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

Percentage Accurate: 99.5% → 99.8%

Time: 13.6s

Alternatives: 15

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

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-def 99.8%

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

   4. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.25 \cdot 10^{+195}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+53}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -32:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-103}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+90}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -2.25e+195)
     t_0
     (if (<= z -1.9e+53)
       t_1
       (if (<= z -32.0)
         t_0
         (if (<= z -7.0)
           t_1
           (if (<= z -6e-294)
             (* x -3.0)
             (if (<= z 1.55e-103)
               (* y 4.0)
               (if (<= z 1.2e-72)
                 (* x -3.0)
                 (if (<= z 0.68)
                   (* y 4.0)
                   (if (<= z 4.2e+90) t_1 t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.25e+195) {
		tmp = t_0;
	} else if (z <= -1.9e+53) {
		tmp = t_1;
	} else if (z <= -32.0) {
		tmp = t_0;
	} else if (z <= -7.0) {
		tmp = t_1;
	} else if (z <= -6e-294) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-103) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 4.2e+90) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-2.25d+195)) then
        tmp = t_0
    else if (z <= (-1.9d+53)) then
        tmp = t_1
    else if (z <= (-32.0d0)) then
        tmp = t_0
    else if (z <= (-7.0d0)) then
        tmp = t_1
    else if (z <= (-6d-294)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.55d-103) then
        tmp = y * 4.0d0
    else if (z <= 1.2d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = y * 4.0d0
    else if (z <= 4.2d+90) then
        tmp = t_1
    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 t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.25e+195) {
		tmp = t_0;
	} else if (z <= -1.9e+53) {
		tmp = t_1;
	} else if (z <= -32.0) {
		tmp = t_0;
	} else if (z <= -7.0) {
		tmp = t_1;
	} else if (z <= -6e-294) {
		tmp = x * -3.0;
	} else if (z <= 1.55e-103) {
		tmp = y * 4.0;
	} else if (z <= 1.2e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 4.2e+90) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.25e+195:
		tmp = t_0
	elif z <= -1.9e+53:
		tmp = t_1
	elif z <= -32.0:
		tmp = t_0
	elif z <= -7.0:
		tmp = t_1
	elif z <= -6e-294:
		tmp = x * -3.0
	elif z <= 1.55e-103:
		tmp = y * 4.0
	elif z <= 1.2e-72:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	elif z <= 4.2e+90:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.25e+195)
		tmp = t_0;
	elseif (z <= -1.9e+53)
		tmp = t_1;
	elseif (z <= -32.0)
		tmp = t_0;
	elseif (z <= -7.0)
		tmp = t_1;
	elseif (z <= -6e-294)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.55e-103)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.2e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.2e+90)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.25e+195)
		tmp = t_0;
	elseif (z <= -1.9e+53)
		tmp = t_1;
	elseif (z <= -32.0)
		tmp = t_0;
	elseif (z <= -7.0)
		tmp = t_1;
	elseif (z <= -6e-294)
		tmp = x * -3.0;
	elseif (z <= 1.55e-103)
		tmp = y * 4.0;
	elseif (z <= 1.2e-72)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = y * 4.0;
	elseif (z <= 4.2e+90)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.25e+195], t$95$0, If[LessEqual[z, -1.9e+53], t$95$1, If[LessEqual[z, -32.0], t$95$0, If[LessEqual[z, -7.0], t$95$1, If[LessEqual[z, -6e-294], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.55e-103], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.2e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.2e+90], t$95$1, t$95$0]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.25000000000000005e195 or -1.89999999999999999e53 < z < -32 or 4.19999999999999961e90 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 68.0%

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

      1. sub-neg 68.0%

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

      2. distribute-rgt-in 68.0%

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

      3. metadata-eval 68.0%

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

      4. metadata-eval 68.0%

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

      5. neg-mul-1 68.0%

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

      6. associate-*r* 68.0%

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

      7. *-commutative 68.0%

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

      8. associate-+r+ 68.0%

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

      9. metadata-eval 68.0%

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

      10. metadata-eval 68.0%

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

      11. associate-*r* 68.0%

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

      12. metadata-eval 68.0%

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

      13. *-commutative 68.0%

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

   6. Simplified 68.0%

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

   7. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

   9. Simplified 66.9%

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

   if -2.25000000000000005e195 < z < -1.89999999999999999e53 or -32 < z < -7 or 0.680000000000000049 < z < 4.19999999999999961e90

