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

Percentage Accurate: 99.5% → 99.8%

Time: 12.0s

Alternatives: 14

Speedup: 1.2×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. +-commutative 99.2%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.5% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. 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. Step-by-step derivation

   1. +-commutative 99.2%

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

   2. *-commutative 99.2%

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

   3. associate-*r* 99.5%

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

   4. fma-define 99.4%

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

6. Applied egg-rr 99.4%

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

7. Final simplification 99.4%

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

Alternative 3: 51.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.09:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-82}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-226}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-303}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-266}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+137}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.09)
     t_0
     (if (<= z -1.15e-82)
       (* y 4.0)
       (if (<= z -2.15e-185)
         (* x -3.0)
         (if (<= z -3.6e-226)
           (* y 4.0)
           (if (<= z 1.05e-303)
             (* x -3.0)
             (if (<= z 4.4e-266)
               (* y 4.0)
               (if (<= z 3.2e-72)
                 (* x -3.0)
                 (if (<= z 0.52)
                   (* y 4.0)
                   (if (<= z 1.85e+137) (* 6.0 (* x z)) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.09) {
		tmp = t_0;
	} else if (z <= -1.15e-82) {
		tmp = y * 4.0;
	} else if (z <= -2.15e-185) {
		tmp = x * -3.0;
	} else if (z <= -3.6e-226) {
		tmp = y * 4.0;
	} else if (z <= 1.05e-303) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-266) {
		tmp = y * 4.0;
	} else if (z <= 3.2e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if (z <= 1.85e+137) {
		tmp = 6.0 * (x * 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 = (-6.0d0) * (y * z)
    if (z <= (-0.09d0)) then
        tmp = t_0
    else if (z <= (-1.15d-82)) then
        tmp = y * 4.0d0
    else if (z <= (-2.15d-185)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.6d-226)) then
        tmp = y * 4.0d0
    else if (z <= 1.05d-303) then
        tmp = x * (-3.0d0)
    else if (z <= 4.4d-266) then
        tmp = y * 4.0d0
    else if (z <= 3.2d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 0.52d0) then
        tmp = y * 4.0d0
    else if (z <= 1.85d+137) then
        tmp = 6.0d0 * (x * 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 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.09) {
		tmp = t_0;
	} else if (z <= -1.15e-82) {
		tmp = y * 4.0;
	} else if (z <= -2.15e-185) {
		tmp = x * -3.0;
	} else if (z <= -3.6e-226) {
		tmp = y * 4.0;
	} else if (z <= 1.05e-303) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-266) {
		tmp = y * 4.0;
	} else if (z <= 3.2e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if (z <= 1.85e+137) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.09:
		tmp = t_0
	elif z <= -1.15e-82:
		tmp = y * 4.0
	elif z <= -2.15e-185:
		tmp = x * -3.0
	elif z <= -3.6e-226:
		tmp = y * 4.0
	elif z <= 1.05e-303:
		tmp = x * -3.0
	elif z <= 4.4e-266:
		tmp = y * 4.0
	elif z <= 3.2e-72:
		tmp = x * -3.0
	elif z <= 0.52:
		tmp = y * 4.0
	elif z <= 1.85e+137:
		tmp = 6.0 * (x * z)
	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 <= -0.09)
		tmp = t_0;
	elseif (z <= -1.15e-82)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.15e-185)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.6e-226)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.05e-303)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.4e-266)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.2e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.52)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.85e+137)
		tmp = Float64(6.0 * Float64(x * z));
	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 <= -0.09)
		tmp = t_0;
	elseif (z <= -1.15e-82)
		tmp = y * 4.0;
	elseif (z <= -2.15e-185)
		tmp = x * -3.0;
	elseif (z <= -3.6e-226)
		tmp = y * 4.0;
	elseif (z <= 1.05e-303)
		tmp = x * -3.0;
	elseif (z <= 4.4e-266)
		tmp = y * 4.0;
	elseif (z <= 3.2e-72)
		tmp = x * -3.0;
	elseif (z <= 0.52)
		tmp = y * 4.0;
	elseif (z <= 1.85e+137)
		tmp = 6.0 * (x * z);
	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, -0.09], t$95$0, If[LessEqual[z, -1.15e-82], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.15e-185], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.6e-226], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.05e-303], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.4e-266], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.2e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.85e+137], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.089999999999999997 or 1.8500000000000001e137 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 59.1%

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

   8. Taylor expanded in z around inf 58.6%

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

   if -0.089999999999999997 < z < -1.14999999999999998e-82 or -2.15e-185 < z < -3.59999999999999994e-226 or 1.05e-303 < z < 4.3999999999999999e-266 or 3.19999999999999999e-72 < z < 0.52000000000000002

   1. Initial program 98.2%

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

      1. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. +-commutative 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*r* 99.2%

