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

Percentage Accurate: 99.5% → 99.7%

Time: 8.4s

Alternatives: 15

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. +-commutative 99.2%

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

   2. associate-*l* 99.8%

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

   3. fma-def 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-75}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-183}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-149}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -7.8e+39)
     t_0
     (if (<= z -4.8e-75)
       (* 6.0 (* y (- 0.6666666666666666 z)))
       (if (<= z -9.5e-183)
         (* x -3.0)
         (if (<= z -7.5e-256)
           (* y 4.0)
           (if (<= z 1.1e-149)
             (* x -3.0)
             (if (<= z 1.5e-130)
               (* 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 <= -7.8e+39) {
		tmp = t_0;
	} else if (z <= -4.8e-75) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -9.5e-183) {
		tmp = x * -3.0;
	} else if (z <= -7.5e-256) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-149) {
		tmp = x * -3.0;
	} else if (z <= 1.5e-130) {
		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 <= (-7.8d+39)) then
        tmp = t_0
    else if (z <= (-4.8d-75)) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else if (z <= (-9.5d-183)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7.5d-256)) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-149) then
        tmp = x * (-3.0d0)
    else if (z <= 1.5d-130) 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 <= -7.8e+39) {
		tmp = t_0;
	} else if (z <= -4.8e-75) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -9.5e-183) {
		tmp = x * -3.0;
	} else if (z <= -7.5e-256) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-149) {
		tmp = x * -3.0;
	} else if (z <= 1.5e-130) {
		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 <= -7.8e+39:
		tmp = t_0
	elif z <= -4.8e-75:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	elif z <= -9.5e-183:
		tmp = x * -3.0
	elif z <= -7.5e-256:
		tmp = y * 4.0
	elif z <= 1.1e-149:
		tmp = x * -3.0
	elif z <= 1.5e-130:
		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 <= -7.8e+39)
		tmp = t_0;
	elseif (z <= -4.8e-75)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	elseif (z <= -9.5e-183)
		tmp = Float64(x * -3.0);
	elseif (z <= -7.5e-256)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-149)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.5e-130)
		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 <= -7.8e+39)
		tmp = t_0;
	elseif (z <= -4.8e-75)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	elseif (z <= -9.5e-183)
		tmp = x * -3.0;
	elseif (z <= -7.5e-256)
		tmp = y * 4.0;
	elseif (z <= 1.1e-149)
		tmp = x * -3.0;
	elseif (z <= 1.5e-130)
		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, -7.8e+39], t$95$0, If[LessEqual[z, -4.8e-75], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -9.5e-183], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7.5e-256], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-149], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.5e-130], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -7.8000000000000002e39 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. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 98.8%

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

   if -7.8000000000000002e39 < z < -4.80000000000000039e-75

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate-*l* 99.8%

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

      3. fma-def 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. expm1-log1p-u 97.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}, x\right) \]

   5. Applied egg-rr 97.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}, x\right) \]

   6. Taylor expanded in y around inf 72.2%

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

   if -4.80000000000000039e-75 < z < -9.5000000000000008e-183 or -7.50000000000000005e-256 < z < 1.0999999999999999e-149 or 1.49999999999999993e-130 < z < 0.5

   1. Initial program 98.4%

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

      1. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in x around inf 64.9%

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

      1. sub-neg 64.9%

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

      2. distribute-rgt-in 64.9%

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

      3. metadata-eval 64.9%

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

      4. metadata-eval 64.9%

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

      5. neg-mul-1 64.9%

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

      6. associate-*r* 64.9%

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

      7. *-commutative 64.9%

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

      8. distribute-lft-in 64.9%

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

      9. distribute-lft-in 64.9%

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

      10. associate-+r+ 64.9%

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

      11. *-commutative 64.9%

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

      12. metadata-eval 64.9%

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

      13. metadata-eval 64.9%

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

      14. *-commutative 64.9%

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

      15. associate-*l* 64.9%

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

      16. metadata-eval 64.9%

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

   6. Simplified 64.9%

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

   7. Taylor expanded in z around 0 63.8%

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

      1. *-commutative 63.8%

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

   9. Simplified 63.8%

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

   if -9.5000000000000008e-183 < z < -7.50000000000000005e-256 or 1.0999999999999999e-149 < z < 1.49999999999999993e-130