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 97.7%

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

   5. Taylor expanded in z around inf 97.7%

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

   6. Taylor expanded in y around inf 69.4%

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

   if -7 < z < -5.9999999999999998e-294 or 1.5500000000000001e-103 < z < 1.2e-72

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 64.4%

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

      1. sub-neg 64.4%

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

      2. distribute-rgt-in 64.4%

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

      3. metadata-eval 64.4%

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

      4. metadata-eval 64.4%

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

      5. neg-mul-1 64.4%

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

      6. associate-*r* 64.4%

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

      7. *-commutative 64.4%

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

      8. associate-+r+ 64.4%

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

      9. metadata-eval 64.4%

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

      10. metadata-eval 64.4%

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

      11. associate-*r* 64.4%

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

      12. metadata-eval 64.4%

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

      13. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 63.2%

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

      1. *-commutative 63.2%

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

   9. Simplified 63.2%

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

   if -5.9999999999999998e-294 < z < 1.5500000000000001e-103 or 1.2e-72 < z < 0.680000000000000049

   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. Step-by-step derivation

      1. add-cbrt-cube 47.0%

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

      2. pow3 46.9%

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

      3. +-commutative 46.9%

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

      4. associate-*l* 47.0%

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

      5. fma-udef 47.0%

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

   5. Applied egg-rr 47.0%

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

   6. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. *-commutative 66.3%

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

   11. Simplified 66.3%

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

4. Final simplification 66.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.25 \cdot 10^{+195}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+53}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -32:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.55 \cdot 10^{-103}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.2 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+90}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(6 \cdot z\right)\\ t_1 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.6 \cdot 10^{+193}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+51}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -820:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+86}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* 6.0 z))) (t_1 (* -6.0 (* y z))))
   (if (<= z -4.6e+193)
     t_0
     (if (<= z -2.7e+51)
       t_1
       (if (<= z -820.0)
         t_0
         (if (<= z -3.5)
           t_1
           (if (<= z -2.8e-294)
             (* x -3.0)
             (if (<= z 2.35e-104)
               (* y 4.0)
               (if (<= z 3e-73)
                 (* x -3.0)
                 (if (<= z 0.68)
                   (* y 4.0)
                   (if (<= z 2.9e+86) t_1 (* 6.0 (* x z)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (6.0 * z);
	double t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -4.6e+193) {
		tmp = t_0;
	} else if (z <= -2.7e+51) {
		tmp = t_1;
	} else if (z <= -820.0) {
		tmp = t_0;
	} else if (z <= -3.5) {
		tmp = t_1;
	} else if (z <= -2.8e-294) {
		tmp = x * -3.0;
	} else if (z <= 2.35e-104) {
		tmp = y * 4.0;
	} else if (z <= 3e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 2.9e+86) {
		tmp = t_1;
	} else {
		tmp = 6.0 * (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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * (6.0d0 * z)
    t_1 = (-6.0d0) * (y * z)
    if (z <= (-4.6d+193)) then
        tmp = t_0
    else if (z <= (-2.7d+51)) then
        tmp = t_1
    else if (z <= (-820.0d0)) then
        tmp = t_0
    else if (z <= (-3.5d0)) then
        tmp = t_1
    else if (z <= (-2.8d-294)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.35d-104) then
        tmp = y * 4.0d0
    else if (z <= 3d-73) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = y * 4.0d0
    else if (z <= 2.9d+86) then
        tmp = t_1
    else
        tmp = 6.0d0 * (x * z)
    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 t_1 = -6.0 * (y * z);
	double tmp;
	if (z <= -4.6e+193) {
		tmp = t_0;
	} else if (z <= -2.7e+51) {
		tmp = t_1;
	} else if (z <= -820.0) {
		tmp = t_0;
	} else if (z <= -3.5) {
		tmp = t_1;
	} else if (z <= -2.8e-294) {
		tmp = x * -3.0;
	} else if (z <= 2.35e-104) {
		tmp = y * 4.0;
	} else if (z <= 3e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 2.9e+86) {
		tmp = t_1;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (6.0 * z)
	t_1 = -6.0 * (y * z)
	tmp = 0
	if z <= -4.6e+193:
		tmp = t_0
	elif z <= -2.7e+51:
		tmp = t_1
	elif z <= -820.0:
		tmp = t_0
	elif z <= -3.5:
		tmp = t_1
	elif z <= -2.8e-294:
		tmp = x * -3.0
	elif z <= 2.35e-104:
		tmp = y * 4.0
	elif z <= 3e-73:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	elif z <= 2.9e+86:
		tmp = t_1
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(6.0 * z))
	t_1 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -4.6e+193)
		tmp = t_0;
	elseif (z <= -2.7e+51)
		tmp = t_1;
	elseif (z <= -820.0)
		tmp = t_0;
	elseif (z <= -3.5)
		tmp = t_1;
	elseif (z <= -2.8e-294)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.35e-104)
		tmp = Float64(y * 4.0);
	elseif (z <= 3e-73)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.9e+86)
		tmp = t_1;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (6.0 * z);
	t_1 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -4.6e+193)
		tmp = t_0;
	elseif (z <= -2.7e+51)
		tmp = t_1;
	elseif (z <= -820.0)
		tmp = t_0;
	elseif (z <= -3.5)
		tmp = t_1;
	elseif (z <= -2.8e-294)
		tmp = x * -3.0;
	elseif (z <= 2.35e-104)
		tmp = y * 4.0;
	elseif (z <= 3e-73)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = y * 4.0;
	elseif (z <= 2.9e+86)
		tmp = t_1;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.6e+193], t$95$0, If[LessEqual[z, -2.7e+51], t$95$1, If[LessEqual[z, -820.0], t$95$0, If[LessEqual[z, -3.5], t$95$1, If[LessEqual[z, -2.8e-294], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.35e-104], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3e-73], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.9e+86], t$95$1, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.60000000000000026e193 or -2.69999999999999992e51 < z < -820