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

      4. fma-define 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in y around inf 71.1%

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

   8. Taylor expanded in z around 0 70.5%

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

   if -1.14999999999999998e-82 < z < -2.15e-185 or -3.59999999999999994e-226 < z < 1.05e-303 or 4.3999999999999999e-266 < z < 3.19999999999999999e-72

   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 66.6%

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

      1. +-commutative 66.6%

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

      2. +-commutative 66.6%

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

      3. metadata-eval 66.6%

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

      4. cancel-sign-sub-inv 66.6%

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

      5. *-commutative 66.6%

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

      6. cancel-sign-sub-inv 66.6%

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

      7. distribute-lft-neg-in 66.6%

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

      8. *-commutative 66.6%

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

      9. sub-neg 66.6%

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

      10. distribute-lft-in 66.6%

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

      11. metadata-eval 66.6%

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

      12. distribute-rgt-neg-in 66.6%

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

      13. distribute-lft-neg-in 66.6%

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

      14. metadata-eval 66.6%

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

      15. mul-1-neg 66.6%

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

      16. distribute-lft-in 66.6%

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

      17. metadata-eval 66.6%

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

      18. associate-+r+ 66.6%

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

      19. metadata-eval 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in z around 0 66.6%

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

      1. *-commutative 66.6%

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

   10. Simplified 66.6%

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

   if 0.52000000000000002 < z < 1.8500000000000001e137

   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 63.0%

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

      1. +-commutative 63.0%

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

      2. +-commutative 63.0%

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

      3. metadata-eval 63.0%

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

      4. cancel-sign-sub-inv 63.0%

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

      5. *-commutative 63.0%

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

      6. cancel-sign-sub-inv 63.0%

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

      7. distribute-lft-neg-in 63.0%

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

      8. *-commutative 63.0%

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

      9. sub-neg 63.0%

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

      10. distribute-lft-in 63.0%

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

      11. metadata-eval 63.0%

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

      12. distribute-rgt-neg-in 63.0%

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

      13. distribute-lft-neg-in 63.0%

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

      14. metadata-eval 63.0%

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

      15. mul-1-neg 63.0%

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

      16. distribute-lft-in 63.0%

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

      17. metadata-eval 63.0%

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

      18. associate-+r+ 63.0%

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

      19. metadata-eval 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in z around inf 63.2%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.09:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-82}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.6 \cdot 10^{-226}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-303}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-266}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{+137}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.09:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-184}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-225}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-304}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+136}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.09)
     t_0
     (if (<= z -3.5e-82)
       (* y 4.0)
       (if (<= z -4.5e-184)
         (* x -3.0)
         (if (<= z -2.2e-225)
           (* y 4.0)
           (if (<= z 3.3e-304)
             (* x -3.0)
             (if (<= z 1.9e-257)
               (* y 4.0)
               (if (<= z 2.35e-73)
                 (* x -3.0)
                 (if (<= z 0.6)
                   (* y 4.0)
                   (if (<= z 3.7e+136) (* z (* x 6.0)) t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.09) {
		tmp = t_0;
	} else if (z <= -3.5e-82) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-184) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-225) {
		tmp = y * 4.0;
	} else if (z <= 3.3e-304) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-257) {
		tmp = y * 4.0;
	} else if (z <= 2.35e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.6) {
		tmp = y * 4.0;
	} else if (z <= 3.7e+136) {
		tmp = z * (x * 6.0);
	} 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 <= (-0.09d0)) then
        tmp = t_0
    else if (z <= (-3.5d-82)) then
        tmp = y * 4.0d0
    else if (z <= (-4.5d-184)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.2d-225)) then
        tmp = y * 4.0d0
    else if (z <= 3.3d-304) then
        tmp = x * (-3.0d0)
    else if (z <= 1.9d-257) then
        tmp = y * 4.0d0
    else if (z <= 2.35d-73) then
        tmp = x * (-3.0d0)
    else if (z <= 0.6d0) then
        tmp = y * 4.0d0
    else if (z <= 3.7d+136) then
        tmp = z * (x * 6.0d0)
    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 <= -0.09) {
		tmp = t_0;
	} else if (z <= -3.5e-82) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-184) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-225) {
		tmp = y * 4.0;
	} else if (z <= 3.3e-304) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-257) {
		tmp = y * 4.0;
	} else if (z <= 2.35e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.6) {
		tmp = y * 4.0;
	} else if (z <= 3.7e+136) {
		tmp = z * (x * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.09:
		tmp = t_0
	elif z <= -3.5e-82:
		tmp = y * 4.0
	elif z <= -4.5e-184:
		tmp = x * -3.0
	elif z <= -2.2e-225:
		tmp = y * 4.0
	elif z <= 3.3e-304:
		tmp = x * -3.0
	elif z <= 1.9e-257:
		tmp = y * 4.0
	elif z <= 2.35e-73:
		tmp = x * -3.0
	elif z <= 0.6:
		tmp = y * 4.0
	elif z <= 3.7e+136:
		tmp = z * (x * 6.0)
	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 <= -0.09)
		tmp = t_0;
	elseif (z <= -3.5e-82)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.5e-184)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.2e-225)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.3e-304)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.9e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.35e-73)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.6)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.7e+136)
		tmp = Float64(z * Float64(x * 6.0));
	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 <= -0.09)
		tmp = t_0;
	elseif (z <= -3.5e-82)
		tmp = y * 4.0;
	elseif (z <= -4.5e-184)
		tmp = x * -3.0;
	elseif (z <= -2.2e-225)
		tmp = y * 4.0;
	elseif (z <= 3.3e-304)
		tmp = x * -3.0;
	elseif (z <= 1.9e-257)
		tmp = y * 4.0;
	elseif (z <= 2.35e-73)
		tmp = x * -3.0;
	elseif (z <= 0.6)
		tmp = y * 4.0;
	elseif (z <= 3.7e+136)
		tmp = z * (x * 6.0);
	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, -0.09], t$95$0, If[LessEqual[z, -3.5e-82], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.5e-184], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.2e-225], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.3e-304], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.9e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.35e-73], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.6], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.7e+136], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.089999999999999997 or 3.7000000000000001e136 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 59.1%

