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

Percentage Accurate: 99.5% → 99.8%

Time: 10.6s

Alternatives: 15

Speedup: 1.2×

• 21.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

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

Alternative 2: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.15 \cdot 10^{+215}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.15e+215)
     (* 6.0 (* x z))
     (if (<= z -1.08e-26)
       t_0
       (if (<= z -1.82e-181)
         (* y 4.0)
         (if (<= z 7.2e-144)
           (* x -3.0)
           (if (<= z 1.9e-77) (* y 4.0) (if (<= z 0.6) (* x -3.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.15e+215) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -1.82e-181) {
		tmp = y * 4.0;
	} else if (z <= 7.2e-144) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-77) {
		tmp = y * 4.0;
	} else if (z <= 0.6) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-1.15d+215)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-1.08d-26)) then
        tmp = t_0
    else if (z <= (-1.82d-181)) then
        tmp = y * 4.0d0
    else if (z <= 7.2d-144) then
        tmp = x * (-3.0d0)
    else if (z <= 1.9d-77) then
        tmp = y * 4.0d0
    else if (z <= 0.6d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.15e+215) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -1.82e-181) {
		tmp = y * 4.0;
	} else if (z <= 7.2e-144) {
		tmp = x * -3.0;
	} else if (z <= 1.9e-77) {
		tmp = y * 4.0;
	} else if (z <= 0.6) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.15e+215:
		tmp = 6.0 * (x * z)
	elif z <= -1.08e-26:
		tmp = t_0
	elif z <= -1.82e-181:
		tmp = y * 4.0
	elif z <= 7.2e-144:
		tmp = x * -3.0
	elif z <= 1.9e-77:
		tmp = y * 4.0
	elif z <= 0.6:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.15e+215)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -1.82e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.2e-144)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.9e-77)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.6)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.15e+215)
		tmp = 6.0 * (x * z);
	elseif (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -1.82e-181)
		tmp = y * 4.0;
	elseif (z <= 7.2e-144)
		tmp = x * -3.0;
	elseif (z <= 1.9e-77)
		tmp = y * 4.0;
	elseif (z <= 0.6)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.15e+215], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-26], t$95$0, If[LessEqual[z, -1.82e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.2e-144], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.9e-77], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.6], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1500000000000001e215

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   6. Taylor expanded in x around inf 67.3%

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

      1. associate-*r/ 67.3%

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

      2. metadata-eval 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in z around inf 67.2%

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

   if -1.1500000000000001e215 < z < -1.07999999999999996e-26 or 0.599999999999999978 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 94.2%

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

   7. Taylor expanded in y around inf 61.0%

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

      1. *-commutative 61.0%

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

   9. Simplified 61.0%

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

   if -1.07999999999999996e-26 < z < -1.8199999999999999e-181 or 7.2000000000000001e-144 < z < 1.8999999999999999e-77

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in y around inf 50.2%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. *-commutative 73.6%

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

   9. Simplified 73.6%

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

   if -1.8199999999999999e-181 < z < 7.2000000000000001e-144 or 1.8999999999999999e-77 < z < 0.599999999999999978