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 70.3%

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

      1. sub-neg 70.3%

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

      2. distribute-rgt-in 70.2%

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

      3. metadata-eval 70.2%

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

      4. metadata-eval 70.2%

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

      5. neg-mul-1 70.2%

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

      6. associate-*r* 70.2%

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

      7. *-commutative 70.2%

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

      8. associate-+r+ 70.2%

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

      9. metadata-eval 70.2%

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

      10. metadata-eval 70.2%

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

      11. associate-*r* 70.2%

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

      12. metadata-eval 70.2%

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

      13. *-commutative 70.2%

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

   6. Simplified 70.2%

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

   7. Taylor expanded in z around inf 66.9%

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

   if -4.60000000000000026e193 < z < -2.69999999999999992e51 or -820 < z < -3.5 or 0.680000000000000049 < z < 2.8999999999999999e86

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 97.7%

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

   5. Taylor expanded in z around inf 97.7%

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

   6. Taylor expanded in y around inf 69.4%

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

   if -3.5 < z < -2.79999999999999991e-294 or 2.35e-104 < z < 3e-73

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 64.4%

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

      1. sub-neg 64.4%

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

      2. distribute-rgt-in 64.4%

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

      3. metadata-eval 64.4%

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

      4. metadata-eval 64.4%

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

      5. neg-mul-1 64.4%

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

      6. associate-*r* 64.4%

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

      7. *-commutative 64.4%

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

      8. associate-+r+ 64.4%

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

      9. metadata-eval 64.4%

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

      10. metadata-eval 64.4%

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

      11. associate-*r* 64.4%

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

      12. metadata-eval 64.4%

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

      13. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 63.2%

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

      1. *-commutative 63.2%

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

   9. Simplified 63.2%

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

   if -2.79999999999999991e-294 < z < 2.35e-104 or 3e-73 < z < 0.680000000000000049

   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. Step-by-step derivation

      1. add-cbrt-cube 47.0%

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

      2. pow3 46.9%

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

      3. +-commutative 46.9%

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

      4. associate-*l* 47.0%

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

      5. fma-udef 47.0%

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

   5. Applied egg-rr 47.0%

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

   6. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. *-commutative 66.3%

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

   11. Simplified 66.3%

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

   if 2.8999999999999999e86 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 66.9%