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

   8. Taylor expanded in z around inf 58.6%

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

   if -0.089999999999999997 < z < -3.4999999999999999e-82 or -4.5000000000000001e-184 < z < -2.2e-225 or 3.30000000000000013e-304 < z < 1.9000000000000002e-257 or 2.34999999999999997e-73 < z < 0.599999999999999978

   1. Initial program 98.2%

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

      1. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. +-commutative 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*r* 99.2%

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

      4. fma-define 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in y around inf 71.1%

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

   8. Taylor expanded in z around 0 70.5%

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

   if -3.4999999999999999e-82 < z < -4.5000000000000001e-184 or -2.2e-225 < z < 3.30000000000000013e-304 or 1.9000000000000002e-257 < z < 2.34999999999999997e-73

   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 66.6%

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

      1. +-commutative 66.6%

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

      2. +-commutative 66.6%

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

      3. metadata-eval 66.6%

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

      4. cancel-sign-sub-inv 66.6%

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

      5. *-commutative 66.6%

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

      6. cancel-sign-sub-inv 66.6%

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

      7. distribute-lft-neg-in 66.6%

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

      8. *-commutative 66.6%

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

      9. sub-neg 66.6%

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

      10. distribute-lft-in 66.6%

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

      11. metadata-eval 66.6%

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

      12. distribute-rgt-neg-in 66.6%

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

      13. distribute-lft-neg-in 66.6%

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

      14. metadata-eval 66.6%

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

      15. mul-1-neg 66.6%

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

      16. distribute-lft-in 66.6%

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

      17. metadata-eval 66.6%

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

      18. associate-+r+ 66.6%

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

      19. metadata-eval 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in z around 0 66.6%

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

      1. *-commutative 66.6%

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

   10. Simplified 66.6%

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

   if 0.599999999999999978 < z < 3.7000000000000001e136

   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 63.0%

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

      1. +-commutative 63.0%

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

      2. +-commutative 63.0%

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

      3. metadata-eval 63.0%

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

      4. cancel-sign-sub-inv 63.0%

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

      5. *-commutative 63.0%

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

      6. cancel-sign-sub-inv 63.0%

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

      7. distribute-lft-neg-in 63.0%

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

      8. *-commutative 63.0%

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

      9. sub-neg 63.0%

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

      10. distribute-lft-in 63.0%

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

      11. metadata-eval 63.0%

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

      12. distribute-rgt-neg-in 63.0%

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

      13. distribute-lft-neg-in 63.0%

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

      14. metadata-eval 63.0%

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

      15. mul-1-neg 63.0%

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

      16. distribute-lft-in 63.0%

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

      17. metadata-eval 63.0%

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

      18. associate-+r+ 63.0%

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

      19. metadata-eval 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in z around inf 63.4%