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 72.0%

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

   6. Taylor expanded in z around 0 72.0%

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

      1. *-commutative 72.0%

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

   8. Simplified 72.0%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.8 \cdot 10^{+39}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-75}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -9.5 \cdot 10^{-183}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-256}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-149}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 3: 51.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.16 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.16e+45)
     (* x (* 6.0 z))
     (if (<= z -7.6e-10)
       t_0
       (if (<= z 6.4e-150)
         (* x -3.0)
         (if (<= z 2.1e-130) (* 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 <= -1.16e+45) {
		tmp = x * (6.0 * z);
	} else if (z <= -7.6e-10) {
		tmp = t_0;
	} else if (z <= 6.4e-150) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-130) {
		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 <= (-1.16d+45)) then
        tmp = x * (6.0d0 * z)
    else if (z <= (-7.6d-10)) then
        tmp = t_0
    else if (z <= 6.4d-150) then
        tmp = x * (-3.0d0)
    else if (z <= 2.1d-130) 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 <= -1.16e+45) {
		tmp = x * (6.0 * z);
	} else if (z <= -7.6e-10) {
		tmp = t_0;
	} else if (z <= 6.4e-150) {
		tmp = x * -3.0;
	} else if (z <= 2.1e-130) {
		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 <= -1.16e+45:
		tmp = x * (6.0 * z)
	elif z <= -7.6e-10:
		tmp = t_0
	elif z <= 6.4e-150:
		tmp = x * -3.0
	elif z <= 2.1e-130:
		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 <= -1.16e+45)
		tmp = Float64(x * Float64(6.0 * z));
	elseif (z <= -7.6e-10)
		tmp = t_0;
	elseif (z <= 6.4e-150)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.1e-130)
		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 <= -1.16e+45)
		tmp = x * (6.0 * z);
	elseif (z <= -7.6e-10)
		tmp = t_0;
	elseif (z <= 6.4e-150)
		tmp = x * -3.0;
	elseif (z <= 2.1e-130)
		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, -1.16e+45], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-10], t$95$0, If[LessEqual[z, 6.4e-150], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.1e-130], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.1600000000000001e45

   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. Taylor expanded in x around inf 62.9%

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

      1. sub-neg 62.9%

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

      2. distribute-rgt-in 62.9%

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

      3. metadata-eval 62.9%

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

      4. metadata-eval 62.9%

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

      5. neg-mul-1 62.9%

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

      6. associate-*r* 62.9%

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

      7. *-commutative 62.9%

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

      8. distribute-lft-in 62.9%

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

      9. distribute-lft-in 62.9%

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

      10. associate-+r+ 62.9%

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

      11. *-commutative 62.9%

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

      12. metadata-eval 62.9%

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

      13. metadata-eval 62.9%

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

      14. *-commutative 62.9%

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

      15. associate-*l* 62.9%

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

      16. metadata-eval 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in z around inf 62.9%

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

   if -1.1600000000000001e45 < z < -7.5999999999999996e-10 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around 0 62.6%

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

   6. Taylor expanded in z around inf 56.6%

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

   if -7.5999999999999996e-10 < z < 6.3999999999999996e-150 or 2.10000000000000002e-130 < z < 0.5

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 59.0%

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

      1. sub-neg 59.0%

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

      2. distribute-rgt-in 59.0%

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

      3. metadata-eval 59.0%

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

      4. metadata-eval 59.0%

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

      5. neg-mul-1 59.0%

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

      6. associate-*r* 59.0%

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

      7. *-commutative 59.0%

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

      8. distribute-lft-in 59.0%

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

      9. distribute-lft-in 59.0%

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

      10. associate-+r+ 59.0%

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

      11. *-commutative 59.0%

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

      12. metadata-eval 59.0%

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

      13. metadata-eval 59.0%

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

      14. *-commutative 59.0%

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

      15. associate-*l* 59.0%

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

      16. metadata-eval 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in z around 0 58.0%

