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

Percentage Accurate: 99.5% → 99.8%

Time: 11.1s

Alternatives: 13

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

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

   3. fma-define 99.7%

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

   4. sub-neg 99.7%

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

   5. +-commutative 99.7%

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

   6. distribute-lft-in 99.7%

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

   7. distribute-rgt-neg-out 99.7%

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

   8. *-commutative 99.7%

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

   9. distribute-rgt-neg-in 99.7%

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

   10. fma-define 99.8%

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

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

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

   3. fma-define 99.7%

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

   4. sub-neg 99.7%

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

   5. distribute-rgt-in 99.7%

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

   6. metadata-eval 99.7%

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

   7. metadata-eval 99.7%

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

   8. distribute-lft-neg-out 99.7%

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

   9. distribute-rgt-neg-in 99.7%

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

   10. metadata-eval 99.7%

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

3. Simplified 99.7%

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

Alternative 3: 60.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(x \cdot 6\right)\\ t_1 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{if}\;y \leq -7.5 \cdot 10^{-83}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.38 \cdot 10^{-281}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-202}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-149}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.26 \cdot 10^{-69}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* x 6.0))) (t_1 (* 6.0 (* y (- 0.6666666666666666 z)))))
   (if (<= y -7.5e-83)
     t_1
     (if (<= y 1.38e-281)
       t_0
       (if (<= y 8.2e-202)
         (* x -3.0)
         (if (<= y 4.4e-149) t_0 (if (<= y 2.26e-69) (* x -3.0) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double t_1 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -7.5e-83) {
		tmp = t_1;
	} else if (y <= 1.38e-281) {
		tmp = t_0;
	} else if (y <= 8.2e-202) {
		tmp = x * -3.0;
	} else if (y <= 4.4e-149) {
		tmp = t_0;
	} else if (y <= 2.26e-69) {
		tmp = x * -3.0;
	} 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 = z * (x * 6.0d0)
    t_1 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    if (y <= (-7.5d-83)) then
        tmp = t_1
    else if (y <= 1.38d-281) then
        tmp = t_0
    else if (y <= 8.2d-202) then
        tmp = x * (-3.0d0)
    else if (y <= 4.4d-149) then
        tmp = t_0
    else if (y <= 2.26d-69) then
        tmp = x * (-3.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (x * 6.0);
	double t_1 = 6.0 * (y * (0.6666666666666666 - z));
	double tmp;
	if (y <= -7.5e-83) {
		tmp = t_1;
	} else if (y <= 1.38e-281) {
		tmp = t_0;
	} else if (y <= 8.2e-202) {
		tmp = x * -3.0;
	} else if (y <= 4.4e-149) {
		tmp = t_0;
	} else if (y <= 2.26e-69) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (x * 6.0)
	t_1 = 6.0 * (y * (0.6666666666666666 - z))
	tmp = 0
	if y <= -7.5e-83:
		tmp = t_1
	elif y <= 1.38e-281:
		tmp = t_0
	elif y <= 8.2e-202:
		tmp = x * -3.0
	elif y <= 4.4e-149:
		tmp = t_0
	elif y <= 2.26e-69:
		tmp = x * -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(x * 6.0))
	t_1 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	tmp = 0.0
	if (y <= -7.5e-83)
		tmp = t_1;
	elseif (y <= 1.38e-281)
		tmp = t_0;
	elseif (y <= 8.2e-202)
		tmp = Float64(x * -3.0);
	elseif (y <= 4.4e-149)
		tmp = t_0;
	elseif (y <= 2.26e-69)
		tmp = Float64(x * -3.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (x * 6.0);
	t_1 = 6.0 * (y * (0.6666666666666666 - z));
	tmp = 0.0;
	if (y <= -7.5e-83)
		tmp = t_1;
	elseif (y <= 1.38e-281)
		tmp = t_0;
	elseif (y <= 8.2e-202)
		tmp = x * -3.0;
	elseif (y <= 4.4e-149)
		tmp = t_0;
	elseif (y <= 2.26e-69)
		tmp = x * -3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7.5e-83], t$95$1, If[LessEqual[y, 1.38e-281], t$95$0, If[LessEqual[y, 8.2e-202], N[(x * -3.0), $MachinePrecision], If[LessEqual[y, 4.4e-149], t$95$0, If[LessEqual[y, 2.26e-69], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4999999999999997e-83 or 2.2599999999999999e-69 < y