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

   9. Taylor expanded in z around inf 63.4%

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

       1. *-commutative 63.4%

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

   11. Simplified 63.4%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.09:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-82}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-184}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-225}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-304}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.7 \cdot 10^{+136}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 51.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.09:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-184}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-226}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-303}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-262}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-71}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.09)
   (* -6.0 (* y z))
   (if (<= z -8.5e-84)
     (* y 4.0)
     (if (<= z -1.4e-184)
       (* x -3.0)
       (if (<= z -4.5e-226)
         (* y 4.0)
         (if (<= z 2.6e-303)
           (* x -3.0)
           (if (<= z 5.5e-262)
             (* y 4.0)
             (if (<= z 1.66e-71)
               (* x -3.0)
               (if (<= z 0.52)
                 (* y 4.0)
                 (if (<= z 3.2e+138) (* z (* x 6.0)) (* z (* y -6.0))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.09) {
		tmp = -6.0 * (y * z);
	} else if (z <= -8.5e-84) {
		tmp = y * 4.0;
	} else if (z <= -1.4e-184) {
		tmp = x * -3.0;
	} else if (z <= -4.5e-226) {
		tmp = y * 4.0;
	} else if (z <= 2.6e-303) {
		tmp = x * -3.0;
	} else if (z <= 5.5e-262) {
		tmp = y * 4.0;
	} else if (z <= 1.66e-71) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if (z <= 3.2e+138) {
		tmp = z * (x * 6.0);
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.09d0)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-8.5d-84)) then
        tmp = y * 4.0d0
    else if (z <= (-1.4d-184)) then
        tmp = x * (-3.0d0)
    else if (z <= (-4.5d-226)) then
        tmp = y * 4.0d0
    else if (z <= 2.6d-303) then
        tmp = x * (-3.0d0)
    else if (z <= 5.5d-262) then
        tmp = y * 4.0d0
    else if (z <= 1.66d-71) then
        tmp = x * (-3.0d0)
    else if (z <= 0.52d0) then
        tmp = y * 4.0d0
    else if (z <= 3.2d+138) then
        tmp = z * (x * 6.0d0)
    else
        tmp = z * (y * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.09) {
		tmp = -6.0 * (y * z);
	} else if (z <= -8.5e-84) {
		tmp = y * 4.0;
	} else if (z <= -1.4e-184) {
		tmp = x * -3.0;
	} else if (z <= -4.5e-226) {
		tmp = y * 4.0;
	} else if (z <= 2.6e-303) {
		tmp = x * -3.0;
	} else if (z <= 5.5e-262) {
		tmp = y * 4.0;
	} else if (z <= 1.66e-71) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else if (z <= 3.2e+138) {
		tmp = z * (x * 6.0);
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.09:
		tmp = -6.0 * (y * z)
	elif z <= -8.5e-84:
		tmp = y * 4.0
	elif z <= -1.4e-184:
		tmp = x * -3.0
	elif z <= -4.5e-226:
		tmp = y * 4.0
	elif z <= 2.6e-303:
		tmp = x * -3.0
	elif z <= 5.5e-262:
		tmp = y * 4.0
	elif z <= 1.66e-71:
		tmp = x * -3.0
	elif z <= 0.52:
		tmp = y * 4.0
	elif z <= 3.2e+138:
		tmp = z * (x * 6.0)
	else:
		tmp = z * (y * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.09)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -8.5e-84)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.4e-184)
		tmp = Float64(x * -3.0);
	elseif (z <= -4.5e-226)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.6e-303)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.5e-262)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.66e-71)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.52)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.2e+138)
		tmp = Float64(z * Float64(x * 6.0));
	else
		tmp = Float64(z * Float64(y * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.09)
		tmp = -6.0 * (y * z);
	elseif (z <= -8.5e-84)
		tmp = y * 4.0;
	elseif (z <= -1.4e-184)
		tmp = x * -3.0;
	elseif (z <= -4.5e-226)
		tmp = y * 4.0;
	elseif (z <= 2.6e-303)
		tmp = x * -3.0;
	elseif (z <= 5.5e-262)
		tmp = y * 4.0;
	elseif (z <= 1.66e-71)
		tmp = x * -3.0;
	elseif (z <= 0.52)
		tmp = y * 4.0;
	elseif (z <= 3.2e+138)
		tmp = z * (x * 6.0);
	else
		tmp = z * (y * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.09], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -8.5e-84], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.4e-184], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -4.5e-226], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.6e-303], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.5e-262], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.66e-71], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.2e+138], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.089999999999999997

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 59.5%

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

   8. Taylor expanded in z around inf 58.7%

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

   if -0.089999999999999997 < z < -8.4999999999999994e-84 or -1.3999999999999999e-184 < z < -4.50000000000000011e-226 or 2.60000000000000005e-303 < z < 5.5000000000000004e-262 or 1.6599999999999999e-71 < z < 0.52000000000000002

   1. Initial program 98.2%

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

      1. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. +-commutative 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*r* 99.2%

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

      4. fma-define 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in y around inf 71.1%

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

   8. Taylor expanded in z around 0 70.5%

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

   if -8.4999999999999994e-84 < z < -1.3999999999999999e-184 or -4.50000000000000011e-226 < z < 2.60000000000000005e-303 or 5.5000000000000004e-262 < z < 1.6599999999999999e-71