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. sub-neg 60.3%

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

      4. distribute-rgt-in 60.3%

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

      5. metadata-eval 60.3%

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

      6. neg-mul-1 60.3%

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

      7. associate-*r* 60.3%

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

      8. *-commutative 60.3%

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

      9. associate-+r+ 60.3%

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

      10. metadata-eval 60.3%

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

      11. associate-*r* 60.3%

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

      12. metadata-eval 60.3%

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

      13. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in z around 0 60.3%

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

      1. *-commutative 60.3%

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

   10. Simplified 60.3%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.15 \cdot 10^{+215}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.6:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+216}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-79}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.2e+216)
   (* 6.0 (* x z))
   (if (<= z -1.08e-26)
     (* y (* z -6.0))
     (if (<= z -3e-181)
       (* y 4.0)
       (if (<= z 3.1e-144)
         (* x -3.0)
         (if (<= z 6.6e-79)
           (* y 4.0)
           (if (<= z 0.68) (* x -3.0) (* -6.0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e+216) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = y * (z * -6.0);
	} else if (z <= -3e-181) {
		tmp = y * 4.0;
	} else if (z <= 3.1e-144) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-79) {
		tmp = y * 4.0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-3.2d+216)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-1.08d-26)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-3d-181)) then
        tmp = y * 4.0d0
    else if (z <= 3.1d-144) then
        tmp = x * (-3.0d0)
    else if (z <= 6.6d-79) then
        tmp = y * 4.0d0
    else if (z <= 0.68d0) then
        tmp = x * (-3.0d0)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.2e+216) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = y * (z * -6.0);
	} else if (z <= -3e-181) {
		tmp = y * 4.0;
	} else if (z <= 3.1e-144) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-79) {
		tmp = y * 4.0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.2e+216:
		tmp = 6.0 * (x * z)
	elif z <= -1.08e-26:
		tmp = y * (z * -6.0)
	elif z <= -3e-181:
		tmp = y * 4.0
	elif z <= 3.1e-144:
		tmp = x * -3.0
	elif z <= 6.6e-79:
		tmp = y * 4.0
	elif z <= 0.68:
		tmp = x * -3.0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.2e+216)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -1.08e-26)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -3e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.1e-144)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.6e-79)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.68)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.2e+216)
		tmp = 6.0 * (x * z);
	elseif (z <= -1.08e-26)
		tmp = y * (z * -6.0);
	elseif (z <= -3e-181)
		tmp = y * 4.0;
	elseif (z <= 3.1e-144)
		tmp = x * -3.0;
	elseif (z <= 6.6e-79)
		tmp = y * 4.0;
	elseif (z <= 0.68)
		tmp = x * -3.0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.2e+216], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-26], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.1e-144], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.6e-79], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(x * -3.0), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.1999999999999997e216

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   6. Taylor expanded in x around inf 67.3%

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

      1. associate-*r/ 67.3%

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

      2. metadata-eval 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in z around inf 67.2%

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

   if -3.1999999999999997e216 < z < -1.07999999999999996e-26

   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 z around 0 99.7%

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

   6. Taylor expanded in z around inf 91.2%

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

   7. Taylor expanded in y around inf 53.7%

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

      1. *-commutative 53.7%

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

      2. associate-*r* 53.8%

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

      3. *-commutative 53.8%

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

      4. associate-*r* 53.8%

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

   9. Simplified 53.8%

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

   10. Taylor expanded in z around 0 53.7%

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

       1. associate-*r* 53.8%

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

       2. *-commutative 53.8%

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

       3. associate-*r* 53.8%

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

   12. Simplified 53.8%

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

   if -1.07999999999999996e-26 < z < -2.99999999999999974e-181 or 3.1000000000000001e-144 < z < 6.5999999999999996e-79

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in y around inf 50.2%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. *-commutative 73.6%

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

   9. Simplified 73.6%

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

   if -2.99999999999999974e-181 < z < 3.1000000000000001e-144 or 6.5999999999999996e-79 < z < 0.680000000000000049

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. sub-neg 60.3%

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

      4. distribute-rgt-in 60.3%

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

      5. metadata-eval 60.3%

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

      6. neg-mul-1 60.3%

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

      7. associate-*r* 60.3%

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

      8. *-commutative 60.3%

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

      9. associate-+r+ 60.3%

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

      10. metadata-eval 60.3%

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

      11. associate-*r* 60.3%

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

      12. metadata-eval 60.3%

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

      13. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in z around 0 60.3%

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

      1. *-commutative 60.3%

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

   10. Simplified 60.3%

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

   if 0.680000000000000049 < 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 0 99.8%