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

      1. sub-neg 66.9%

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

      2. distribute-rgt-in 66.9%

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

      3. metadata-eval 66.9%

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

      4. metadata-eval 66.9%

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

      5. neg-mul-1 66.9%

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

      6. associate-*r* 66.9%

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

      7. *-commutative 66.9%

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

      8. associate-+r+ 66.9%

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

      9. metadata-eval 66.9%

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

      10. metadata-eval 66.9%

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

      11. associate-*r* 66.9%

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

      12. metadata-eval 66.9%

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

      13. *-commutative 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

   9. Simplified 66.9%

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

4. Final simplification 66.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.6 \cdot 10^{+193}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{+51}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -820:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -3.5:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-294}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.35 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{+86}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 50.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.9 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -64:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-100}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+86}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.9e+52)
     (* y (* z -6.0))
     (if (<= z -64.0)
       (* x (* 6.0 z))
       (if (<= z -1.3)
         t_0
         (if (<= z -7.6e-295)
           (* x -3.0)
           (if (<= z 3.65e-100)
             (* y 4.0)
             (if (<= z 6.5e-73)
               (* x -3.0)
               (if (<= z 0.68)
                 (* y 4.0)
                 (if (<= z 8e+86) t_0 (* 6.0 (* x z))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.9e+52) {
		tmp = y * (z * -6.0);
	} else if (z <= -64.0) {
		tmp = x * (6.0 * z);
	} else if (z <= -1.3) {
		tmp = t_0;
	} else if (z <= -7.6e-295) {
		tmp = x * -3.0;
	} else if (z <= 3.65e-100) {
		tmp = y * 4.0;
	} else if (z <= 6.5e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 8e+86) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (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) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-1.9d+52)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-64.0d0)) then
        tmp = x * (6.0d0 * z)
    else if (z <= (-1.3d0)) then
        tmp = t_0
    else if (z <= (-7.6d-295)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.65d-100) then
        tmp = y * 4.0d0
    else if (z <= 6.5d-73) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) then
        tmp = y * 4.0d0
    else if (z <= 8d+86) then
        tmp = t_0
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.9e+52) {
		tmp = y * (z * -6.0);
	} else if (z <= -64.0) {
		tmp = x * (6.0 * z);
	} else if (z <= -1.3) {
		tmp = t_0;
	} else if (z <= -7.6e-295) {
		tmp = x * -3.0;
	} else if (z <= 3.65e-100) {
		tmp = y * 4.0;
	} else if (z <= 6.5e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		tmp = y * 4.0;
	} else if (z <= 8e+86) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.9e+52:
		tmp = y * (z * -6.0)
	elif z <= -64.0:
		tmp = x * (6.0 * z)
	elif z <= -1.3:
		tmp = t_0
	elif z <= -7.6e-295:
		tmp = x * -3.0
	elif z <= 3.65e-100:
		tmp = y * 4.0
	elif z <= 6.5e-73:
		tmp = x * -3.0
	elif z <= 0.68:
		tmp = y * 4.0
	elif z <= 8e+86:
		tmp = t_0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.9e+52)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -64.0)
		tmp = Float64(x * Float64(6.0 * z));
	elseif (z <= -1.3)
		tmp = t_0;
	elseif (z <= -7.6e-295)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.65e-100)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.5e-73)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		tmp = Float64(y * 4.0);
	elseif (z <= 8e+86)
		tmp = t_0;
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.9e+52)
		tmp = y * (z * -6.0);
	elseif (z <= -64.0)
		tmp = x * (6.0 * z);
	elseif (z <= -1.3)
		tmp = t_0;
	elseif (z <= -7.6e-295)
		tmp = x * -3.0;
	elseif (z <= 3.65e-100)
		tmp = y * 4.0;
	elseif (z <= 6.5e-73)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		tmp = y * 4.0;
	elseif (z <= 8e+86)
		tmp = t_0;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.9e+52], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -64.0], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.3], t$95$0, If[LessEqual[z, -7.6e-295], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.65e-100], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.5e-73], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8e+86], t$95$0, N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.9e52

   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. Taylor expanded in z around inf 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   6. Taylor expanded in y around inf 59.2%

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

      1. *-commutative 59.2%

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

      2. associate-*l* 61.1%

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

   8. Simplified 61.1%

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

   if -1.9e52 < z < -64

   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. Taylor expanded in x around inf 82.3%

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

      1. sub-neg 82.3%

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

      2. distribute-rgt-in 82.0%

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

      3. metadata-eval 82.0%

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

      4. metadata-eval 82.0%

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

      5. neg-mul-1 82.0%

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

      6. associate-*r* 82.0%

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

      7. *-commutative 82.0%

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

      8. associate-+r+ 82.0%

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

      9. metadata-eval 82.0%

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

      10. metadata-eval 82.0%

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

      11. associate-*r* 82.0%

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

      12. metadata-eval 82.0%

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

      13. *-commutative 82.0%

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

   6. Simplified 82.0%

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

   7. Taylor expanded in z around inf 70.7%

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

   if -64 < z < -1.30000000000000004 or 0.680000000000000049 < z < 8.0000000000000001e86