   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 66.6%

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

      1. +-commutative 66.6%

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

      2. +-commutative 66.6%

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

      3. metadata-eval 66.6%

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

      4. cancel-sign-sub-inv 66.6%

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

      5. *-commutative 66.6%

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

      6. cancel-sign-sub-inv 66.6%

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

      7. distribute-lft-neg-in 66.6%

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

      8. *-commutative 66.6%

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

      9. sub-neg 66.6%

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

      10. distribute-lft-in 66.6%

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

      11. metadata-eval 66.6%

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

      12. distribute-rgt-neg-in 66.6%

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

      13. distribute-lft-neg-in 66.6%

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

      14. metadata-eval 66.6%

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

      15. mul-1-neg 66.6%

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

      16. distribute-lft-in 66.6%

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

      17. metadata-eval 66.6%

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

      18. associate-+r+ 66.6%

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

      19. metadata-eval 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in z around 0 66.6%

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

      1. *-commutative 66.6%

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

   10. Simplified 66.6%

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

   if 0.52000000000000002 < z < 3.2000000000000001e138

   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 63.0%

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

      1. +-commutative 63.0%

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

      2. +-commutative 63.0%

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

      3. metadata-eval 63.0%

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

      4. cancel-sign-sub-inv 63.0%

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

      5. *-commutative 63.0%

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

      6. cancel-sign-sub-inv 63.0%

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

      7. distribute-lft-neg-in 63.0%

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

      8. *-commutative 63.0%

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

      9. sub-neg 63.0%

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

      10. distribute-lft-in 63.0%

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

      11. metadata-eval 63.0%

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

      12. distribute-rgt-neg-in 63.0%

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

      13. distribute-lft-neg-in 63.0%

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

      14. metadata-eval 63.0%

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

      15. mul-1-neg 63.0%

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

      16. distribute-lft-in 63.0%

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

      17. metadata-eval 63.0%

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

      18. associate-+r+ 63.0%

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

      19. metadata-eval 63.0%

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

   7. Simplified 63.0%

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

   8. Taylor expanded in z around inf 63.4%

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

   9. Taylor expanded in z around inf 63.4%

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

       1. *-commutative 63.4%

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

   11. Simplified 63.4%

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

   if 3.2000000000000001e138 < 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. Step-by-step derivation

      1. +-commutative 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 58.4%

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

   8. Taylor expanded in z around inf 58.4%

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

      1. associate-*r* 58.5%

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

      2. *-commutative 58.5%

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

      3. associate-*r* 58.4%

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

   10. Simplified 58.4%

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

   11. Taylor expanded in y around 0 58.4%

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

       1. associate-*r* 58.5%

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

       2. *-commutative 58.5%

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

       3. *-commutative 58.5%

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

   13. Simplified 58.5%

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

4. Final simplification 64.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.09:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-84}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-184}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-226}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-303}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-262}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.66 \cdot 10^{-71}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.2 \cdot 10^{+138}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 51.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.09:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-83}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-184}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-225}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-303}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-74}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.09)
     t_0
     (if (<= z -3.3e-83)
       (* y 4.0)
       (if (<= z -2e-184)
         (* x -3.0)
         (if (<= z -9.5e-225)
           (* y 4.0)
           (if (<= z 1.02e-303)
             (* x -3.0)
             (if (<= z 1.35e-257)
               (* y 4.0)
               (if (<= z 5.5e-74)
                 (* x -3.0)
                 (if (<= z 0.66) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.09) {
		tmp = t_0;
	} else if (z <= -3.3e-83) {
		tmp = y * 4.0;
	} else if (z <= -2e-184) {
		tmp = x * -3.0;
	} else if (z <= -9.5e-225) {
		tmp = y * 4.0;
	} else if (z <= 1.02e-303) {
		tmp = x * -3.0;
	} else if (z <= 1.35e-257) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-74) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.09d0)) then
        tmp = t_0
    else if (z <= (-3.3d-83)) then
        tmp = y * 4.0d0
    else if (z <= (-2d-184)) then
        tmp = x * (-3.0d0)
    else if (z <= (-9.5d-225)) then
        tmp = y * 4.0d0
    else if (z <= 1.02d-303) then
        tmp = x * (-3.0d0)
    else if (z <= 1.35d-257) then
        tmp = y * 4.0d0
    else if (z <= 5.5d-74) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.09) {
		tmp = t_0;
	} else if (z <= -3.3e-83) {
		tmp = y * 4.0;
	} else if (z <= -2e-184) {
		tmp = x * -3.0;
	} else if (z <= -9.5e-225) {
		tmp = y * 4.0;
	} else if (z <= 1.02e-303) {
		tmp = x * -3.0;
	} else if (z <= 1.35e-257) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-74) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.09:
		tmp = t_0
	elif z <= -3.3e-83:
		tmp = y * 4.0
	elif z <= -2e-184:
		tmp = x * -3.0
	elif z <= -9.5e-225:
		tmp = y * 4.0
	elif z <= 1.02e-303:
		tmp = x * -3.0
	elif z <= 1.35e-257:
		tmp = y * 4.0
	elif z <= 5.5e-74:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.09)
		tmp = t_0;
	elseif (z <= -3.3e-83)
		tmp = Float64(y * 4.0);
	elseif (z <= -2e-184)
		tmp = Float64(x * -3.0);
	elseif (z <= -9.5e-225)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.02e-303)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.35e-257)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.5e-74)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.09)
		tmp = t_0;
	elseif (z <= -3.3e-83)
		tmp = y * 4.0;
	elseif (z <= -2e-184)
		tmp = x * -3.0;
	elseif (z <= -9.5e-225)
		tmp = y * 4.0;
	elseif (z <= 1.02e-303)
		tmp = x * -3.0;
	elseif (z <= 1.35e-257)
		tmp = y * 4.0;
	elseif (z <= 5.5e-74)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.09], t$95$0, If[LessEqual[z, -3.3e-83], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2e-184], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -9.5e-225], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.02e-303], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.35e-257], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.5e-74], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.089999999999999997 or 0.660000000000000031 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 56.2%