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

   6. Taylor expanded in z around inf 96.6%

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

   7. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   9. Simplified 66.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+216}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.1 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-79}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+211}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+211)
   (* 6.0 (* x z))
   (if (<= z -1.08e-26)
     (* z (* y -6.0))
     (if (<= z -2.2e-181)
       (* y 4.0)
       (if (<= z 1.16e-144)
         (* x -3.0)
         (if (<= z 5.2e-78)
           (* y 4.0)
           (if (<= z 0.58) (* x -3.0) (* -6.0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+211) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = z * (y * -6.0);
	} else if (z <= -2.2e-181) {
		tmp = y * 4.0;
	} else if (z <= 1.16e-144) {
		tmp = x * -3.0;
	} else if (z <= 5.2e-78) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-9d+211)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-1.08d-26)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-2.2d-181)) then
        tmp = y * 4.0d0
    else if (z <= 1.16d-144) then
        tmp = x * (-3.0d0)
    else if (z <= 5.2d-78) then
        tmp = y * 4.0d0
    else if (z <= 0.58d0) then
        tmp = x * (-3.0d0)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+211) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = z * (y * -6.0);
	} else if (z <= -2.2e-181) {
		tmp = y * 4.0;
	} else if (z <= 1.16e-144) {
		tmp = x * -3.0;
	} else if (z <= 5.2e-78) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+211:
		tmp = 6.0 * (x * z)
	elif z <= -1.08e-26:
		tmp = z * (y * -6.0)
	elif z <= -2.2e-181:
		tmp = y * 4.0
	elif z <= 1.16e-144:
		tmp = x * -3.0
	elif z <= 5.2e-78:
		tmp = y * 4.0
	elif z <= 0.58:
		tmp = x * -3.0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+211)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -1.08e-26)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -2.2e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.16e-144)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.2e-78)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.58)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+211)
		tmp = 6.0 * (x * z);
	elseif (z <= -1.08e-26)
		tmp = z * (y * -6.0);
	elseif (z <= -2.2e-181)
		tmp = y * 4.0;
	elseif (z <= 1.16e-144)
		tmp = x * -3.0;
	elseif (z <= 5.2e-78)
		tmp = y * 4.0;
	elseif (z <= 0.58)
		tmp = x * -3.0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+211], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-26], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.16e-144], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.2e-78], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.58], N[(x * -3.0), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9e211

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   6. Taylor expanded in x around inf 67.3%

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

      1. associate-*r/ 67.3%

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

      2. metadata-eval 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in z around inf 67.2%

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

   if -9e211 < z < -1.07999999999999996e-26

   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 z around 0 99.7%

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

   6. Taylor expanded in z around inf 91.2%

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

   7. Taylor expanded in y around inf 53.7%

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

      1. *-commutative 53.7%

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

      2. associate-*r* 53.8%

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

      3. *-commutative 53.8%

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

      4. associate-*r* 53.8%

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

   9. Simplified 53.8%

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

   if -1.07999999999999996e-26 < z < -2.19999999999999997e-181 or 1.15999999999999994e-144 < z < 5.2000000000000002e-78

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in y around inf 50.2%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. *-commutative 73.6%

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

   9. Simplified 73.6%

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

   if -2.19999999999999997e-181 < z < 1.15999999999999994e-144 or 5.2000000000000002e-78 < z < 0.57999999999999996

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. sub-neg 60.3%

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

      4. distribute-rgt-in 60.3%

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

      5. metadata-eval 60.3%

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

      6. neg-mul-1 60.3%

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

      7. associate-*r* 60.3%

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

      8. *-commutative 60.3%

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

      9. associate-+r+ 60.3%

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

      10. metadata-eval 60.3%

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

      11. associate-*r* 60.3%

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

      12. metadata-eval 60.3%

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

      13. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in z around 0 60.3%

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

      1. *-commutative 60.3%

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

   10. Simplified 60.3%

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

   if 0.57999999999999996 < 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 0 99.8%