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 73.4%

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

   if -7.4999999999999997e-83 < y < 1.37999999999999993e-281 or 8.2000000000000008e-202 < y < 4.3999999999999996e-149

   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 93.1%

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

   6. Taylor expanded in z around inf 63.4%

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

      1. *-commutative 63.4%

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

   8. Simplified 63.4%

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

   9. Taylor expanded in y around 0 49.3%

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

       1. *-commutative 49.3%

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

   11. Simplified 49.3%

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

   if 1.37999999999999993e-281 < y < 8.2000000000000008e-202 or 4.3999999999999996e-149 < y < 2.2599999999999999e-69

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 90.3%

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

      1. sub-neg 90.3%

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

      2. distribute-rgt-in 90.3%

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

      3. metadata-eval 90.3%

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

      4. distribute-lft-neg-in 90.3%

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

      5. associate-+r+ 90.3%

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

      6. metadata-eval 90.3%

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

      7. distribute-rgt-neg-in 90.3%

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

      8. metadata-eval 90.3%

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

   7. Simplified 90.3%

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

   8. Taylor expanded in z around 0 70.9%

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

      1. *-commutative 70.9%

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

   10. Simplified 70.9%

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

Alternative 4: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.0026:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+114}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.0026)
   (* z (* y -6.0))
   (if (<= z 2.2e-16)
     (* x -3.0)
     (if (<= z 6e+114) (* 6.0 (* x z)) (* -6.0 (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0026) {
		tmp = z * (y * -6.0);
	} else if (z <= 2.2e-16) {
		tmp = x * -3.0;
	} else if (z <= 6e+114) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.0026d0)) then
        tmp = z * (y * (-6.0d0))
    else if (z <= 2.2d-16) then
        tmp = x * (-3.0d0)
    else if (z <= 6d+114) then
        tmp = 6.0d0 * (x * z)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.0026) {
		tmp = z * (y * -6.0);
	} else if (z <= 2.2e-16) {
		tmp = x * -3.0;
	} else if (z <= 6e+114) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.0026:
		tmp = z * (y * -6.0)
	elif z <= 2.2e-16:
		tmp = x * -3.0
	elif z <= 6e+114:
		tmp = 6.0 * (x * z)
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.0026)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= 2.2e-16)
		tmp = Float64(x * -3.0);
	elseif (z <= 6e+114)
		tmp = Float64(6.0 * Float64(x * z));
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.0026)
		tmp = z * (y * -6.0);
	elseif (z <= 2.2e-16)
		tmp = x * -3.0;
	elseif (z <= 6e+114)
		tmp = 6.0 * (x * z);
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.0026], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-16], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6e+114], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0025999999999999999

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in z around inf 98.3%

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

      1. *-commutative 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in y around inf 54.4%

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

   if -0.0025999999999999999 < z < 2.2e-16

   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 53.8%

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

      1. sub-neg 53.8%

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

      2. distribute-rgt-in 53.8%

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

      3. metadata-eval 53.8%

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

      4. distribute-lft-neg-in 53.8%

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

      5. associate-+r+ 53.8%

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

      6. metadata-eval 53.8%

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

      7. distribute-rgt-neg-in 53.8%

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

      8. metadata-eval 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in z around 0 53.8%

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

      1. *-commutative 53.8%

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

   10. Simplified 53.8%

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

   if 2.2e-16 < z < 6.0000000000000001e114

   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 68.6%

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

      1. sub-neg 68.6%

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

      2. distribute-rgt-in 68.6%

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

      3. metadata-eval 68.6%

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

      4. distribute-lft-neg-in 68.6%

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

      5. associate-+r+ 68.6%

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

      6. metadata-eval 68.6%

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

      7. distribute-rgt-neg-in 68.6%

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

      8. metadata-eval 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in z around inf 61.7%