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

   8. Taylor expanded in z around inf 54.5%

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

   if -0.089999999999999997 < z < -3.2999999999999999e-83 or -2.0000000000000001e-184 < z < -9.50000000000000006e-225 or 1.01999999999999996e-303 < z < 1.3499999999999999e-257 or 5.5000000000000001e-74 < z < 0.660000000000000031

   1. Initial program 98.2%

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

      1. metadata-eval 98.2%

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

   3. Simplified 98.2%

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

      1. +-commutative 98.2%

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

      2. *-commutative 98.2%

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

      3. associate-*r* 99.2%

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

      4. fma-define 99.2%

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

   6. Applied egg-rr 99.2%

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

   7. Taylor expanded in y around inf 71.1%

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

   8. Taylor expanded in z around 0 70.5%

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

   if -3.2999999999999999e-83 < z < -2.0000000000000001e-184 or -9.50000000000000006e-225 < z < 1.01999999999999996e-303 or 1.3499999999999999e-257 < z < 5.5000000000000001e-74

   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 66.6%

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

      1. +-commutative 66.6%

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

      2. +-commutative 66.6%

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

      3. metadata-eval 66.6%

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

      4. cancel-sign-sub-inv 66.6%

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

      5. *-commutative 66.6%

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

      6. cancel-sign-sub-inv 66.6%

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

      7. distribute-lft-neg-in 66.6%

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

      8. *-commutative 66.6%

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

      9. sub-neg 66.6%

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

      10. distribute-lft-in 66.6%

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

      11. metadata-eval 66.6%

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

      12. distribute-rgt-neg-in 66.6%

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

      13. distribute-lft-neg-in 66.6%

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

      14. metadata-eval 66.6%

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

      15. mul-1-neg 66.6%

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

      16. distribute-lft-in 66.6%

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

      17. metadata-eval 66.6%

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

      18. associate-+r+ 66.6%

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

      19. metadata-eval 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in z around 0 66.6%

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

      1. *-commutative 66.6%

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

   10. Simplified 66.6%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.09:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-83}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-184}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-225}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-303}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-257}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-74}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 36.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+79} \lor \neg \left(x \leq -2.36 \cdot 10^{-51} \lor \neg \left(x \leq -2.5 \cdot 10^{-156}\right) \land x \leq 5.4 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e+79)
         (not
          (or (<= x -2.36e-51) (and (not (<= x -2.5e-156)) (<= x 5.4e-41)))))
   (* x -3.0)
   (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e+79) || !((x <= -2.36e-51) || (!(x <= -2.5e-156) && (x <= 5.4e-41)))) {
		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 <= (-6d+79)) .or. (.not. (x <= (-2.36d-51)) .or. (.not. (x <= (-2.5d-156))) .and. (x <= 5.4d-41))) 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 <= -6e+79) || !((x <= -2.36e-51) || (!(x <= -2.5e-156) && (x <= 5.4e-41)))) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e+79) or not ((x <= -2.36e-51) or (not (x <= -2.5e-156) and (x <= 5.4e-41))):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e+79) || !((x <= -2.36e-51) || (!(x <= -2.5e-156) && (x <= 5.4e-41))))
		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 <= -6e+79) || ~(((x <= -2.36e-51) || (~((x <= -2.5e-156)) && (x <= 5.4e-41)))))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e+79], N[Not[Or[LessEqual[x, -2.36e-51], And[N[Not[LessEqual[x, -2.5e-156]], $MachinePrecision], LessEqual[x, 5.4e-41]]]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.99999999999999948e79 or -2.36000000000000008e-51 < x < -2.50000000000000004e-156 or 5.4e-41 < 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 72.3%

