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

Percentage Accurate: 99.5% → 99.7%

Time: 11.1s

Alternatives: 13

Speedup: 1.2×

• 21.3% 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 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.9%

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

   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. Add Preprocessing

5. Final simplification 99.9%

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

Alternative 2: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -60000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-86}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -60000000000000.0)
     t_0
     (if (<= z 4.4e-86) (* 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 * (x * z);
	double tmp;
	if (z <= -60000000000000.0) {
		tmp = t_0;
	} else if (z <= 4.4e-86) {
		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 * (x * z)
    if (z <= (-60000000000000.0d0)) then
        tmp = t_0
    else if (z <= 4.4d-86) 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 * (x * z);
	double tmp;
	if (z <= -60000000000000.0) {
		tmp = t_0;
	} else if (z <= 4.4e-86) {
		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 * (x * z)
	tmp = 0
	if z <= -60000000000000.0:
		tmp = t_0
	elif z <= 4.4e-86:
		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(x * z))
	tmp = 0.0
	if (z <= -60000000000000.0)
		tmp = t_0;
	elseif (z <= 4.4e-86)
		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 * (x * z);
	tmp = 0.0;
	if (z <= -60000000000000.0)
		tmp = t_0;
	elseif (z <= 4.4e-86)
		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[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -60000000000000.0], t$95$0, If[LessEqual[z, 4.4e-86], 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 < -6e13 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 59.3%

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

      1. metadata-eval 59.3%

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

      2. cancel-sign-sub-inv 59.3%

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

      3. *-commutative 59.3%

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

      4. cancel-sign-sub-inv 59.3%

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

      5. distribute-lft-neg-in 59.3%

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

      6. *-commutative 59.3%

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

      7. sub-neg 59.3%

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

      8. distribute-lft-in 59.3%

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

      9. metadata-eval 59.3%

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

      10. distribute-rgt-neg-out 59.3%

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

      11. distribute-lft-neg-in 59.3%

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

      12. metadata-eval 59.3%

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

      13. mul-1-neg 59.3%

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

      14. distribute-lft-in 59.3%

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

      15. metadata-eval 59.3%

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

      16. associate-+r+ 59.3%

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

      17. metadata-eval 59.3%

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

      18. associate-*r* 59.3%

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

      19. metadata-eval 59.3%

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

      20. *-commutative 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in z around inf 58.3%

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

      1. *-commutative 58.3%

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

   10. Simplified 58.3%

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

   if -6e13 < z < 4.4000000000000003e-86

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 97.9%

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

   6. Taylor expanded in x around 0 63.8%

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

      1. *-commutative 63.8%

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

   8. Simplified 63.8%

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

   if 4.4000000000000003e-86 < z < 0.5

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 66.6%

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

      1. metadata-eval 66.6%

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

      2. cancel-sign-sub-inv 66.6%

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

      3. *-commutative 66.6%

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

      4. cancel-sign-sub-inv 66.6%

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

      5. distribute-lft-neg-in 66.6%

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

      6. *-commutative 66.6%

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

      7. sub-neg 66.6%

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

      8. distribute-lft-in 66.6%

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

      9. metadata-eval 66.6%

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

      10. distribute-rgt-neg-out 66.6%

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

      11. distribute-lft-neg-in 66.6%

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

      12. metadata-eval 66.6%

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

      13. mul-1-neg 66.6%

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

      14. distribute-lft-in 66.6%

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

      15. metadata-eval 66.6%

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

      16. associate-+r+ 66.6%

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

      17. metadata-eval 66.6%

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

      18. associate-*r* 66.6%

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

      19. metadata-eval 66.6%

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

      20. *-commutative 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in z around 0 62.5%

