taylor expanded in y around inf 64.3%

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

      1. *-commutative 64.3%

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

   8. Simplified 64.3%

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

   if 1.05000000000000008e153 < x

   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 x around inf 93.7%

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

      1. sub-neg 93.7%

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

      2. distribute-rgt-in 93.7%

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

      3. metadata-eval 93.7%

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

      4. metadata-eval 93.7%

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

      5. neg-mul-1 93.7%

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

      6. associate-*r* 93.7%

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

      7. *-commutative 93.7%

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

      8. associate-+r+ 93.7%

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

      9. metadata-eval 93.7%

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

      10. metadata-eval 93.7%

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

      11. associate-*r* 93.7%

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

      12. metadata-eval 93.7%

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

      13. *-commutative 93.7%

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

   7. Simplified 93.7%

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

   8. Taylor expanded in z around inf 58.0%

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

4. Final simplification 62.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.22 \cdot 10^{+135}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+153}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 37.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+76} \lor \neg \left(x \leq 6 \cdot 10^{-27}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.7e+76) (not (<= x 6e-27))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.7e+76) || !(x <= 6e-27)) {
		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 <= (-1.7d+76)) .or. (.not. (x <= 6d-27))) 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 <= -1.7e+76) || !(x <= 6e-27)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.7e+76) or not (x <= 6e-27):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.7e+76) || !(x <= 6e-27))
		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 <= -1.7e+76) || ~((x <= 6e-27)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.7e+76], N[Not[LessEqual[x, 6e-27]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.6999999999999999e76 or 6.0000000000000002e-27 < x

   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 x around inf 80.4%

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

      1. sub-neg 80.4%

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

      2. distribute-rgt-in 80.5%

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

      3. metadata-eval 80.5%

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

      4. metadata-eval 80.5%

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

      5. neg-mul-1 80.5%

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

      6. associate-*r* 80.5%

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

      7. *-commutative 80.5%

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

      8. associate-+r+ 80.5%

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

      9. metadata-eval 80.5%

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

      10. metadata-eval 80.5%

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

      11. associate-*r* 80.5%

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

      12. metadata-eval 80.5%

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

      13. *-commutative 80.5%

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

   7. Simplified 80.5%

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

   8. Taylor expanded in z around 0 42.1%

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

      1. *-commutative 42.1%

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

   10. Simplified 42.1%

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

   if -1.6999999999999999e76 < x < 6.0000000000000002e-27

   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 x around 0 99.6%

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

      1. fma-def 99.5%

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

      2. *-commutative 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in z around 0 46.5%

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

   9. Taylor expanded in x around 0 38.5%

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

       1. *-commutative 38.5%

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

   11. Simplified 38.5%

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

4. Final simplification 40.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.7 \cdot 10^{+76} \lor \neg \left(x \leq 6 \cdot 10^{-27}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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. Final simplification 99.5%

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

Alternative 14: 99.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

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

   4. metadata-eval 99.7%

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

3. Simplified 99.7%

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

   1. fma-udef 99.7%

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

6. Applied egg-rr 99.7%

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

7. Final simplification 99.7%

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

Alternative 15: 26.1% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 x around inf 51.5%

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

   1. sub-neg 51.5%

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

   2. distribute-rgt-in 51.5%

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

   3. metadata-eval 51.5%

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

   4. metadata-eval 51.5%

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

   5. neg-mul-1 51.5%

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

   6. associate-*r* 51.5%

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

   7. *-commutative 51.5%

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

   8. associate-+r+ 51.5%

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

   9. metadata-eval 51.5%

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

   10. metadata-eval 51.5%

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

   11. associate-*r* 51.5%

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

   12. metadata-eval 51.5%

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

   13. *-commutative 51.5%

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

7. Simplified 51.5%

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

8. Taylor expanded in z around 0 25.0%

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

   1. *-commutative 25.0%

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

10. Simplified 25.0%

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

11. Final simplification 25.0%

    \[\leadsto x \cdot -3 \]
12. Add Preprocessing

Alternative 16: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 50.6%

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

6. Taylor expanded in x around inf 2.6%

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

7. Final simplification 2.6%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024036 
(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))))