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

      1. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if 6.3999999999999996e-150 < z < 2.10000000000000002e-130

   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. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in x around 0 88.1%

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

   6. Taylor expanded in z around 0 88.1%

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

      1. *-commutative 88.1%

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

   8. Simplified 88.1%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.16 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6.4 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 4: 51.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -1.75 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z -6.0))))
   (if (<= z -1.75e+46)
     (* x (* 6.0 z))
     (if (<= z -7.6e-10)
       t_0
       (if (<= z 5e-150)
         (* x -3.0)
         (if (<= z 1.6e-130) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double tmp;
	if (z <= -1.75e+46) {
		tmp = x * (6.0 * z);
	} else if (z <= -7.6e-10) {
		tmp = t_0;
	} else if (z <= 5e-150) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-130) {
		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 = y * (z * (-6.0d0))
    if (z <= (-1.75d+46)) then
        tmp = x * (6.0d0 * z)
    else if (z <= (-7.6d-10)) then
        tmp = t_0
    else if (z <= 5d-150) then
        tmp = x * (-3.0d0)
    else if (z <= 1.6d-130) 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 = y * (z * -6.0);
	double tmp;
	if (z <= -1.75e+46) {
		tmp = x * (6.0 * z);
	} else if (z <= -7.6e-10) {
		tmp = t_0;
	} else if (z <= 5e-150) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-130) {
		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 = y * (z * -6.0)
	tmp = 0
	if z <= -1.75e+46:
		tmp = x * (6.0 * z)
	elif z <= -7.6e-10:
		tmp = t_0
	elif z <= 5e-150:
		tmp = x * -3.0
	elif z <= 1.6e-130:
		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(y * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -1.75e+46)
		tmp = Float64(x * Float64(6.0 * z));
	elseif (z <= -7.6e-10)
		tmp = t_0;
	elseif (z <= 5e-150)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.6e-130)
		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 = y * (z * -6.0);
	tmp = 0.0;
	if (z <= -1.75e+46)
		tmp = x * (6.0 * z);
	elseif (z <= -7.6e-10)
		tmp = t_0;
	elseif (z <= 5e-150)
		tmp = x * -3.0;
	elseif (z <= 1.6e-130)
		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[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.75e+46], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-10], t$95$0, If[LessEqual[z, 5e-150], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.6e-130], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.74999999999999992e46

   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. Taylor expanded in x around inf 62.9%

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

      1. sub-neg 62.9%

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

      2. distribute-rgt-in 62.9%

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

      3. metadata-eval 62.9%

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

      4. metadata-eval 62.9%

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

      5. neg-mul-1 62.9%

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

      6. associate-*r* 62.9%

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

      7. *-commutative 62.9%

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

      8. distribute-lft-in 62.9%

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

      9. distribute-lft-in 62.9%

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

      10. associate-+r+ 62.9%

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

      11. *-commutative 62.9%

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

      12. metadata-eval 62.9%

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

      13. metadata-eval 62.9%

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

      14. *-commutative 62.9%

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

      15. associate-*l* 62.9%

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

      16. metadata-eval 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in z around inf 62.9%

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

   if -1.74999999999999992e46 < z < -7.5999999999999996e-10 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around 0 62.6%

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

   6. Taylor expanded in z around inf 56.6%

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

      1. *-commutative 56.6%

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

      2. associate-*r* 56.7%

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

   8. Simplified 56.7%

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

   if -7.5999999999999996e-10 < z < 4.9999999999999999e-150 or 1.6e-130 < z < 0.5

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 59.0%

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

      1. sub-neg 59.0%

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

      2. distribute-rgt-in 59.0%

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

      3. metadata-eval 59.0%

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

      4. metadata-eval 59.0%

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

      5. neg-mul-1 59.0%

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

      6. associate-*r* 59.0%

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

      7. *-commutative 59.0%

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

      8. distribute-lft-in 59.0%

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

      9. distribute-lft-in 59.0%

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

      10. associate-+r+ 59.0%

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

      11. *-commutative 59.0%

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

      12. metadata-eval 59.0%

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

      13. metadata-eval 59.0%

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

      14. *-commutative 59.0%

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

      15. associate-*l* 59.0%

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

      16. metadata-eval 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in z around 0 58.0%