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

   if 6.0000000000000001e114 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 75.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0026:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+114}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.45:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+114}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.45)
   (* y (* z -6.0))
   (if (<= z 2.2e-16)
     (* x -3.0)
     (if (<= z 4.8e+114) (* 6.0 (* x z)) (* -6.0 (* y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.45) {
		tmp = y * (z * -6.0);
	} else if (z <= 2.2e-16) {
		tmp = x * -3.0;
	} else if (z <= 4.8e+114) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.45d0)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= 2.2d-16) then
        tmp = x * (-3.0d0)
    else if (z <= 4.8d+114) then
        tmp = 6.0d0 * (x * z)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.45) {
		tmp = y * (z * -6.0);
	} else if (z <= 2.2e-16) {
		tmp = x * -3.0;
	} else if (z <= 4.8e+114) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.45:
		tmp = y * (z * -6.0)
	elif z <= 2.2e-16:
		tmp = x * -3.0
	elif z <= 4.8e+114:
		tmp = 6.0 * (x * z)
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.45)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= 2.2e-16)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.8e+114)
		tmp = Float64(6.0 * Float64(x * z));
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.45)
		tmp = y * (z * -6.0);
	elseif (z <= 2.2e-16)
		tmp = x * -3.0;
	elseif (z <= 4.8e+114)
		tmp = 6.0 * (x * z);
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.45], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.2e-16], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.8e+114], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.450000000000000011

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in z around inf 98.3%

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

      1. *-commutative 98.3%

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

   8. Simplified 98.3%

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

   9. Taylor expanded in y around inf 54.4%

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

   10. Taylor expanded in z around 0 54.4%

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

       1. associate-*r* 54.4%

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

       2. *-commutative 54.4%

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

       3. associate-*r* 54.4%

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

   12. Simplified 54.4%

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

   if -0.450000000000000011 < z < 2.2e-16

   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 53.8%

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

      1. sub-neg 53.8%

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

      2. distribute-rgt-in 53.8%

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

      3. metadata-eval 53.8%

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

      4. distribute-lft-neg-in 53.8%

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

      5. associate-+r+ 53.8%

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

      6. metadata-eval 53.8%

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

      7. distribute-rgt-neg-in 53.8%

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

      8. metadata-eval 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in z around 0 53.8%

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

      1. *-commutative 53.8%

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

   10. Simplified 53.8%

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

   if 2.2e-16 < z < 4.8e114

   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 68.6%

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

      1. sub-neg 68.6%

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

      2. distribute-rgt-in 68.6%

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

      3. metadata-eval 68.6%

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

      4. distribute-lft-neg-in 68.6%

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

      5. associate-+r+ 68.6%

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

      6. metadata-eval 68.6%

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

      7. distribute-rgt-neg-in 68.6%

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

      8. metadata-eval 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in z around inf 61.7%

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

   if 4.8e114 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 75.8%

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

4. Final simplification 58.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.45:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+114}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 49.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.7:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-16}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+113}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.7)
     t_0
     (if (<= z 2.2e-16) (* x -3.0) (if (<= z 8e+113) (* 6.0 (* x z)) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.7) {
		tmp = t_0;
	} else if (z <= 2.2e-16) {
		tmp = x * -3.0;
	} else if (z <= 8e+113) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.7d0)) then
        tmp = t_0
    else if (z <= 2.2d-16) then
        tmp = x * (-3.0d0)
    else if (z <= 8d+113) then
        tmp = 6.0d0 * (x * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.7) {
		tmp = t_0;
	} else if (z <= 2.2e-16) {
		tmp = x * -3.0;
	} else if (z <= 8e+113) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.7:
		tmp = t_0
	elif z <= 2.2e-16:
		tmp = x * -3.0
	elif z <= 8e+113:
		tmp = 6.0 * (x * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.7)
		tmp = t_0;
	elseif (z <= 2.2e-16)
		tmp = Float64(x * -3.0);
	elseif (z <= 8e+113)
		tmp = Float64(6.0 * Float64(x * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.7)
		tmp = t_0;
	elseif (z <= 2.2e-16)
		tmp = x * -3.0;
	elseif (z <= 8e+113)
		tmp = 6.0 * (x * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.7], t$95$0, If[LessEqual[z, 2.2e-16], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8e+113], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.69999999999999996 or 8e113 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in z around inf 98.8%

