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

Percentage Accurate: 99.5% → 99.7%

Time: 18.4s

Alternatives: 12

Speedup: 1.2×

• 21.2% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-197}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-293}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1150000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -2.55e+17)
     t_1
     (if (<= z -7e-197)
       t_0
       (if (<= z 8e-293) (* x -3.0) (if (<= z 1150000.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2.55e+17) {
		tmp = t_1;
	} else if (z <= -7e-197) {
		tmp = t_0;
	} else if (z <= 8e-293) {
		tmp = x * -3.0;
	} else if (z <= 1150000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-2.55d+17)) then
        tmp = t_1
    else if (z <= (-7d-197)) then
        tmp = t_0
    else if (z <= 8d-293) then
        tmp = x * (-3.0d0)
    else if (z <= 1150000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2.55e+17) {
		tmp = t_1;
	} else if (z <= -7e-197) {
		tmp = t_0;
	} else if (z <= 8e-293) {
		tmp = x * -3.0;
	} else if (z <= 1150000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -2.55e+17:
		tmp = t_1
	elif z <= -7e-197:
		tmp = t_0
	elif z <= 8e-293:
		tmp = x * -3.0
	elif z <= 1150000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -2.55e+17)
		tmp = t_1;
	elseif (z <= -7e-197)
		tmp = t_0;
	elseif (z <= 8e-293)
		tmp = Float64(x * -3.0);
	elseif (z <= 1150000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -2.55e+17)
		tmp = t_1;
	elseif (z <= -7e-197)
		tmp = t_0;
	elseif (z <= 8e-293)
		tmp = x * -3.0;
	elseif (z <= 1150000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+17], t$95$1, If[LessEqual[z, -7e-197], t$95$0, If[LessEqual[z, 8e-293], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1150000.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55e17 or 1.15e6 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      2. pow3 99.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right)}^{3}} \]

      3. +-commutative 99.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x}}\right)}^{3} \]

      4. associate-*l* 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x}\right)}^{3} \]

      5. fma-define 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}\right)}^{3} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}\right)}^{3}} \]

   7. Taylor expanded in z around inf 99.7%

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

   if -2.55e17 < z < -6.9999999999999996e-197 or 8.0000000000000004e-293 < z < 1.15e6

   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* 99.9%

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

      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 63.4%

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

   if -6.9999999999999996e-197 < z < 8.0000000000000004e-293

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 67.7%

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

      1. *-lft-identity 67.7%

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

      2. *-commutative 67.7%

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

      3. +-commutative 67.7%

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

      4. *-commutative 67.7%

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

      5. fma-define 67.7%

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

      6. associate-*r* 67.7%

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

      7. fma-define 67.7%

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

      8. distribute-lft-in 67.7%

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

      9. neg-mul-1 67.7%

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

      10. distribute-lft-neg-in 67.7%

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

      11. metadata-eval 67.7%

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

      12. metadata-eval 67.7%

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

      13. distribute-rgt-in 67.7%

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

      14. +-commutative 67.7%

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

      15. sub-neg 67.7%

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

      16. distribute-rgt-in 67.7%

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

      17. sub-neg 67.7%

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

      18. distribute-rgt-in 67.7%

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

      19. metadata-eval 67.7%

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

      20. distribute-lft-neg-in 67.7%

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

      21. associate-+r+ 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   10. Simplified 67.7%