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

      1. *-commutative 62.5%

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

   10. Simplified 62.5%

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

4. Final simplification 60.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -60000000000000:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-86}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(6 \cdot z\right)\\ \mathbf{if}\;z \leq -60000000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* 6.0 z))))
   (if (<= z -60000000000000.0)
     t_0
     (if (<= z 7.5e-86) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x * (6.0 * z);
	double tmp;
	if (z <= -60000000000000.0) {
		tmp = t_0;
	} else if (z <= 7.5e-86) {
		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 = x * (6.0d0 * z)
    if (z <= (-60000000000000.0d0)) then
        tmp = t_0
    else if (z <= 7.5d-86) 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 = x * (6.0 * z);
	double tmp;
	if (z <= -60000000000000.0) {
		tmp = t_0;
	} else if (z <= 7.5e-86) {
		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 = x * (6.0 * z)
	tmp = 0
	if z <= -60000000000000.0:
		tmp = t_0
	elif z <= 7.5e-86:
		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(x * Float64(6.0 * z))
	tmp = 0.0
	if (z <= -60000000000000.0)
		tmp = t_0;
	elseif (z <= 7.5e-86)
		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 = x * (6.0 * z);
	tmp = 0.0;
	if (z <= -60000000000000.0)
		tmp = t_0;
	elseif (z <= 7.5e-86)
		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[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -60000000000000.0], t$95$0, If[LessEqual[z, 7.5e-86], 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 < -6e13 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 59.3%

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

      1. metadata-eval 59.3%

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

      2. cancel-sign-sub-inv 59.3%

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

      3. *-commutative 59.3%

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

      4. cancel-sign-sub-inv 59.3%

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

      5. distribute-lft-neg-in 59.3%

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

      6. *-commutative 59.3%

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

      7. sub-neg 59.3%

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

      8. distribute-lft-in 59.3%

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

      9. metadata-eval 59.3%

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

      10. distribute-rgt-neg-out 59.3%

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

      11. distribute-lft-neg-in 59.3%

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

      12. metadata-eval 59.3%

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

      13. mul-1-neg 59.3%

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

      14. distribute-lft-in 59.3%

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

      15. metadata-eval 59.3%

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

      16. associate-+r+ 59.3%

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

      17. metadata-eval 59.3%

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

      18. associate-*r* 59.3%

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

      19. metadata-eval 59.3%

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

      20. *-commutative 59.3%

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

   7. Simplified 59.3%

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

   8. Taylor expanded in z around inf 58.4%

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

   if -6e13 < z < 7.50000000000000055e-86

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 97.9%

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

   6. Taylor expanded in x around 0 63.8%

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

      1. *-commutative 63.8%

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

   8. Simplified 63.8%

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

   if 7.50000000000000055e-86 < z < 0.5

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 66.6%

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

      1. metadata-eval 66.6%

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

      2. cancel-sign-sub-inv 66.6%

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

      3. *-commutative 66.6%

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

      4. cancel-sign-sub-inv 66.6%

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

      5. distribute-lft-neg-in 66.6%

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

      6. *-commutative 66.6%

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

      7. sub-neg 66.6%

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

      8. distribute-lft-in 66.6%

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

      9. metadata-eval 66.6%

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

      10. distribute-rgt-neg-out 66.6%

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

      11. distribute-lft-neg-in 66.6%

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

      12. metadata-eval 66.6%

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

      13. mul-1-neg 66.6%

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

      14. distribute-lft-in 66.6%

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

      15. metadata-eval 66.6%

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

      16. associate-+r+ 66.6%

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

      17. metadata-eval 66.6%

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

      18. associate-*r* 66.6%

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

      19. metadata-eval 66.6%

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

      20. *-commutative 66.6%

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

   7. Simplified 66.6%

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

   8. Taylor expanded in z around 0 62.5%

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

      1. *-commutative 62.5%

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

   10. Simplified 62.5%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -60000000000000:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{-86}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.65 \lor \neg \left(z \leq 0.62\right):\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.65) (not (<= z 0.62)))
   (+ x (* -6.0 (* (- y x) z)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.65) || !(z <= 0.62)) {
		tmp = x + (-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 <= (-0.65d0)) .or. (.not. (z <= 0.62d0))) then
        tmp = x + ((-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 <= -0.65) || !(z <= 0.62)) {
		tmp = x + (-6.0 * ((y - x) * z));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.65) or not (z <= 0.62):
		tmp = x + (-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 <= -0.65) || !(z <= 0.62))
		tmp = Float64(x + 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 <= -0.65) || ~((z <= 0.62)))
		tmp = x + (-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, -0.65], N[Not[LessEqual[z, 0.62]], $MachinePrecision]], N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.650000000000000022 or 0.619999999999999996 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 98.3%