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

      1. *-commutative 98.8%

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

   8. Simplified 98.8%

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

   9. Taylor expanded in y around inf 62.0%

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

   if -0.69999999999999996 < z < 2.2e-16

   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 53.8%

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

      1. sub-neg 53.8%

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

      2. distribute-rgt-in 53.8%

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

      3. metadata-eval 53.8%

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

      4. distribute-lft-neg-in 53.8%

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

      5. associate-+r+ 53.8%

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

      6. metadata-eval 53.8%

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

      7. distribute-rgt-neg-in 53.8%

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

      8. metadata-eval 53.8%

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

   7. Simplified 53.8%

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

   8. Taylor expanded in z around 0 53.8%

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

      1. *-commutative 53.8%

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

   10. Simplified 53.8%

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

   if 2.2e-16 < z < 8e113

   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 68.6%

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

      1. sub-neg 68.6%

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

      2. distribute-rgt-in 68.6%

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

      3. metadata-eval 68.6%

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

      4. distribute-lft-neg-in 68.6%

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

      5. associate-+r+ 68.6%

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

      6. metadata-eval 68.6%

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

      7. distribute-rgt-neg-in 68.6%

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

      8. metadata-eval 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in z around inf 61.7%

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

Alternative 7: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.52)
   (* z (* (- y x) -6.0))
   (if (<= z 0.65) (+ x (* (- y x) 4.0)) (+ x (* -6.0 (* (- y x) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.52) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (-6.0 * ((y - x) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.52d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.65d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x + ((-6.0d0) * ((y - x) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.52) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (-6.0 * ((y - x) * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.52:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.65:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x + (-6.0 * ((y - x) * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.52)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.65)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(Float64(y - x) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.52)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.65)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x + (-6.0 * ((y - x) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.52], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.52000000000000002

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in z around inf 98.3%

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

      1. *-commutative 98.3%

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

   8. Simplified 98.3%

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

   if -0.52000000000000002 < z < 0.650000000000000022

   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 99.8%

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

   if 0.650000000000000022 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 97.1%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56 \lor \neg \left(z \leq 0.58\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.56) (not (<= z 0.58)))
   (* z (* (- y x) -6.0))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.56) || !(z <= 0.58)) {
		tmp = z * ((y - x) * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.56d0)) .or. (.not. (z <= 0.58d0))) then
        tmp = z * ((y - x) * (-6.0d0))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.56) || !(z <= 0.58)) {
		tmp = z * ((y - x) * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.56) or not (z <= 0.58):
		tmp = z * ((y - x) * -6.0)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.56) || !(z <= 0.58))
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.56) || ~((z <= 0.58)))
		tmp = z * ((y - x) * -6.0);
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.56], N[Not[LessEqual[z, 0.58]], $MachinePrecision]], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.56000000000000005 or 0.57999999999999996 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 97.7%

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

      1. *-commutative 97.7%

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

   8. Simplified 97.7%

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

   if -0.56000000000000005 < 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 z around 0 99.8%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56 \lor \neg \left(z \leq 0.58\right):\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-25} \lor \neg \left(x \leq 3.9 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.7e-25) (not (<= x 3.9e-23)))
   (* 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 <= -3.7e-25) || !(x <= 3.9e-23)) {
		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 <= (-3.7d-25)) .or. (.not. (x <= 3.9d-23))) 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 <= -3.7e-25) || !(x <= 3.9e-23)) {
		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 <= -3.7e-25) or not (x <= 3.9e-23):
		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 <= -3.7e-25) || !(x <= 3.9e-23))
		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 <= -3.7e-25) || ~((x <= 3.9e-23)))
		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, -3.7e-25], N[Not[LessEqual[x, 3.9e-23]], $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 < -3.70000000000000009e-25 or 3.9e-23 < 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 79.1%