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

4. Final simplification 84.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+17}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-197}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-293}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1150000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -2.55 \cdot 10^{+17}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-198}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3300000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y (- 0.6666666666666666 z))))
        (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -2.55e+17)
     t_1
     (if (<= z -6.5e-198)
       t_0
       (if (<= z 1.5e-292) (* x -3.0) (if (<= z 3300000.0) t_0 t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2.55e+17) {
		tmp = t_1;
	} else if (z <= -6.5e-198) {
		tmp = t_0;
	} else if (z <= 1.5e-292) {
		tmp = x * -3.0;
	} else if (z <= 3300000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * (0.6666666666666666d0 - z))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-2.55d+17)) then
        tmp = t_1
    else if (z <= (-6.5d-198)) then
        tmp = t_0
    else if (z <= 1.5d-292) then
        tmp = x * (-3.0d0)
    else if (z <= 3300000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * (0.6666666666666666 - z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -2.55e+17) {
		tmp = t_1;
	} else if (z <= -6.5e-198) {
		tmp = t_0;
	} else if (z <= 1.5e-292) {
		tmp = x * -3.0;
	} else if (z <= 3300000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * (0.6666666666666666 - z))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -2.55e+17:
		tmp = t_1
	elif z <= -6.5e-198:
		tmp = t_0
	elif z <= 1.5e-292:
		tmp = x * -3.0
	elif z <= 3300000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -2.55e+17)
		tmp = t_1;
	elseif (z <= -6.5e-198)
		tmp = t_0;
	elseif (z <= 1.5e-292)
		tmp = Float64(x * -3.0);
	elseif (z <= 3300000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * (0.6666666666666666 - z));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -2.55e+17)
		tmp = t_1;
	elseif (z <= -6.5e-198)
		tmp = t_0;
	elseif (z <= 1.5e-292)
		tmp = x * -3.0;
	elseif (z <= 3300000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.55e+17], t$95$1, If[LessEqual[z, -6.5e-198], t$95$0, If[LessEqual[z, 1.5e-292], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3300000.0], t$95$0, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -2.55e17 or 3.3e6 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      2. pow3 99.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right)}^{3}} \]

      3. +-commutative 99.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x}}\right)}^{3} \]

      4. associate-*l* 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x}\right)}^{3} \]

      5. fma-define 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}\right)}^{3} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}\right)}^{3}} \]

   7. Taylor expanded in z around inf 99.7%

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

   if -2.55e17 < z < -6.5000000000000004e-198 or 1.50000000000000008e-292 < z < 3.3e6

   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 y around inf 62.6%

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

   6. Taylor expanded in x around 0 63.1%

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

   if -6.5000000000000004e-198 < z < 1.50000000000000008e-292

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 67.7%

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

      1. *-lft-identity 67.7%

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

      2. *-commutative 67.7%

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

      3. +-commutative 67.7%

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

      4. *-commutative 67.7%

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

      5. fma-define 67.7%

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

      6. associate-*r* 67.7%

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

      7. fma-define 67.7%

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

      8. distribute-lft-in 67.7%

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

      9. neg-mul-1 67.7%

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

      10. distribute-lft-neg-in 67.7%

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

      11. metadata-eval 67.7%

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

      12. metadata-eval 67.7%

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

      13. distribute-rgt-in 67.7%

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

      14. +-commutative 67.7%

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

      15. sub-neg 67.7%

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

      16. distribute-rgt-in 67.7%

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

      17. sub-neg 67.7%

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

      18. distribute-rgt-in 67.7%

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

      19. metadata-eval 67.7%

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

      20. distribute-lft-neg-in 67.7%

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

      21. associate-+r+ 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   10. Simplified 67.7%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.55 \cdot 10^{+17}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-198}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-292}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3300000:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.026:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.026)
     t_0
     (if (<= z -1.1e-197)
       (* y 4.0)
       (if (<= z 3.3e-294) (* x -3.0) (if (<= z 0.65) (* y 4.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.026) {
		tmp = t_0;
	} else if (z <= -1.1e-197) {
		tmp = y * 4.0;
	} else if (z <= 3.3e-294) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.026d0)) then
        tmp = t_0
    else if (z <= (-1.1d-197)) then
        tmp = y * 4.0d0
    else if (z <= 3.3d-294) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.026) {
		tmp = t_0;
	} else if (z <= -1.1e-197) {
		tmp = y * 4.0;
	} else if (z <= 3.3e-294) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.026:
		tmp = t_0
	elif z <= -1.1e-197:
		tmp = y * 4.0
	elif z <= 3.3e-294:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	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 <= -0.026)
		tmp = t_0;
	elseif (z <= -1.1e-197)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.3e-294)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.026)
		tmp = t_0;
	elseif (z <= -1.1e-197)
		tmp = y * 4.0;
	elseif (z <= 3.3e-294)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.026], t$95$0, If[LessEqual[z, -1.1e-197], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.3e-294], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.0259999999999999988 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      2. pow3 99.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right)}^{3}} \]