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

      1. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if 4.9999999999999999e-150 < z < 1.6e-130

   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. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in x around 0 88.1%

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

   6. Taylor expanded in z around 0 88.1%

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

      1. *-commutative 88.1%

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

   8. Simplified 88.1%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.75 \cdot 10^{+46}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]

Alternative 5: 51.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.2e+45)
   (* x (* 6.0 z))
   (if (<= z -7.6e-10)
     (* y (* z -6.0))
     (if (<= z 5.3e-150)
       (* x -3.0)
       (if (<= z 2.25e-130)
         (* y 4.0)
         (if (<= z 0.5) (* x -3.0) (* z (* y -6.0))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e+45) {
		tmp = x * (6.0 * z);
	} else if (z <= -7.6e-10) {
		tmp = y * (z * -6.0);
	} else if (z <= 5.3e-150) {
		tmp = x * -3.0;
	} else if (z <= 2.25e-130) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.2d+45)) then
        tmp = x * (6.0d0 * z)
    else if (z <= (-7.6d-10)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= 5.3d-150) then
        tmp = x * (-3.0d0)
    else if (z <= 2.25d-130) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = z * (y * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.2e+45) {
		tmp = x * (6.0 * z);
	} else if (z <= -7.6e-10) {
		tmp = y * (z * -6.0);
	} else if (z <= 5.3e-150) {
		tmp = x * -3.0;
	} else if (z <= 2.25e-130) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = z * (y * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.2e+45:
		tmp = x * (6.0 * z)
	elif z <= -7.6e-10:
		tmp = y * (z * -6.0)
	elif z <= 5.3e-150:
		tmp = x * -3.0
	elif z <= 2.25e-130:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = z * (y * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.2e+45)
		tmp = Float64(x * Float64(6.0 * z));
	elseif (z <= -7.6e-10)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= 5.3e-150)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.25e-130)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(z * Float64(y * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.2e+45)
		tmp = x * (6.0 * z);
	elseif (z <= -7.6e-10)
		tmp = y * (z * -6.0);
	elseif (z <= 5.3e-150)
		tmp = x * -3.0;
	elseif (z <= 2.25e-130)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = z * (y * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.2e+45], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.6e-10], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.3e-150], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.25e-130], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.19999999999999995e45

   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. Taylor expanded in x around inf 62.9%

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

      1. sub-neg 62.9%

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

      2. distribute-rgt-in 62.9%

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

      3. metadata-eval 62.9%

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

      4. metadata-eval 62.9%

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

      5. neg-mul-1 62.9%

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

      6. associate-*r* 62.9%

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

      7. *-commutative 62.9%

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

      8. distribute-lft-in 62.9%

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

      9. distribute-lft-in 62.9%

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

      10. associate-+r+ 62.9%

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

      11. *-commutative 62.9%

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

      12. metadata-eval 62.9%

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

      13. metadata-eval 62.9%

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

      14. *-commutative 62.9%

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

      15. associate-*l* 62.9%

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

      16. metadata-eval 62.9%

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

   6. Simplified 62.9%

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

   7. Taylor expanded in z around inf 62.9%

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

   if -1.19999999999999995e45 < z < -7.5999999999999996e-10

   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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around 0 90.8%