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

      1. +-commutative 72.3%

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

      2. +-commutative 72.3%

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

      3. metadata-eval 72.3%

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

      4. cancel-sign-sub-inv 72.3%

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

      5. *-commutative 72.3%

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

      6. cancel-sign-sub-inv 72.3%

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

      7. distribute-lft-neg-in 72.3%

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

      8. *-commutative 72.3%

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

      9. sub-neg 72.3%

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

      10. distribute-lft-in 72.3%

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

      11. metadata-eval 72.3%

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

      12. distribute-rgt-neg-in 72.3%

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

      13. distribute-lft-neg-in 72.3%

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

      14. metadata-eval 72.3%

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

      15. mul-1-neg 72.3%

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

      16. distribute-lft-in 72.3%

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

      17. metadata-eval 72.3%

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

      18. associate-+r+ 72.3%

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

      19. metadata-eval 72.3%

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

   7. Simplified 72.3%

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

   8. Taylor expanded in z around 0 48.2%

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

      1. *-commutative 48.2%

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

   10. Simplified 48.2%

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

   if -5.99999999999999948e79 < x < -2.36000000000000008e-51 or -2.50000000000000004e-156 < x < 5.4e-41

   1. Initial program 99.0%

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

      1. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

      1. +-commutative 99.0%

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

      2. *-commutative 99.0%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in y around inf 74.3%

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

   8. Taylor expanded in z around 0 46.7%

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

4. Final simplification 47.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+79} \lor \neg \left(x \leq -2.36 \cdot 10^{-51} \lor \neg \left(x \leq -2.5 \cdot 10^{-156}\right) \land x \leq 5.4 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 58.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+88} \lor \neg \left(x \leq 1.5 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.25e+88) (not (<= x 1.5e-16)))
   (* x -3.0)
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.25e+88) || !(x <= 1.5e-16)) {
		tmp = x * -3.0;
	} 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 <= (-1.25d+88)) .or. (.not. (x <= 1.5d-16))) then
        tmp = x * (-3.0d0)
    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 <= -1.25e+88) || !(x <= 1.5e-16)) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.25e+88) or not (x <= 1.5e-16):
		tmp = x * -3.0
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.25e+88) || !(x <= 1.5e-16))
		tmp = Float64(x * -3.0);
	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 <= -1.25e+88) || ~((x <= 1.5e-16)))
		tmp = x * -3.0;
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.25e+88], N[Not[LessEqual[x, 1.5e-16]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999999e88 or 1.49999999999999997e-16 < 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 76.2%

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

      1. +-commutative 76.2%

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

      2. +-commutative 76.2%

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

      3. metadata-eval 76.2%

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

      4. cancel-sign-sub-inv 76.2%

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

      5. *-commutative 76.2%

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

      6. cancel-sign-sub-inv 76.2%

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

      7. distribute-lft-neg-in 76.2%

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

      8. *-commutative 76.2%

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

      9. sub-neg 76.2%

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

      10. distribute-lft-in 76.2%

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

      11. metadata-eval 76.2%

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

      12. distribute-rgt-neg-in 76.2%

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

      13. distribute-lft-neg-in 76.2%

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

      14. metadata-eval 76.2%

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

      15. mul-1-neg 76.2%

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

      16. distribute-lft-in 76.2%

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

      17. metadata-eval 76.2%

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

      18. associate-+r+ 76.2%

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

      19. metadata-eval 76.2%

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

   7. Simplified 76.2%

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

   8. Taylor expanded in z around 0 51.3%

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

      1. *-commutative 51.3%

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

   10. Simplified 51.3%

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

   if -1.24999999999999999e88 < x < 1.49999999999999997e-16

   1. Initial program 99.1%

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

      1. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

      1. +-commutative 99.1%

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

      2. *-commutative 99.1%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 68.9%

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

4. Final simplification 61.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+88} \lor \neg \left(x \leq 1.5 \cdot 10^{-16}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-118} \lor \neg \left(x \leq 7.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.6e-118) (not (<= x 7.5e-38)))
   (* 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 <= -5.6e-118) || !(x <= 7.5e-38)) {
		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 <= (-5.6d-118)) .or. (.not. (x <= 7.5d-38))) 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 <= -5.6e-118) || !(x <= 7.5e-38)) {
		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 <= -5.6e-118) or not (x <= 7.5e-38):
		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 <= -5.6e-118) || !(x <= 7.5e-38))
		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 <= -5.6e-118) || ~((x <= 7.5e-38)))
		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, -5.6e-118], N[Not[LessEqual[x, 7.5e-38]], $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 < -5.6e-118 or 7.5e-38 < x