      3. +-commutative 99.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x}}\right)}^{3} \]

      4. associate-*l* 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x}\right)}^{3} \]

      5. fma-define 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}\right)}^{3} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}\right)}^{3}} \]

   7. Taylor expanded in z around inf 99.4%

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

   if -0.0259999999999999988 < z < -1.1e-197 or 3.3e-294 < z < 0.650000000000000022

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 97.2%

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

   6. Taylor expanded in x around 0 60.3%

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

      1. *-commutative 60.3%

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

   8. Simplified 60.3%

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

   if -1.1e-197 < z < 3.3e-294

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 67.7%

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

      1. *-lft-identity 67.7%

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

      2. *-commutative 67.7%

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

      3. +-commutative 67.7%

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

      4. *-commutative 67.7%

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

      5. fma-define 67.7%

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

      6. associate-*r* 67.7%

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

      7. fma-define 67.7%

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

      8. distribute-lft-in 67.7%

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

      9. neg-mul-1 67.7%

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

      10. distribute-lft-neg-in 67.7%

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

      11. metadata-eval 67.7%

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

      12. metadata-eval 67.7%

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

      13. distribute-rgt-in 67.7%

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

      14. +-commutative 67.7%

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

      15. sub-neg 67.7%

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

      16. distribute-rgt-in 67.7%

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

      17. sub-neg 67.7%

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

      18. distribute-rgt-in 67.7%

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

      19. metadata-eval 67.7%

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

      20. distribute-lft-neg-in 67.7%

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

      21. associate-+r+ 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   10. Simplified 67.7%

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

4. Final simplification 83.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.026:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-197}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.3 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-192}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.66)
     t_0
     (if (<= z -6.2e-192)
       (* y 4.0)
       (if (<= z 4.4e-295) (* x -3.0) (if (<= z 3.5e+15) (* y 4.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -6.2e-192) {
		tmp = y * 4.0;
	} else if (z <= 4.4e-295) {
		tmp = x * -3.0;
	} else if (z <= 3.5e+15) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.66d0)) then
        tmp = t_0
    else if (z <= (-6.2d-192)) then
        tmp = y * 4.0d0
    else if (z <= 4.4d-295) then
        tmp = x * (-3.0d0)
    else if (z <= 3.5d+15) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.66) {
		tmp = t_0;
	} else if (z <= -6.2e-192) {
		tmp = y * 4.0;
	} else if (z <= 4.4e-295) {
		tmp = x * -3.0;
	} else if (z <= 3.5e+15) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.66:
		tmp = t_0
	elif z <= -6.2e-192:
		tmp = y * 4.0
	elif z <= 4.4e-295:
		tmp = x * -3.0
	elif z <= 3.5e+15:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -6.2e-192)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.4e-295)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.5e+15)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.66)
		tmp = t_0;
	elseif (z <= -6.2e-192)
		tmp = y * 4.0;
	elseif (z <= 4.4e-295)
		tmp = x * -3.0;
	elseif (z <= 3.5e+15)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.66], t$95$0, If[LessEqual[z, -6.2e-192], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.4e-295], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.5e+15], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.660000000000000031 or 3.5e15 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      2. pow3 99.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right)}^{3}} \]

      3. +-commutative 99.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x}}\right)}^{3} \]

      4. associate-*l* 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x}\right)}^{3} \]