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

   6. Taylor expanded in z around inf 61.6%

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

      1. *-commutative 61.6%

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

      2. associate-*r* 61.8%

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

   8. Simplified 61.8%

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

   if -7.5999999999999996e-10 < z < 5.29999999999999991e-150 or 2.25e-130 < z < 0.5

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 59.0%

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

      1. sub-neg 59.0%

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

      2. distribute-rgt-in 59.0%

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

      3. metadata-eval 59.0%

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

      4. metadata-eval 59.0%

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

      5. neg-mul-1 59.0%

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

      6. associate-*r* 59.0%

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

      7. *-commutative 59.0%

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

      8. distribute-lft-in 59.0%

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

      9. distribute-lft-in 59.0%

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

      10. associate-+r+ 59.0%

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

      11. *-commutative 59.0%

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

      12. metadata-eval 59.0%

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

      13. metadata-eval 59.0%

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

      14. *-commutative 59.0%

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

      15. associate-*l* 59.0%

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

      16. metadata-eval 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in z around 0 58.0%

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

      1. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if 5.29999999999999991e-150 < z < 2.25e-130

   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. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in x around 0 88.1%

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

   6. Taylor expanded in z around 0 88.1%

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

      1. *-commutative 88.1%

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

   8. Simplified 88.1%

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

   if 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. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in x around 0 57.6%

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

   6. Taylor expanded in z around inf 55.7%

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

      1. *-commutative 55.7%

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

      2. associate-*r* 55.8%

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

   8. Simplified 55.8%

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

   9. Taylor expanded in y around 0 55.7%

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

       1. associate-*r* 55.8%

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

       2. *-commutative 55.8%

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

   11. Simplified 55.8%

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

4. Final simplification 59.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.2 \cdot 10^{+45}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 5.3 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]

Alternative 6: 74.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -7.6e-10)
     t_0
     (if (<= z 9.2e-150)
       (* x -3.0)
       (if (<= z 4.6e-130) (* 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 <= -7.6e-10) {
		tmp = t_0;
	} else if (z <= 9.2e-150) {
		tmp = x * -3.0;
	} else if (z <= 4.6e-130) {
		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 <= (-7.6d-10)) then
        tmp = t_0
    else if (z <= 9.2d-150) then
        tmp = x * (-3.0d0)
    else if (z <= 4.6d-130) 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 <= -7.6e-10) {
		tmp = t_0;
	} else if (z <= 9.2e-150) {
		tmp = x * -3.0;
	} else if (z <= 4.6e-130) {
		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 <= -7.6e-10:
		tmp = t_0
	elif z <= 9.2e-150:
		tmp = x * -3.0
	elif z <= 4.6e-130:
		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 <= -7.6e-10)
		tmp = t_0;
	elseif (z <= 9.2e-150)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.6e-130)
		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 <= -7.6e-10)
		tmp = t_0;
	elseif (z <= 9.2e-150)
		tmp = x * -3.0;
	elseif (z <= 4.6e-130)
		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, -7.6e-10], t$95$0, If[LessEqual[z, 9.2e-150], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.6e-130], 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 < -7.5999999999999996e-10 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. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 96.2%

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

   if -7.5999999999999996e-10 < z < 9.20000000000000011e-150 or 4.6000000000000002e-130 < z < 0.5

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 59.0%

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

      1. sub-neg 59.0%

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

      2. distribute-rgt-in 59.0%

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

      3. metadata-eval 59.0%

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

      4. metadata-eval 59.0%

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

      5. neg-mul-1 59.0%

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

      6. associate-*r* 59.0%

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

      7. *-commutative 59.0%

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

      8. distribute-lft-in 59.0%

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

      9. distribute-lft-in 59.0%

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

      10. associate-+r+ 59.0%

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

      11. *-commutative 59.0%

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

      12. metadata-eval 59.0%

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

      13. metadata-eval 59.0%

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

      14. *-commutative 59.0%

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

      15. associate-*l* 59.0%

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

      16. metadata-eval 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in z around 0 58.0%

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

      1. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if 9.20000000000000011e-150 < z < 4.6000000000000002e-130

   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. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in x around 0 88.1%

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

   6. Taylor expanded in z around 0 88.1%

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

      1. *-commutative 88.1%

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

   8. Simplified 88.1%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 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 99.2%

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

   1. metadata-eval 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in z around 0 99.8%