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

   6. Taylor expanded in z around inf 96.6%

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

   7. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   9. Simplified 66.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+211}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.16 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9e+213)
   (* z (* x 6.0))
   (if (<= z -1.08e-26)
     (* z (* y -6.0))
     (if (<= z -2.15e-181)
       (* y 4.0)
       (if (<= z 2.15e-144)
         (* x -3.0)
         (if (<= z 1.7e-77)
           (* y 4.0)
           (if (<= z 0.58) (* x -3.0) (* -6.0 (* y z)))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+213) {
		tmp = z * (x * 6.0);
	} else if (z <= -1.08e-26) {
		tmp = z * (y * -6.0);
	} else if (z <= -2.15e-181) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-144) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-77) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-9d+213)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-1.08d-26)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= (-2.15d-181)) then
        tmp = y * 4.0d0
    else if (z <= 2.15d-144) then
        tmp = x * (-3.0d0)
    else if (z <= 1.7d-77) then
        tmp = y * 4.0d0
    else if (z <= 0.58d0) then
        tmp = x * (-3.0d0)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9e+213) {
		tmp = z * (x * 6.0);
	} else if (z <= -1.08e-26) {
		tmp = z * (y * -6.0);
	} else if (z <= -2.15e-181) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-144) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-77) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9e+213:
		tmp = z * (x * 6.0)
	elif z <= -1.08e-26:
		tmp = z * (y * -6.0)
	elif z <= -2.15e-181:
		tmp = y * 4.0
	elif z <= 2.15e-144:
		tmp = x * -3.0
	elif z <= 1.7e-77:
		tmp = y * 4.0
	elif z <= 0.58:
		tmp = x * -3.0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9e+213)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -1.08e-26)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= -2.15e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.15e-144)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.7e-77)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.58)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9e+213)
		tmp = z * (x * 6.0);
	elseif (z <= -1.08e-26)
		tmp = z * (y * -6.0);
	elseif (z <= -2.15e-181)
		tmp = y * 4.0;
	elseif (z <= 2.15e-144)
		tmp = x * -3.0;
	elseif (z <= 1.7e-77)
		tmp = y * 4.0;
	elseif (z <= 0.58)
		tmp = x * -3.0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9e+213], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-26], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.15e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.15e-144], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.7e-77], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.58], N[(x * -3.0), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -9.0000000000000003e213

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   6. Taylor expanded in x around inf 67.3%

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

      1. associate-*r/ 67.3%

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

      2. metadata-eval 67.3%

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

   8. Simplified 67.3%

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

   9. Taylor expanded in z around inf 67.2%

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

       1. associate-*r* 67.3%

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

   11. Simplified 67.3%

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

   if -9.0000000000000003e213 < z < -1.07999999999999996e-26

   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 z around 0 99.7%

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

   6. Taylor expanded in z around inf 91.2%

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

   7. Taylor expanded in y around inf 53.7%

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

      1. *-commutative 53.7%

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

      2. associate-*r* 53.8%

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

      3. *-commutative 53.8%

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

      4. associate-*r* 53.8%

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

   9. Simplified 53.8%

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

   if -1.07999999999999996e-26 < z < -2.15e-181 or 2.14999999999999995e-144 < z < 1.69999999999999991e-77

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in y around inf 50.2%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. *-commutative 73.6%

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

   9. Simplified 73.6%

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

   if -2.15e-181 < z < 2.14999999999999995e-144 or 1.69999999999999991e-77 < z < 0.57999999999999996

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. sub-neg 60.3%

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

      4. distribute-rgt-in 60.3%

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

      5. metadata-eval 60.3%

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

      6. neg-mul-1 60.3%

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

      7. associate-*r* 60.3%

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

      8. *-commutative 60.3%

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

      9. associate-+r+ 60.3%

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

      10. metadata-eval 60.3%

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

      11. associate-*r* 60.3%

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

      12. metadata-eval 60.3%

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

      13. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in z around 0 60.3%

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

      1. *-commutative 60.3%

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

   10. Simplified 60.3%

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

   if 0.57999999999999996 < 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 0 99.8%

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

   6. Taylor expanded in z around inf 96.6%

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

   7. Taylor expanded in y around inf 66.9%

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

      1. *-commutative 66.9%

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

   9. Simplified 66.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.15 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-79}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -1.08e-26)
     t_0
     (if (<= z -2.05e-181)
       (* y 4.0)
       (if (<= z 4.1e-144)
         (* x -3.0)
         (if (<= z 9.2e-79) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -2.05e-181) {
		tmp = y * 4.0;
	} else if (z <= 4.1e-144) {
		tmp = x * -3.0;
	} else if (z <= 9.2e-79) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-1.08d-26)) then
        tmp = t_0
    else if (z <= (-2.05d-181)) then
        tmp = y * 4.0d0
    else if (z <= 4.1d-144) then
        tmp = x * (-3.0d0)
    else if (z <= 9.2d-79) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -2.05e-181) {
		tmp = y * 4.0;
	} else if (z <= 4.1e-144) {
		tmp = x * -3.0;
	} else if (z <= 9.2e-79) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -1.08e-26:
		tmp = t_0
	elif z <= -2.05e-181:
		tmp = y * 4.0
	elif z <= 4.1e-144:
		tmp = x * -3.0
	elif z <= 9.2e-79:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -2.05e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.1e-144)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.2e-79)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -2.05e-181)
		tmp = y * 4.0;
	elseif (z <= 4.1e-144)
		tmp = x * -3.0;
	elseif (z <= 9.2e-79)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-26], t$95$0, If[LessEqual[z, -2.05e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.1e-144], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.2e-79], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.07999999999999996e-26 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 94.8%