      5. fma-define 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}\right)}^{3} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}\right)}^{3}} \]

   7. Taylor expanded in z around inf 99.4%

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

   8. Taylor expanded in y around inf 59.7%

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

   if -0.660000000000000031 < z < -6.2000000000000001e-192 or 4.4000000000000004e-295 < z < 3.5e15

   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 96.0%

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

   6. Taylor expanded in x around 0 59.7%

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

      1. *-commutative 59.7%

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

   8. Simplified 59.7%

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

   if -6.2000000000000001e-192 < z < 4.4000000000000004e-295

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 67.7%

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

      1. *-lft-identity 67.7%

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

      2. *-commutative 67.7%

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

      3. +-commutative 67.7%

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

      4. *-commutative 67.7%

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

      5. fma-define 67.7%

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

      6. associate-*r* 67.7%

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

      7. fma-define 67.7%

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

      8. distribute-lft-in 67.7%

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

      9. neg-mul-1 67.7%

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

      10. distribute-lft-neg-in 67.7%

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

      11. metadata-eval 67.7%

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

      12. metadata-eval 67.7%

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

      13. distribute-rgt-in 67.7%

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

      14. +-commutative 67.7%

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

      15. sub-neg 67.7%

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

      16. distribute-rgt-in 67.7%

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

      17. sub-neg 67.7%

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

      18. distribute-rgt-in 67.7%

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

      19. metadata-eval 67.7%

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

      20. distribute-lft-neg-in 67.7%

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

      21. associate-+r+ 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   10. Simplified 67.7%

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

4. Final simplification 60.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.66:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-192}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.62:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.62)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.55) (+ x (* (- y x) 4.0)) (+ x (* (- y x) (* z -6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.62) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.55) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + ((y - x) * (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 (z <= (-0.62d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.55d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x + ((y - x) * (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.62) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.55) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + ((y - x) * (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.62:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.55:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x + ((y - x) * (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.62)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.55)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x + Float64(Float64(y - x) * Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.62)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.55)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x + ((y - x) * (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.62], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.55], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.619999999999999996

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. add-cube-cbrt 99.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      2. pow3 99.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right)}^{3}} \]

      3. +-commutative 99.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x}}\right)}^{3} \]

      4. associate-*l* 99.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x}\right)}^{3} \]

      5. fma-define 99.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}\right)}^{3} \]

   6. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}\right)}^{3}} \]

   7. Taylor expanded in z around inf 99.1%

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

   if -0.619999999999999996 < z < 0.55000000000000004

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 97.8%

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

   if 0.55000000000000004 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. *-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*l* 99.8%

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

      4. *-commutative 99.8%

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

   7. Simplified 99.8%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.62:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.56) (not (<= z 0.56)))
   (* -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 <= 0.56)) {
		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 <= 0.56d0))) 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 <= 0.56)) {
		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 <= 0.56):
		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 <= 0.56))
		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 <= 0.56)))
		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, 0.56]], $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 0.56000000000000005 < 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. Step-by-step derivation

      1. add-cube-cbrt 99.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

      2. pow3 99.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right)}^{3}} \]

      3. +-commutative 99.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x}}\right)}^{3} \]

      4. associate-*l* 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x}\right)}^{3} \]

      5. fma-define 98.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}\right)}^{3} \]

   6. Applied egg-rr 98.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}\right)}^{3}} \]

   7. Taylor expanded in z around inf 99.4%

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

   if -0.56000000000000005 < z < 0.56000000000000005

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 97.8%

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

4. Final simplification 98.7%

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

Alternative 8: 36.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+22} \lor \neg \left(x \leq 1.2 \cdot 10^{+189}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.5e+22) (not (<= x 1.2e+189))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.5e+22) || !(x <= 1.2e+189)) {
		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 <= (-9.5d+22)) .or. (.not. (x <= 1.2d+189))) 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 <= -9.5e+22) || !(x <= 1.2e+189)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.5e+22) or not (x <= 1.2e+189):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.5e+22) || !(x <= 1.2e+189))
		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 <= -9.5e+22) || ~((x <= 1.2e+189)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.5e+22], N[Not[LessEqual[x, 1.2e+189]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.49999999999999937e22 or 1.2e189 < x