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

5. Final simplification 99.8%

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

Alternative 8: 50.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -7.6e-10)
     t_0
     (if (<= z 6.2e-150)
       (* x -3.0)
       (if (<= z 1.5e-130) (* y 4.0) (if (<= z 0.65) (* 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 <= -7.6e-10) {
		tmp = t_0;
	} else if (z <= 6.2e-150) {
		tmp = x * -3.0;
	} else if (z <= 1.5e-130) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		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 <= (-7.6d-10)) then
        tmp = t_0
    else if (z <= 6.2d-150) then
        tmp = x * (-3.0d0)
    else if (z <= 1.5d-130) then
        tmp = y * 4.0d0
    else if (z <= 0.65d0) 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 <= -7.6e-10) {
		tmp = t_0;
	} else if (z <= 6.2e-150) {
		tmp = x * -3.0;
	} else if (z <= 1.5e-130) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		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 <= -7.6e-10:
		tmp = t_0
	elif z <= 6.2e-150:
		tmp = x * -3.0
	elif z <= 1.5e-130:
		tmp = y * 4.0
	elif z <= 0.65:
		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 <= -7.6e-10)
		tmp = t_0;
	elseif (z <= 6.2e-150)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.5e-130)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.65)
		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 <= -7.6e-10)
		tmp = t_0;
	elseif (z <= 6.2e-150)
		tmp = x * -3.0;
	elseif (z <= 1.5e-130)
		tmp = y * 4.0;
	elseif (z <= 0.65)
		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, -7.6e-10], t$95$0, If[LessEqual[z, 6.2e-150], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.5e-130], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -7.5999999999999996e-10 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. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 53.0%

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

   6. Taylor expanded in z around inf 49.5%

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

   if -7.5999999999999996e-10 < z < 6.19999999999999996e-150 or 1.49999999999999993e-130 < z < 0.650000000000000022

   1. Initial program 98.6%

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

      1. metadata-eval 98.6%

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

   3. Simplified 98.6%

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

   4. Taylor expanded in x around inf 59.0%

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

      1. sub-neg 59.0%

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

      2. distribute-rgt-in 59.0%

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

      3. metadata-eval 59.0%

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

      4. metadata-eval 59.0%

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

      5. neg-mul-1 59.0%

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

      6. associate-*r* 59.0%

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

      7. *-commutative 59.0%

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

      8. distribute-lft-in 59.0%

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

      9. distribute-lft-in 59.0%

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

      10. associate-+r+ 59.0%

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

      11. *-commutative 59.0%

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

      12. metadata-eval 59.0%

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

      13. metadata-eval 59.0%

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

      14. *-commutative 59.0%

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

      15. associate-*l* 59.0%

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

      16. metadata-eval 59.0%

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

   6. Simplified 59.0%

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

   7. Taylor expanded in z around 0 58.0%

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

      1. *-commutative 58.0%

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

   9. Simplified 58.0%

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

   if 6.19999999999999996e-150 < z < 1.49999999999999993e-130

   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. Taylor expanded in z around 0 100.0%

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

   5. Taylor expanded in x around 0 88.1%

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

   6. Taylor expanded in z around 0 88.1%

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

      1. *-commutative 88.1%

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

   8. Simplified 88.1%

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

4. Final simplification 54.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -7.6 \cdot 10^{-10}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-130}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 9: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. metadata-eval 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in y around 0 99.2%

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

5. Final simplification 99.2%

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

Alternative 10: 75.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-6} \lor \neg \left(x \leq 1.1 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.7e-6) (not (<= x 1.1e-5)))
   (* x (+ -3.0 (* 6.0 z)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.7e-6) || !(x <= 1.1e-5)) {
		tmp = x * (-3.0 + (6.0 * z));
	} 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 <= (-2.7d-6)) .or. (.not. (x <= 1.1d-5))) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    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 <= -2.7e-6) || !(x <= 1.1e-5)) {
		tmp = x * (-3.0 + (6.0 * z));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.7e-6) or not (x <= 1.1e-5):
		tmp = x * (-3.0 + (6.0 * z))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.7e-6) || !(x <= 1.1e-5))
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	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 <= -2.7e-6) || ~((x <= 1.1e-5)))
		tmp = x * (-3.0 + (6.0 * z));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.7e-6], N[Not[LessEqual[x, 1.1e-5]], $MachinePrecision]], N[(x * N[(-3.0 + N[(6.0 * z), $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 < -2.69999999999999998e-6 or 1.1e-5 < x