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

   if -1.07999999999999996e-26 < z < -2.0500000000000001e-181 or 4.1e-144 < z < 9.20000000000000047e-79

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in y around inf 50.2%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. *-commutative 73.6%

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

   9. Simplified 73.6%

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

   if -2.0500000000000001e-181 < z < 4.1e-144 or 9.20000000000000047e-79 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. sub-neg 60.3%

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

      4. distribute-rgt-in 60.3%

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

      5. metadata-eval 60.3%

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

      6. neg-mul-1 60.3%

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

      7. associate-*r* 60.3%

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

      8. *-commutative 60.3%

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

      9. associate-+r+ 60.3%

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

      10. metadata-eval 60.3%

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

      11. associate-*r* 60.3%

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

      12. metadata-eval 60.3%

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

      13. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in z around 0 60.3%

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

      1. *-commutative 60.3%

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

   10. Simplified 60.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -2.05 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-79}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-144}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 27000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -1.08e-26)
     t_1
     (if (<= z -1.82e-181)
       (* y 4.0)
       (if (<= z 1.06e-144)
         t_0
         (if (<= z 1.45e-77) (* y 4.0) (if (<= z 27000.0) t_0 t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -1.08e-26) {
		tmp = t_1;
	} else if (z <= -1.82e-181) {
		tmp = y * 4.0;
	} else if (z <= 1.06e-144) {
		tmp = t_0;
	} else if (z <= 1.45e-77) {
		tmp = y * 4.0;
	} else if (z <= 27000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-1.08d-26)) then
        tmp = t_1
    else if (z <= (-1.82d-181)) then
        tmp = y * 4.0d0
    else if (z <= 1.06d-144) then
        tmp = t_0
    else if (z <= 1.45d-77) then
        tmp = y * 4.0d0
    else if (z <= 27000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -1.08e-26) {
		tmp = t_1;
	} else if (z <= -1.82e-181) {
		tmp = y * 4.0;
	} else if (z <= 1.06e-144) {
		tmp = t_0;
	} else if (z <= 1.45e-77) {
		tmp = y * 4.0;
	} else if (z <= 27000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -1.08e-26:
		tmp = t_1
	elif z <= -1.82e-181:
		tmp = y * 4.0
	elif z <= 1.06e-144:
		tmp = t_0
	elif z <= 1.45e-77:
		tmp = y * 4.0
	elif z <= 27000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -1.08e-26)
		tmp = t_1;
	elseif (z <= -1.82e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.06e-144)
		tmp = t_0;
	elseif (z <= 1.45e-77)
		tmp = Float64(y * 4.0);
	elseif (z <= 27000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -1.08e-26)
		tmp = t_1;
	elseif (z <= -1.82e-181)
		tmp = y * 4.0;
	elseif (z <= 1.06e-144)
		tmp = t_0;
	elseif (z <= 1.45e-77)
		tmp = y * 4.0;
	elseif (z <= 27000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-26], t$95$1, If[LessEqual[z, -1.82e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.06e-144], t$95$0, If[LessEqual[z, 1.45e-77], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 27000.0], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.07999999999999996e-26 or 27000 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 95.8%

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

   if -1.07999999999999996e-26 < z < -1.8199999999999999e-181 or 1.06e-144 < z < 1.4499999999999999e-77

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in y around inf 50.2%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. *-commutative 73.6%

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

   9. Simplified 73.6%

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

   if -1.8199999999999999e-181 < z < 1.06e-144 or 1.4499999999999999e-77 < z < 27000