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around inf 92.6%

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

   5. Taylor expanded in z around inf 92.6%

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

   6. Taylor expanded in y around inf 69.9%

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

   if -1.30000000000000004 < z < -7.60000000000000037e-295 or 3.6499999999999998e-100 < z < 6.4999999999999999e-73

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 64.4%

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

      1. sub-neg 64.4%

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

      2. distribute-rgt-in 64.4%

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

      3. metadata-eval 64.4%

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

      4. metadata-eval 64.4%

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

      5. neg-mul-1 64.4%

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

      6. associate-*r* 64.4%

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

      7. *-commutative 64.4%

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

      8. associate-+r+ 64.4%

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

      9. metadata-eval 64.4%

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

      10. metadata-eval 64.4%

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

      11. associate-*r* 64.4%

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

      12. metadata-eval 64.4%

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

      13. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 63.2%

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

      1. *-commutative 63.2%

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

   9. Simplified 63.2%

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

   if -7.60000000000000037e-295 < z < 3.6499999999999998e-100 or 6.4999999999999999e-73 < z < 0.680000000000000049

   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. Step-by-step derivation

      1. add-cbrt-cube 47.0%

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

      2. pow3 46.9%

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

      3. +-commutative 46.9%

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

      4. associate-*l* 47.0%

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

      5. fma-udef 47.0%

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

   5. Applied egg-rr 47.0%

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

   6. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. *-commutative 66.3%

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

   11. Simplified 66.3%

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

   if 8.0000000000000001e86 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 66.9%

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

      1. sub-neg 66.9%

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

      2. distribute-rgt-in 66.9%

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

      3. metadata-eval 66.9%

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

      4. metadata-eval 66.9%

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

      5. neg-mul-1 66.9%

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

      6. associate-*r* 66.9%

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

      7. *-commutative 66.9%

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

      8. associate-+r+ 66.9%

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

      9. metadata-eval 66.9%

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

      10. metadata-eval 66.9%

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

      11. associate-*r* 66.9%

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

      12. metadata-eval 66.9%

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

      13. *-commutative 66.9%

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

   6. Simplified 66.9%

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

   7. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

   9. Simplified 66.9%

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

4. Final simplification 64.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.9 \cdot 10^{+52}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -64:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.65 \cdot 10^{-100}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8 \cdot 10^{+86}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 5: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.12:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.9 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.12)
     t_0
     (if (<= z -7.6e-295)
       (* x -3.0)
       (if (<= z 8.9e-104)
         (* y 4.0)
         (if (<= z 1.05e-73) (* x -3.0) (if (<= z 0.62) (* 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 <= -0.12) {
		tmp = t_0;
	} else if (z <= -7.6e-295) {
		tmp = x * -3.0;
	} else if (z <= 8.9e-104) {
		tmp = y * 4.0;
	} else if (z <= 1.05e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		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 <= (-0.12d0)) then
        tmp = t_0
    else if (z <= (-7.6d-295)) then
        tmp = x * (-3.0d0)
    else if (z <= 8.9d-104) then
        tmp = y * 4.0d0
    else if (z <= 1.05d-73) then
        tmp = x * (-3.0d0)
    else if (z <= 0.62d0) 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 <= -0.12) {
		tmp = t_0;
	} else if (z <= -7.6e-295) {
		tmp = x * -3.0;
	} else if (z <= 8.9e-104) {
		tmp = y * 4.0;
	} else if (z <= 1.05e-73) {
		tmp = x * -3.0;
	} else if (z <= 0.62) {
		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 <= -0.12:
		tmp = t_0
	elif z <= -7.6e-295:
		tmp = x * -3.0
	elif z <= 8.9e-104:
		tmp = y * 4.0
	elif z <= 1.05e-73:
		tmp = x * -3.0
	elif z <= 0.62:
		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 <= -0.12)
		tmp = t_0;
	elseif (z <= -7.6e-295)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.9e-104)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.05e-73)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.62)
		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 <= -0.12)
		tmp = t_0;
	elseif (z <= -7.6e-295)
		tmp = x * -3.0;
	elseif (z <= 8.9e-104)
		tmp = y * 4.0;
	elseif (z <= 1.05e-73)
		tmp = x * -3.0;
	elseif (z <= 0.62)
		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, -0.12], t$95$0, If[LessEqual[z, -7.6e-295], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.9e-104], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.05e-73], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.12 or 0.619999999999999996 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 98.2%