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

   if -0.650000000000000022 < z < 0.619999999999999996

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 98.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65 \lor \neg \left(z \leq 0.62\right):\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.65 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.65) (not (<= z 0.5)))
   (+ x (* (- y x) (* z -6.0)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.65) || !(z <= 0.5)) {
		tmp = x + ((y - x) * (z * -6.0));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.65d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = x + ((y - x) * (z * (-6.0d0)))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.65) || !(z <= 0.5)) {
		tmp = x + ((y - x) * (z * -6.0));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.65) or not (z <= 0.5):
		tmp = x + ((y - x) * (z * -6.0))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.65) || !(z <= 0.5))
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.65) || ~((z <= 0.5)))
		tmp = x + ((y - x) * (z * -6.0));
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.65], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.650000000000000022 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 98.3%

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

      1. associate-*r* 98.4%

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

      2. *-commutative 98.4%

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

   7. Simplified 98.4%

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

   if -0.650000000000000022 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 98.2%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.65)
   (+ x (* z (* (- y x) -6.0)))
   (if (<= z 0.5) (+ x (* (- y x) 4.0)) (+ x (* -6.0 (* (- y x) z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + (z * ((y - x) * -6.0));
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (-6.0 * ((y - x) * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.65d0)) then
        tmp = x + (z * ((y - x) * (-6.0d0)))
    else if (z <= 0.5d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x + ((-6.0d0) * ((y - x) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + (z * ((y - x) * -6.0));
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (-6.0 * ((y - x) * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.65:
		tmp = x + (z * ((y - x) * -6.0))
	elif z <= 0.5:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x + (-6.0 * ((y - x) * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.65)
		tmp = Float64(x + Float64(z * Float64(Float64(y - x) * -6.0)));
	elseif (z <= 0.5)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(Float64(y - x) * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.65)
		tmp = x + (z * ((y - x) * -6.0));
	elseif (z <= 0.5)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x + (-6.0 * ((y - x) * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.65], N[(x + N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around 0 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*r* 99.6%

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

      3. *-commutative 99.6%

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

   10. Simplified 99.6%

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

   if -0.650000000000000022 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 98.2%

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

   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. Add Preprocessing

   5. Taylor expanded in z around inf 97.1%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 59.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-159} \lor \neg \left(y \leq 9.4 \cdot 10^{-54}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -6.4e-159) (not (<= y 9.4e-54)))
   (* 6.0 (* y (- 0.6666666666666666 z)))
   (* x (* 6.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.4e-159) || !(y <= 9.4e-54)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (6.0 * 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 ((y <= (-6.4d-159)) .or. (.not. (y <= 9.4d-54))) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = x * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -6.4e-159) || !(y <= 9.4e-54)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -6.4e-159) or not (y <= 9.4e-54):
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -6.4e-159) || !(y <= 9.4e-54))
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(x * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -6.4e-159) || ~((y <= 9.4e-54)))
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -6.4e-159], N[Not[LessEqual[y, 9.4e-54]], $MachinePrecision]], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.3999999999999999e-159 or 9.4e-54 < y