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 60.1%

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

      1. +-commutative 60.1%

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

      2. +-commutative 60.1%

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

      3. sub-neg 60.1%

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

      4. distribute-rgt-in 60.1%

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

      5. metadata-eval 60.1%

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

      6. neg-mul-1 60.1%

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

      7. associate-*r* 60.1%

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

      8. *-commutative 60.1%

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

      9. associate-+r+ 60.1%

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

      10. metadata-eval 60.1%

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

      11. associate-*r* 60.1%

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

      12. metadata-eval 60.1%

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

      13. *-commutative 60.1%

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

   7. Simplified 60.1%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-144}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-77}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 27000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-79}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.08e-26)
     t_0
     (if (<= z -2.6e-181)
       (* y 4.0)
       (if (<= z 1.06e-144)
         (* x -3.0)
         (if (<= z 5e-79) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -2.6e-181) {
		tmp = y * 4.0;
	} else if (z <= 1.06e-144) {
		tmp = x * -3.0;
	} else if (z <= 5e-79) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-1.08d-26)) then
        tmp = t_0
    else if (z <= (-2.6d-181)) then
        tmp = y * 4.0d0
    else if (z <= 1.06d-144) then
        tmp = x * (-3.0d0)
    else if (z <= 5d-79) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -2.6e-181) {
		tmp = y * 4.0;
	} else if (z <= 1.06e-144) {
		tmp = x * -3.0;
	} else if (z <= 5e-79) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.08e-26:
		tmp = t_0
	elif z <= -2.6e-181:
		tmp = y * 4.0
	elif z <= 1.06e-144:
		tmp = x * -3.0
	elif z <= 5e-79:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -2.6e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.06e-144)
		tmp = Float64(x * -3.0);
	elseif (z <= 5e-79)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -2.6e-181)
		tmp = y * 4.0;
	elseif (z <= 1.06e-144)
		tmp = x * -3.0;
	elseif (z <= 5e-79)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-26], t$95$0, If[LessEqual[z, -2.6e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.06e-144], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5e-79], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.07999999999999996e-26 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 94.8%

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

   7. Taylor expanded in y around inf 58.0%

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

      1. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if -1.07999999999999996e-26 < z < -2.59999999999999999e-181 or 1.06e-144 < z < 4.99999999999999999e-79

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around inf 70.9%

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

   6. Taylor expanded in y around inf 50.2%

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

   7. Taylor expanded in z around 0 73.6%

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

      1. *-commutative 73.6%

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

   9. Simplified 73.6%

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

   if -2.59999999999999999e-181 < z < 1.06e-144 or 4.99999999999999999e-79 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 60.3%

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

      1. +-commutative 60.3%

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

      2. +-commutative 60.3%

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

      3. sub-neg 60.3%

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

      4. distribute-rgt-in 60.3%

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

      5. metadata-eval 60.3%

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

      6. neg-mul-1 60.3%

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

      7. associate-*r* 60.3%

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

      8. *-commutative 60.3%

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

      9. associate-+r+ 60.3%

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

      10. metadata-eval 60.3%

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

      11. associate-*r* 60.3%

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

      12. metadata-eval 60.3%

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

      13. *-commutative 60.3%

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

   7. Simplified 60.3%

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

   8. Taylor expanded in z around 0 60.3%

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

      1. *-commutative 60.3%

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

   10. Simplified 60.3%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.06 \cdot 10^{-144}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-79}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -36000000000 \lor \neg \left(x \leq 1.45 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -36000000000.0) (not (<= x 1.45e+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 <= -36000000000.0) || !(x <= 1.45e+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 <= (-36000000000.0d0)) .or. (.not. (x <= 1.45d+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 <= -36000000000.0) || !(x <= 1.45e+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 <= -36000000000.0) or not (x <= 1.45e+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 <= -36000000000.0) || !(x <= 1.45e+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 <= -36000000000.0) || ~((x <= 1.45e+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, -36000000000.0], N[Not[LessEqual[x, 1.45e+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 < -3.6e10 or 1.44999999999999994e41 < x