   1. Initial program 99.0%

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

      1. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. +-commutative 69.0%

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

      3. metadata-eval 69.0%

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

      4. cancel-sign-sub-inv 69.0%

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

      5. *-commutative 69.0%

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

      6. cancel-sign-sub-inv 69.0%

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

      7. distribute-lft-neg-in 69.0%

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

      8. *-commutative 69.0%

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

      9. sub-neg 69.0%

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

      10. distribute-lft-in 69.0%

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

      11. metadata-eval 69.0%

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

      12. distribute-rgt-neg-in 69.0%

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

      13. distribute-lft-neg-in 69.0%

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

      14. metadata-eval 69.0%

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

      15. mul-1-neg 69.0%

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

      16. distribute-lft-in 69.0%

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

      17. metadata-eval 69.0%

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

      18. associate-+r+ 69.0%

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

      19. metadata-eval 69.0%

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

   7. Simplified 69.0%

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

   if -5.6e-118 < x < 7.5e-38

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.4%

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

   6. Applied egg-rr 99.4%

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

   7. Taylor expanded in y around inf 81.8%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.6 \cdot 10^{-118} \lor \neg \left(x \leq 7.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 74.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{-120} \lor \neg \left(x \leq 8.5 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.26e-120) (not (<= x 8.5e-41)))
   (* 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 <= -1.26e-120) || !(x <= 8.5e-41)) {
		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 <= (-1.26d-120)) .or. (.not. (x <= 8.5d-41))) 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 <= -1.26e-120) || !(x <= 8.5e-41)) {
		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 <= -1.26e-120) or not (x <= 8.5e-41):
		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 <= -1.26e-120) || !(x <= 8.5e-41))
		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 <= -1.26e-120) || ~((x <= 8.5e-41)))
		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, -1.26e-120], N[Not[LessEqual[x, 8.5e-41]], $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 < -1.25999999999999992e-120 or 8.4999999999999996e-41 < x

   1. Initial program 99.0%

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

      1. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   5. Taylor expanded in x around inf 69.0%

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

      1. +-commutative 69.0%

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

      2. +-commutative 69.0%

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

      3. metadata-eval 69.0%

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

      4. cancel-sign-sub-inv 69.0%

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

      5. *-commutative 69.0%

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

      6. cancel-sign-sub-inv 69.0%

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

      7. distribute-lft-neg-in 69.0%

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

      8. *-commutative 69.0%

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

      9. sub-neg 69.0%

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

      10. distribute-lft-in 69.0%

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

      11. metadata-eval 69.0%

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

      12. distribute-rgt-neg-in 69.0%

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

      13. distribute-lft-neg-in 69.0%

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

      14. metadata-eval 69.0%

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

      15. mul-1-neg 69.0%

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

      16. distribute-lft-in 69.0%

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

      17. metadata-eval 69.0%

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

      18. associate-+r+ 69.0%

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

      19. metadata-eval 69.0%

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

   7. Simplified 69.0%

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

   if -1.25999999999999992e-120 < x < 8.4999999999999996e-41

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 82.0%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.26 \cdot 10^{-120} \lor \neg \left(x \leq 8.5 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* (- y x) (* z -6.0))
   (if (<= z 0.6) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.6) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.6d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.6) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.6:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.6)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.6)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.6], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 97.7%

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

      1. associate-*r* 97.7%

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

      2. *-commutative 97.7%

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

   9. Simplified 97.7%

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

   if -0.57999999999999996 < z < 0.599999999999999978

   1. Initial program 98.9%

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

      1. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   5. Taylor expanded in z around 0 98.5%

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

   if 0.599999999999999978 < 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 z around inf 99.8%

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

   6. Taylor expanded in z around inf 96.9%

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

      1. *-commutative 96.9%

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

   8. Simplified 96.9%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Final simplification 99.2%

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

Alternative 13: 26.2% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. +-commutative 99.2%

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

   2. *-commutative 99.2%

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

   3. associate-*r* 99.5%

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

   4. fma-define 99.4%

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

6. Applied egg-rr 99.4%

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

7. Taylor expanded in y around inf 52.3%

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

8. Taylor expanded in z around 0 29.3%

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

9. Final simplification 29.3%

   \[\leadsto y \cdot 4 \]
10. Add Preprocessing

Alternative 14: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.2%

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

   1. metadata-eval 99.2%

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

3. Simplified 99.2%

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

5. Taylor expanded in y around inf 51.8%

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

6. Taylor expanded in x around inf 2.4%

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

7. Final simplification 2.4%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024053 
(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))))