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 83.3%

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

   6. Taylor expanded in x around 0 76.2%

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

   if -6.3999999999999999e-159 < y < 9.4e-54

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 86.7%

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

      1. metadata-eval 86.7%

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

      2. cancel-sign-sub-inv 86.7%

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

      3. *-commutative 86.7%

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

      4. cancel-sign-sub-inv 86.7%

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

      5. distribute-lft-neg-in 86.7%

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

      6. *-commutative 86.7%

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

      7. sub-neg 86.7%

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

      8. distribute-lft-in 86.7%

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

      9. metadata-eval 86.7%

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

      10. distribute-rgt-neg-out 86.7%

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

      11. distribute-lft-neg-in 86.7%

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

      12. metadata-eval 86.7%

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

      13. mul-1-neg 86.7%

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

      14. distribute-lft-in 86.7%

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

      15. metadata-eval 86.7%

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

      16. associate-+r+ 86.7%

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

      17. metadata-eval 86.7%

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

      18. associate-*r* 86.7%

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

      19. metadata-eval 86.7%

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

      20. *-commutative 86.7%

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

   7. Simplified 86.7%

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

   8. Taylor expanded in z around inf 53.4%

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

4. Final simplification 67.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.4 \cdot 10^{-159} \lor \neg \left(y \leq 9.4 \cdot 10^{-54}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-58} \lor \neg \left(y \leq 2.7 \cdot 10^{-53}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -7e-58) (not (<= y 2.7e-53)))
   (* 6.0 (* y (- 0.6666666666666666 z)))
   (* x (+ -3.0 (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e-58) || !(y <= 2.7e-53)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (6.0 * 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 ((y <= (-7d-58)) .or. (.not. (y <= 2.7d-53))) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -7e-58) || !(y <= 2.7e-53)) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (-3.0 + (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -7e-58) or not (y <= 2.7e-53):
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * (-3.0 + (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -7e-58) || !(y <= 2.7e-53))
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -7e-58) || ~((y <= 2.7e-53)))
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * (-3.0 + (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -7e-58], N[Not[LessEqual[y, 2.7e-53]], $MachinePrecision]], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999998e-58 or 2.6999999999999999e-53 < y

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 82.0%

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

   6. Taylor expanded in x around 0 80.2%

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

   if -6.9999999999999998e-58 < y < 2.6999999999999999e-53

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 82.7%

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

      1. metadata-eval 82.7%

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

      2. cancel-sign-sub-inv 82.7%

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

      3. *-commutative 82.7%

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

      4. cancel-sign-sub-inv 82.7%

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

      5. distribute-lft-neg-in 82.7%

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

      6. *-commutative 82.7%

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

      7. sub-neg 82.7%

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

      8. distribute-lft-in 82.7%

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

      9. metadata-eval 82.7%

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

      10. distribute-rgt-neg-out 82.7%

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

      11. distribute-lft-neg-in 82.7%

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

      12. metadata-eval 82.7%

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

      13. mul-1-neg 82.7%

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

      14. distribute-lft-in 82.7%

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

      15. metadata-eval 82.7%

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

      16. associate-+r+ 82.7%

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

      17. metadata-eval 82.7%

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

      18. associate-*r* 82.7%

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

      19. metadata-eval 82.7%

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

      20. *-commutative 82.7%

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

   7. Simplified 82.7%

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

4. Final simplification 81.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-58} \lor \neg \left(y \leq 2.7 \cdot 10^{-53}\right):\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-60} \lor \neg \left(y \leq 2.8 \cdot 10^{-53}\right):\\ \;\;\;\;y \cdot \left(z \cdot -6 + 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.6e-60) (not (<= y 2.8e-53)))
   (* y (+ (* z -6.0) 4.0))
   (* x (+ -3.0 (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.6e-60) || !(y <= 2.8e-53)) {
		tmp = y * ((z * -6.0) + 4.0);
	} else {
		tmp = x * (-3.0 + (6.0 * 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 ((y <= (-9.6d-60)) .or. (.not. (y <= 2.8d-53))) then
        tmp = y * ((z * (-6.0d0)) + 4.0d0)
    else
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.6e-60) || !(y <= 2.8e-53)) {
		tmp = y * ((z * -6.0) + 4.0);
	} else {
		tmp = x * (-3.0 + (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.6e-60) or not (y <= 2.8e-53):
		tmp = y * ((z * -6.0) + 4.0)
	else:
		tmp = x * (-3.0 + (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.6e-60) || !(y <= 2.8e-53))
		tmp = Float64(y * Float64(Float64(z * -6.0) + 4.0));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.6e-60) || ~((y <= 2.8e-53)))
		tmp = y * ((z * -6.0) + 4.0);
	else
		tmp = x * (-3.0 + (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.6e-60], N[Not[LessEqual[y, 2.8e-53]], $MachinePrecision]], N[(y * N[(N[(z * -6.0), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.60000000000000038e-60 or 2.79999999999999985e-53 < y

   1. Initial program 99.6%

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

      1. +-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-define 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. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 79.9%