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

   5. Taylor expanded in z around inf 98.2%

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

   if -0.12 < z < -7.60000000000000037e-295 or 8.9000000000000006e-104 < z < 1.0499999999999999e-73

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 64.4%

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

      1. sub-neg 64.4%

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

      2. distribute-rgt-in 64.4%

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

      3. metadata-eval 64.4%

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

      4. metadata-eval 64.4%

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

      5. neg-mul-1 64.4%

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

      6. associate-*r* 64.4%

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

      7. *-commutative 64.4%

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

      8. associate-+r+ 64.4%

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

      9. metadata-eval 64.4%

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

      10. metadata-eval 64.4%

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

      11. associate-*r* 64.4%

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

      12. metadata-eval 64.4%

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

      13. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 63.2%

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

      1. *-commutative 63.2%

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

   9. Simplified 63.2%

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

   if -7.60000000000000037e-295 < z < 8.9000000000000006e-104 or 1.0499999999999999e-73 < z < 0.619999999999999996

   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. Step-by-step derivation

      1. add-cbrt-cube 47.0%

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

      2. pow3 46.9%

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

      3. +-commutative 46.9%

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

      4. associate-*l* 47.0%

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

      5. fma-udef 47.0%

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

   5. Applied egg-rr 47.0%

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

   6. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. *-commutative 66.3%

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

   11. Simplified 66.3%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.12:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -7.6 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.9 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-73}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 6: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -420000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -420000000.0)
     t_0
     (if (<= z -2.7e-294)
       (* x (+ -3.0 (* 6.0 z)))
       (if (<= z 2.4e-104)
         (* y 4.0)
         (if (<= z 1.05e-72) (* x -3.0) (if (<= z 0.68) (* 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 <= -420000000.0) {
		tmp = t_0;
	} else if (z <= -2.7e-294) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 2.4e-104) {
		tmp = y * 4.0;
	} else if (z <= 1.05e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		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 <= (-420000000.0d0)) then
        tmp = t_0
    else if (z <= (-2.7d-294)) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else if (z <= 2.4d-104) then
        tmp = y * 4.0d0
    else if (z <= 1.05d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) 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 <= -420000000.0) {
		tmp = t_0;
	} else if (z <= -2.7e-294) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 2.4e-104) {
		tmp = y * 4.0;
	} else if (z <= 1.05e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		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 <= -420000000.0:
		tmp = t_0
	elif z <= -2.7e-294:
		tmp = x * (-3.0 + (6.0 * z))
	elif z <= 2.4e-104:
		tmp = y * 4.0
	elif z <= 1.05e-72:
		tmp = x * -3.0
	elif z <= 0.68:
		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 <= -420000000.0)
		tmp = t_0;
	elseif (z <= -2.7e-294)
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	elseif (z <= 2.4e-104)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.05e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		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 <= -420000000.0)
		tmp = t_0;
	elseif (z <= -2.7e-294)
		tmp = x * (-3.0 + (6.0 * z));
	elseif (z <= 2.4e-104)
		tmp = y * 4.0;
	elseif (z <= 1.05e-72)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		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, -420000000.0], t$95$0, If[LessEqual[z, -2.7e-294], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.4e-104], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.05e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.2e8 or 0.680000000000000049 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 99.5%

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

   5. Taylor expanded in z around inf 99.5%

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

   if -4.2e8 < z < -2.7000000000000001e-294

   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. Taylor expanded in x around inf 62.9%

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

      1. sub-neg 62.9%

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

      2. distribute-rgt-in 62.9%

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

      3. metadata-eval 62.9%

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

      4. metadata-eval 62.9%

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

      5. neg-mul-1 62.9%

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

      6. associate-*r* 62.9%

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

      7. *-commutative 62.9%

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

      8. associate-+r+ 62.9%

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

      9. metadata-eval 62.9%

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

      10. metadata-eval 62.9%

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

      11. associate-*r* 62.9%

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

      12. metadata-eval 62.9%

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

      13. *-commutative 62.9%

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

   6. Simplified 62.9%

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

   if -2.7000000000000001e-294 < z < 2.4000000000000001e-104 or 1.05e-72 < z < 0.680000000000000049