   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 80.6%

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

      1. +-commutative 80.6%

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

      2. +-commutative 80.6%

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

      3. sub-neg 80.6%

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

      4. distribute-rgt-in 80.6%

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

      5. metadata-eval 80.6%

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

      6. neg-mul-1 80.6%

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

      7. associate-*r* 80.6%

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

      8. *-commutative 80.6%

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

      9. associate-+r+ 80.6%

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

      10. metadata-eval 80.6%

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

      11. associate-*r* 80.6%

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

      12. metadata-eval 80.6%

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

      13. *-commutative 80.6%

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

   7. Simplified 80.6%

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

   if -3.6e10 < x < 1.44999999999999994e41

   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 75.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -36000000000 \lor \neg \left(x \leq 1.45 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.64) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.64) {
		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 <= (-0.6d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.64d0) 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 <= -0.6) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.64) {
		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 <= -0.6:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.64:
		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 <= -0.6)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.64)
		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 <= -0.6)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.64)
		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, -0.6], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.64], 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 < -0.599999999999999978

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 95.8%

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

   if -0.599999999999999978 < z < 0.640000000000000013

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 98.8%

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

   if 0.640000000000000013 < z

   1. Initial program 99.8%

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

      1. 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 0 99.8%

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

   6. Taylor expanded in z around inf 96.6%

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

      1. *-commutative 96.6%

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

      2. associate-*l* 96.6%

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

      3. *-commutative 96.6%

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

   8. Simplified 96.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in z around 0 99.8%

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

6. Final simplification 99.8%

   \[\leadsto x + \left(-6 \cdot \left(\left(y - x\right) \cdot z\right) + \left(y - x\right) \cdot 4\right) \]
7. Add Preprocessing

Alternative 12: 38.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-72} \lor \neg \left(x \leq 4.5 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.8e-72) (not (<= x 4.5e+41))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.8e-72) || !(x <= 4.5e+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 <= (-1.8d-72)) .or. (.not. (x <= 4.5d+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 <= -1.8e-72) || !(x <= 4.5e+41)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.8e-72) or not (x <= 4.5e+41):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.8e-72) || !(x <= 4.5e+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 <= -1.8e-72) || ~((x <= 4.5e+41)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.8e-72], N[Not[LessEqual[x, 4.5e+41]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.8e-72 or 4.5000000000000001e41 < x

   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 77.0%

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

      1. +-commutative 77.0%

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

      2. +-commutative 77.0%

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

      3. sub-neg 77.0%

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

      4. distribute-rgt-in 77.0%

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

      5. metadata-eval 77.0%

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

      6. neg-mul-1 77.0%

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

      7. associate-*r* 77.0%

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

      8. *-commutative 77.0%

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

      9. associate-+r+ 77.0%

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

      10. metadata-eval 77.0%

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

      11. associate-*r* 77.0%

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

      12. metadata-eval 77.0%

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

      13. *-commutative 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in z around 0 46.0%

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

      1. *-commutative 46.0%

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

   10. Simplified 46.0%

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

   if -1.8e-72 < x < 4.5000000000000001e41

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around inf 89.5%

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

   6. Taylor expanded in y around inf 78.7%

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

   7. Taylor expanded in z around 0 35.0%

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

      1. *-commutative 35.0%

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

   9. Simplified 35.0%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-72} \lor \neg \left(x \leq 4.5 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 14: 26.5% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 46.3%

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

   1. +-commutative 46.3%

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

   2. +-commutative 46.3%

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

   3. sub-neg 46.3%

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

   4. distribute-rgt-in 46.3%

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

   5. metadata-eval 46.3%

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

   6. neg-mul-1 46.3%

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

   7. associate-*r* 46.3%

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

   8. *-commutative 46.3%

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

   9. associate-+r+ 46.3%

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

   10. metadata-eval 46.3%

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

   11. associate-*r* 46.3%

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

   12. metadata-eval 46.3%

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

   13. *-commutative 46.3%

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

7. Simplified 46.3%

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

8. Taylor expanded in z around 0 26.4%

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

   1. *-commutative 26.4%

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

10. Simplified 26.4%

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

11. Final simplification 26.4%

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

Alternative 15: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in z around inf 50.1%

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

6. Taylor expanded in z around 0 2.5%

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

7. Final simplification 2.5%

   \[\leadsto x \]
8. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(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))))