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

   if -9.60000000000000038e-60 < y < 2.79999999999999985e-53

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 83.2%

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

      1. metadata-eval 83.2%

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

      2. cancel-sign-sub-inv 83.2%

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

      3. *-commutative 83.2%

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

      4. cancel-sign-sub-inv 83.2%

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

      5. distribute-lft-neg-in 83.2%

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

      6. *-commutative 83.2%

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

      7. sub-neg 83.2%

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

      8. distribute-lft-in 83.2%

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

      9. metadata-eval 83.2%

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

      10. distribute-rgt-neg-out 83.2%

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

      11. distribute-lft-neg-in 83.2%

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

      12. metadata-eval 83.2%

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

      13. mul-1-neg 83.2%

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

      14. distribute-lft-in 83.2%

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

      15. metadata-eval 83.2%

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

      16. associate-+r+ 83.2%

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

      17. metadata-eval 83.2%

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

      18. associate-*r* 83.2%

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

      19. metadata-eval 83.2%

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

      20. *-commutative 83.2%

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

   7. Simplified 83.2%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{-60} \lor \neg \left(y \leq 2.8 \cdot 10^{-53}\right):\\ \;\;\;\;y \cdot \left(z \cdot -6 + 4\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 37.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-80} \lor \neg \left(y \leq 5.3 \cdot 10^{-55}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -8.5e-80) (not (<= y 5.3e-55))) (* y 4.0) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.5e-80) || !(y <= 5.3e-55)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-8.5d-80)) .or. (.not. (y <= 5.3d-55))) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -8.5e-80) || !(y <= 5.3e-55)) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -8.5e-80) or not (y <= 5.3e-55):
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -8.5e-80) || !(y <= 5.3e-55))
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -8.5e-80) || ~((y <= 5.3e-55)))
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -8.5e-80], N[Not[LessEqual[y, 5.3e-55]], $MachinePrecision]], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.49999999999999939e-80 or 5.3000000000000003e-55 < y

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 50.9%

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

   6. Taylor expanded in x around 0 42.8%

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

      1. *-commutative 42.8%

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

   8. Simplified 42.8%

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

   if -8.49999999999999939e-80 < y < 5.3000000000000003e-55

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 83.7%

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

      1. metadata-eval 83.7%

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

      2. cancel-sign-sub-inv 83.7%

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

      3. *-commutative 83.7%

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

      4. cancel-sign-sub-inv 83.7%

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

      5. distribute-lft-neg-in 83.7%

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

      6. *-commutative 83.7%

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

      7. sub-neg 83.7%

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

      8. distribute-lft-in 83.7%

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

      9. metadata-eval 83.7%

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

      10. distribute-rgt-neg-out 83.7%

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

      11. distribute-lft-neg-in 83.7%

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

      12. metadata-eval 83.7%

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

      13. mul-1-neg 83.7%

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

      14. distribute-lft-in 83.7%

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

      15. metadata-eval 83.7%

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

      16. associate-+r+ 83.7%

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

      17. metadata-eval 83.7%

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

      18. associate-*r* 83.7%

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

      19. metadata-eval 83.7%

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

      20. *-commutative 83.7%

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

   7. Simplified 83.7%

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

   8. Taylor expanded in z around 0 36.3%

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

      1. *-commutative 36.3%

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

   10. Simplified 36.3%

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

4. Final simplification 40.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{-80} \lor \neg \left(y \leq 5.3 \cdot 10^{-55}\right):\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 12: 26.1% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 51.4%

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

   1. metadata-eval 51.4%

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

   2. cancel-sign-sub-inv 51.4%

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

   3. *-commutative 51.4%

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

   4. cancel-sign-sub-inv 51.4%

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

   5. distribute-lft-neg-in 51.4%

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

   6. *-commutative 51.4%

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

   7. sub-neg 51.4%

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

   8. distribute-lft-in 51.4%

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

   9. metadata-eval 51.4%

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

   10. distribute-rgt-neg-out 51.4%

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

   11. distribute-lft-neg-in 51.4%

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

   12. metadata-eval 51.4%

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

   13. mul-1-neg 51.4%

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

   14. distribute-lft-in 51.4%

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

   15. metadata-eval 51.4%

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

   16. associate-+r+ 51.4%

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

   17. metadata-eval 51.4%

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

   18. associate-*r* 51.4%

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

   19. metadata-eval 51.4%

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

   20. *-commutative 51.4%

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

7. Simplified 51.4%

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

8. Taylor expanded in z around 0 20.8%

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

   1. *-commutative 20.8%

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

10. Simplified 20.8%

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

11. Final simplification 20.8%

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

Alternative 13: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around inf 53.7%

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

   1. associate-*r* 53.7%

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

7. Simplified 53.7%

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

8. Taylor expanded in x around inf 2.7%

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

9. Final simplification 2.7%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024096 
(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))))