   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. Step-by-step derivation

      1. add-cbrt-cube 47.0%

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

      2. pow3 46.9%

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

      3. +-commutative 46.9%

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

      4. associate-*l* 47.0%

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

      5. fma-udef 47.0%

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

   5. Applied egg-rr 47.0%

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

   6. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. *-commutative 66.3%

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

   11. Simplified 66.3%

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

   if 2.4000000000000001e-104 < z < 1.05e-72

   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. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 78.3%

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

      1. sub-neg 78.3%

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

      2. distribute-rgt-in 78.3%

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

      3. metadata-eval 78.3%

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

      4. metadata-eval 78.3%

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

      5. neg-mul-1 78.3%

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

      6. associate-*r* 78.3%

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

      7. *-commutative 78.3%

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

      8. associate-+r+ 78.3%

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

      9. metadata-eval 78.3%

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

      10. metadata-eval 78.3%

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

      11. associate-*r* 78.3%

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

      12. metadata-eval 78.3%

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

      13. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

   9. Simplified 78.3%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -420000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-294}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -530000000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -530000000.0)
     t_0
     (if (<= z -1.9e-295)
       (* x (+ -3.0 (* 6.0 z)))
       (if (<= z 9.6e-104)
         (* y 4.0)
         (if (<= z 6.5e-72)
           (* x -3.0)
           (if (<= z 4.2e+15) (* y (+ 4.0 (* z -6.0))) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -530000000.0) {
		tmp = t_0;
	} else if (z <= -1.9e-295) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 9.6e-104) {
		tmp = y * 4.0;
	} else if (z <= 6.5e-72) {
		tmp = x * -3.0;
	} else if (z <= 4.2e+15) {
		tmp = y * (4.0 + (z * -6.0));
	} 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 <= (-530000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.9d-295)) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else if (z <= 9.6d-104) then
        tmp = y * 4.0d0
    else if (z <= 6.5d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 4.2d+15) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    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 <= -530000000.0) {
		tmp = t_0;
	} else if (z <= -1.9e-295) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 9.6e-104) {
		tmp = y * 4.0;
	} else if (z <= 6.5e-72) {
		tmp = x * -3.0;
	} else if (z <= 4.2e+15) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -530000000.0:
		tmp = t_0
	elif z <= -1.9e-295:
		tmp = x * (-3.0 + (6.0 * z))
	elif z <= 9.6e-104:
		tmp = y * 4.0
	elif z <= 6.5e-72:
		tmp = x * -3.0
	elif z <= 4.2e+15:
		tmp = y * (4.0 + (z * -6.0))
	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 <= -530000000.0)
		tmp = t_0;
	elseif (z <= -1.9e-295)
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	elseif (z <= 9.6e-104)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.5e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.2e+15)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	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 <= -530000000.0)
		tmp = t_0;
	elseif (z <= -1.9e-295)
		tmp = x * (-3.0 + (6.0 * z));
	elseif (z <= 9.6e-104)
		tmp = y * 4.0;
	elseif (z <= 6.5e-72)
		tmp = x * -3.0;
	elseif (z <= 4.2e+15)
		tmp = y * (4.0 + (z * -6.0));
	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, -530000000.0], t$95$0, If[LessEqual[z, -1.9e-295], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 9.6e-104], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.5e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.2e+15], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -5.3e8 or 4.2e15 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 99.7%

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

   5. Taylor expanded in z around inf 99.7%

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

   if -5.3e8 < z < -1.90000000000000009e-295

   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. Taylor expanded in x around inf 62.9%

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

      1. sub-neg 62.9%

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

      2. distribute-rgt-in 62.9%

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

      3. metadata-eval 62.9%

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

      4. metadata-eval 62.9%

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

      5. neg-mul-1 62.9%

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

      6. associate-*r* 62.9%

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

      7. *-commutative 62.9%

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

      8. associate-+r+ 62.9%

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

      9. metadata-eval 62.9%

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

      10. metadata-eval 62.9%

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

      11. associate-*r* 62.9%

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

      12. metadata-eval 62.9%

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

      13. *-commutative 62.9%

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

   6. Simplified 62.9%

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

   if -1.90000000000000009e-295 < z < 9.6000000000000003e-104

   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. Step-by-step derivation

      1. add-cbrt-cube 46.1%

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

      2. pow3 45.9%

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

      3. +-commutative 45.9%

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

      4. associate-*l* 46.1%

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

      5. fma-udef 46.1%

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

   5. Applied egg-rr 46.1%

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

   6. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in x around 0 66.2%

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

       1. *-commutative 66.2%

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

   11. Simplified 66.2%

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

   if 9.6000000000000003e-104 < z < 6.4999999999999997e-72

   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. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 78.3%