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 84.8%

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

      1. sub-neg 84.8%

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

      2. distribute-rgt-in 84.8%

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

      3. metadata-eval 84.8%

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

      4. metadata-eval 84.8%

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

      5. neg-mul-1 84.8%

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

      6. associate-*r* 84.8%

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

      7. *-commutative 84.8%

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

      8. distribute-lft-in 84.8%

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

      9. distribute-lft-in 84.8%

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

      10. associate-+r+ 84.8%

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

      11. *-commutative 84.8%

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

      12. metadata-eval 84.8%

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

      13. metadata-eval 84.8%

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

      14. *-commutative 84.8%

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

      15. associate-*l* 84.8%

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

      16. metadata-eval 84.8%

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

   6. Simplified 84.8%

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

   if -2.69999999999999998e-6 < x < 1.1e-5

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

      1. expm1-log1p-u 74.1%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}, x\right) \]

   5. Applied egg-rr 74.1%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(6 \cdot \left(0.6666666666666666 - z\right)\right)\right)}, x\right) \]

   6. Taylor expanded in y around inf 82.6%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.7 \cdot 10^{-6} \lor \neg \left(x \leq 1.1 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]

Alternative 11: 75.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-6} \lor \neg \left(x \leq 2.3 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -5.8e-6) (not (<= x 2.3e-5)))
   (* x (+ -3.0 (* 6.0 z)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -5.8e-6) || !(x <= 2.3e-5)) {
		tmp = x * (-3.0 + (6.0 * z));
	} 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 <= (-5.8d-6)) .or. (.not. (x <= 2.3d-5))) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    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 <= -5.8e-6) || !(x <= 2.3e-5)) {
		tmp = x * (-3.0 + (6.0 * z));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -5.8e-6) or not (x <= 2.3e-5):
		tmp = x * (-3.0 + (6.0 * z))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -5.8e-6) || !(x <= 2.3e-5))
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	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 <= -5.8e-6) || ~((x <= 2.3e-5)))
		tmp = x * (-3.0 + (6.0 * z));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -5.8e-6], N[Not[LessEqual[x, 2.3e-5]], $MachinePrecision]], N[(x * N[(-3.0 + N[(6.0 * z), $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 < -5.8000000000000004e-6 or 2.3e-5 < x

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in x around inf 84.8%

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

      1. sub-neg 84.8%

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

      2. distribute-rgt-in 84.8%

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

      3. metadata-eval 84.8%

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

      4. metadata-eval 84.8%

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

      5. neg-mul-1 84.8%

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

      6. associate-*r* 84.8%

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

      7. *-commutative 84.8%

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

      8. distribute-lft-in 84.8%

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

      9. distribute-lft-in 84.8%

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

      10. associate-+r+ 84.8%

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

      11. *-commutative 84.8%

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

      12. metadata-eval 84.8%

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

      13. metadata-eval 84.8%

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

      14. *-commutative 84.8%

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

      15. associate-*l* 84.8%

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

      16. metadata-eval 84.8%

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

   6. Simplified 84.8%

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

   if -5.8000000000000004e-6 < x < 2.3e-5

   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* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. distribute-rgt-neg-out 99.9%

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

      8. *-commutative 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. fma-def 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. Taylor expanded in y around inf 83.0%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-6} \lor \neg \left(x \leq 2.3 \cdot 10^{-5}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]