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

      1. sub-neg 79.1%

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

      2. distribute-rgt-in 79.1%

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

      3. metadata-eval 79.1%

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

      4. distribute-lft-neg-in 79.1%

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

      5. associate-+r+ 79.1%

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

      6. metadata-eval 79.1%

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

      7. distribute-rgt-neg-in 79.1%

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

      8. metadata-eval 79.1%

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

   7. Simplified 79.1%

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

   if -3.70000000000000009e-25 < x < 3.9e-23

   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 79.4%

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

4. Final simplification 79.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.7 \cdot 10^{-25} \lor \neg \left(x \leq 3.9 \cdot 10^{-23}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{-25} \lor \neg \left(x \leq 1.04 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7.1e-25) (not (<= x 1.04e-29)))
   (* x (+ -3.0 (* z 6.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.1e-25) || !(x <= 1.04e-29)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7.1d-25)) .or. (.not. (x <= 1.04d-29))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7.1e-25) || !(x <= 1.04e-29)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7.1e-25) or not (x <= 1.04e-29):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7.1e-25) || !(x <= 1.04e-29))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7.1e-25) || ~((x <= 1.04e-29)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7.1e-25], N[Not[LessEqual[x, 1.04e-29]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7.1000000000000001e-25 or 1.03999999999999995e-29 < 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 79.1%

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

      1. sub-neg 79.1%

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

      2. distribute-rgt-in 79.1%

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

      3. metadata-eval 79.1%

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

      4. distribute-lft-neg-in 79.1%

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

      5. associate-+r+ 79.1%

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

      6. metadata-eval 79.1%

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

      7. distribute-rgt-neg-in 79.1%

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

      8. metadata-eval 79.1%

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

   7. Simplified 79.1%

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

   if -7.1000000000000001e-25 < x < 1.03999999999999995e-29

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.6%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 79.2%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.1 \cdot 10^{-25} \lor \neg \left(x \leq 1.04 \cdot 10^{-29}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.08 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.08) (not (<= z 0.65))) (* -6.0 (* y z)) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.08) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.08d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.08) || !(z <= 0.65)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.08) or not (z <= 0.65):
		tmp = -6.0 * (y * z)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.08) || !(z <= 0.65))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.08) || ~((z <= 0.65)))
		tmp = -6.0 * (y * z);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.08], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.0800000000000000017 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in z around inf 97.7%

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

      1. *-commutative 97.7%

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

   8. Simplified 97.7%

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

   9. Taylor expanded in y around inf 56.9%

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

   if -0.0800000000000000017 < z < 0.650000000000000022

   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 53.4%

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

      1. sub-neg 53.4%

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

      2. distribute-rgt-in 53.4%

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

      3. metadata-eval 53.4%

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

      4. distribute-lft-neg-in 53.4%

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

      5. associate-+r+ 53.4%

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

      6. metadata-eval 53.4%

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

      7. distribute-rgt-neg-in 53.4%

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

      8. metadata-eval 53.4%

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

   7. Simplified 53.4%

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

   8. Taylor expanded in z around 0 53.4%

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

      1. *-commutative 53.4%

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

   10. Simplified 53.4%

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

4. Final simplification 55.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.08 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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. Add Preprocessing

Alternative 13: 25.4% 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 52.2%

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

   1. sub-neg 52.2%

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

   2. distribute-rgt-in 52.2%

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

   3. metadata-eval 52.2%

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

   4. distribute-lft-neg-in 52.2%

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

   5. associate-+r+ 52.2%

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

   6. metadata-eval 52.2%

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

   7. distribute-rgt-neg-in 52.2%

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

   8. metadata-eval 52.2%

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

7. Simplified 52.2%

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

8. Taylor expanded in z around 0 27.9%

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

   1. *-commutative 27.9%

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

10. Simplified 27.9%

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

Reproduce

herbie shell --seed 2024101 
(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))))