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 84.4%

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

      1. *-lft-identity 84.4%

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

      2. *-commutative 84.4%

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

      3. +-commutative 84.4%

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

      4. *-commutative 84.4%

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

      5. fma-define 84.4%

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

      6. associate-*r* 84.4%

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

      7. fma-define 84.4%

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

      8. distribute-lft-in 84.4%

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

      9. neg-mul-1 84.4%

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

      10. distribute-lft-neg-in 84.4%

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

      11. metadata-eval 84.4%

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

      12. metadata-eval 84.4%

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

      13. distribute-rgt-in 84.4%

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

      14. +-commutative 84.4%

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

      15. sub-neg 84.4%

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

      16. distribute-rgt-in 84.4%

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

      17. sub-neg 84.4%

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

      18. distribute-rgt-in 84.4%

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

      19. metadata-eval 84.4%

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

      20. distribute-lft-neg-in 84.4%

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

      21. associate-+r+ 84.4%

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

   7. Simplified 84.4%

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

   8. Taylor expanded in z around 0 42.1%

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

      1. *-commutative 42.1%

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

   10. Simplified 42.1%

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

   if -9.49999999999999937e22 < x < 1.2e189

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 42.5%

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

   6. Taylor expanded in x around 0 32.1%

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

      1. *-commutative 32.1%

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

   8. Simplified 32.1%

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

4. Final simplification 35.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+22} \lor \neg \left(x \leq 1.2 \cdot 10^{+189}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Step-by-step derivation

   1. add-cube-cbrt 98.5%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right) \cdot \sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}} \]

   2. pow3 98.5%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)}\right)}^{3}} \]

   3. +-commutative 98.5%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + x}}\right)}^{3} \]

   4. associate-*l* 98.4%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + x}\right)}^{3} \]

   5. fma-define 98.4%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}}\right)}^{3} \]

6. Applied egg-rr 98.4%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\mathsf{fma}\left(y - x, 6 \cdot \left(0.6666666666666666 - z\right), x\right)}\right)}^{3}} \]
7. Step-by-step derivation

   1. rem-cube-cbrt 99.8%

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

   2. fma-undefine 99.8%

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

8. Applied egg-rr 99.8%

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

9. Final simplification 99.8%

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

Alternative 10: 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 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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. Final simplification 99.5%

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

Alternative 11: 26.3% 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 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around 0 44.7%

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

   1. *-lft-identity 44.7%

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

   2. *-commutative 44.7%

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

   3. +-commutative 44.7%

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

   4. *-commutative 44.7%

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

   5. fma-define 44.7%

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

   6. associate-*r* 44.7%

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

   7. fma-define 44.7%

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

   8. distribute-lft-in 44.7%

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

   9. neg-mul-1 44.7%

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

   10. distribute-lft-neg-in 44.7%

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

   11. metadata-eval 44.7%

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

   12. metadata-eval 44.7%

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

   13. distribute-rgt-in 44.7%

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

   14. +-commutative 44.7%

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

   15. sub-neg 44.7%

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

   16. distribute-rgt-in 44.7%

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

   17. sub-neg 44.7%

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

   18. distribute-rgt-in 44.7%

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

   19. metadata-eval 44.7%

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

   20. distribute-lft-neg-in 44.7%

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

   21. associate-+r+ 44.7%

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

7. Simplified 44.7%

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

8. Taylor expanded in z around 0 21.1%

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

   1. *-commutative 21.1%

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

10. Simplified 21.1%

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

Alternative 12: 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 99.5%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 y around inf 57.2%

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

6. Taylor expanded in x around inf 2.7%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024157 
(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))))