Alternative 12: 97.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.56) (not (<= z 0.65)))
   (* -6.0 (* (- y x) z))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.56) || !(z <= 0.65)) {
		tmp = -6.0 * ((y - x) * z);
	} 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 <= 0.65d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    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 <= 0.65)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.56) or not (z <= 0.65):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.56) || !(z <= 0.65))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	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 <= 0.65)))
		tmp = -6.0 * ((y - x) * z);
	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, 0.65]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $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 0.650000000000000022 < 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. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 98.3%

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

   if -0.56000000000000005 < z < 0.650000000000000022

   1. Initial program 98.7%

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

      1. metadata-eval 98.7%

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

   3. Simplified 98.7%

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

   4. Taylor expanded in z around 0 97.1%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]

Alternative 13: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.2%

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

   1. metadata-eval 99.2%

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

3. Simplified 99.2%

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

4. Final simplification 99.2%

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

Alternative 14: 37.4% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-84} \lor \neg \left(x \leq 1.36 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.15e-84) (not (<= x 1.36e-17))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.15e-84) || !(x <= 1.36e-17)) {
		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 <= (-1.15d-84)) .or. (.not. (x <= 1.36d-17))) 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 <= -1.15e-84) || !(x <= 1.36e-17)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.15e-84) or not (x <= 1.36e-17):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.15e-84) || !(x <= 1.36e-17))
		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 <= -1.15e-84) || ~((x <= 1.36e-17)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.15e-84], N[Not[LessEqual[x, 1.36e-17]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.1499999999999999e-84 or 1.36e-17 < x

   1. Initial program 98.9%

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

      1. metadata-eval 98.9%

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

   3. Simplified 98.9%

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

   4. Taylor expanded in x around inf 81.4%

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

      1. sub-neg 81.4%

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

      2. distribute-rgt-in 81.4%

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

      3. metadata-eval 81.4%

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

      4. metadata-eval 81.4%

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

      5. neg-mul-1 81.4%

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

      6. associate-*r* 81.4%

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

      7. *-commutative 81.4%

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

      8. distribute-lft-in 81.4%

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

      9. distribute-lft-in 81.4%

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

      10. associate-+r+ 81.4%

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

      11. *-commutative 81.4%

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

      12. metadata-eval 81.4%

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

      13. metadata-eval 81.4%

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

      14. *-commutative 81.4%

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

      15. associate-*l* 81.4%

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

      16. metadata-eval 81.4%

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

   6. Simplified 81.4%

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

   7. Taylor expanded in z around 0 43.1%

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

      1. *-commutative 43.1%

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

   9. Simplified 43.1%

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

   if -1.1499999999999999e-84 < x < 1.36e-17

   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. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 86.5%

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

   6. Taylor expanded in z around 0 49.6%

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

      1. *-commutative 49.6%

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

   8. Simplified 49.6%

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

4. Final simplification 45.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-84} \lor \neg \left(x \leq 1.36 \cdot 10^{-17}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]

Alternative 15: 25.7% 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 99.2%

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

   1. metadata-eval 99.2%

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

3. Simplified 99.2%

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

4. Taylor expanded in x around inf 55.0%

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

   1. sub-neg 55.0%

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

   2. distribute-rgt-in 55.0%

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

   3. metadata-eval 55.0%

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

   4. metadata-eval 55.0%

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

   5. neg-mul-1 55.0%

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

   6. associate-*r* 55.0%

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

   7. *-commutative 55.0%

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

   8. distribute-lft-in 55.0%

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

   9. distribute-lft-in 55.0%

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

   10. associate-+r+ 55.0%

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

   11. *-commutative 55.0%

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

   12. metadata-eval 55.0%

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

   13. metadata-eval 55.0%

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

   14. *-commutative 55.0%

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

   15. associate-*l* 55.0%

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

   16. metadata-eval 55.0%

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

6. Simplified 55.0%

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

7. Taylor expanded in z around 0 30.2%

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

   1. *-commutative 30.2%

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

9. Simplified 30.2%

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

10. Final simplification 30.2%

    \[\leadsto x \cdot -3 \]

Reproduce

herbie shell --seed 2023298 
(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))))