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

      1. sub-neg 78.3%

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

      2. distribute-rgt-in 78.3%

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

      3. metadata-eval 78.3%

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

      4. metadata-eval 78.3%

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

      5. neg-mul-1 78.3%

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

      6. associate-*r* 78.3%

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

      7. *-commutative 78.3%

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

      8. associate-+r+ 78.3%

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

      9. metadata-eval 78.3%

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

      10. metadata-eval 78.3%

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

      11. associate-*r* 78.3%

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

      12. metadata-eval 78.3%

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

      13. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

   9. Simplified 78.3%

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

   if 6.4999999999999997e-72 < z < 4.2e15

   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* 99.9%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-lft-in 99.9%

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

      7. distribute-rgt-neg-out 99.9%

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

      8. distribute-lft-neg-in 99.9%

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

      9. *-commutative 99.9%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 74.0%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 81.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -530000000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 9.6 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 8: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -420000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-103}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -420000000.0)
   (* z (* (- y x) -6.0))
   (if (<= z -1.55e-295)
     (* x (+ -3.0 (* 6.0 z)))
     (if (<= z 2.7e-103)
       (* y 4.0)
       (if (<= z 8.4e-72)
         (* x -3.0)
         (if (<= z 4.2e+15)
           (* y (+ 4.0 (* z -6.0)))
           (* -6.0 (* (- y x) z))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -420000000.0) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= -1.55e-295) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 2.7e-103) {
		tmp = y * 4.0;
	} else if (z <= 8.4e-72) {
		tmp = x * -3.0;
	} else if (z <= 4.2e+15) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = -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 <= (-420000000.0d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= (-1.55d-295)) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else if (z <= 2.7d-103) then
        tmp = y * 4.0d0
    else if (z <= 8.4d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 4.2d+15) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = (-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 <= -420000000.0) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= -1.55e-295) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 2.7e-103) {
		tmp = y * 4.0;
	} else if (z <= 8.4e-72) {
		tmp = x * -3.0;
	} else if (z <= 4.2e+15) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -420000000.0:
		tmp = z * ((y - x) * -6.0)
	elif z <= -1.55e-295:
		tmp = x * (-3.0 + (6.0 * z))
	elif z <= 2.7e-103:
		tmp = y * 4.0
	elif z <= 8.4e-72:
		tmp = x * -3.0
	elif z <= 4.2e+15:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -420000000.0)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= -1.55e-295)
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	elseif (z <= 2.7e-103)
		tmp = Float64(y * 4.0);
	elseif (z <= 8.4e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.2e+15)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = 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 <= -420000000.0)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= -1.55e-295)
		tmp = x * (-3.0 + (6.0 * z));
	elseif (z <= 2.7e-103)
		tmp = y * 4.0;
	elseif (z <= 8.4e-72)
		tmp = x * -3.0;
	elseif (z <= 4.2e+15)
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -420000000.0], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.55e-295], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.7e-103], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8.4e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.2e+15], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.2e8

   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. Taylor expanded in z around inf 99.6%

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

   5. Taylor expanded in z around inf 99.6%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*l* 99.8%

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

   7. Simplified 99.8%

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

   if -4.2e8 < z < -1.5500000000000001e-295

   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. Taylor expanded in x around inf 62.9%

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

      1. sub-neg 62.9%

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

      2. distribute-rgt-in 62.9%

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

      3. metadata-eval 62.9%

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

      4. metadata-eval 62.9%

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

      5. neg-mul-1 62.9%

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

      6. associate-*r* 62.9%

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

      7. *-commutative 62.9%

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

      8. associate-+r+ 62.9%

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

      9. metadata-eval 62.9%

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

      10. metadata-eval 62.9%

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

      11. associate-*r* 62.9%

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

      12. metadata-eval 62.9%

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

      13. *-commutative 62.9%

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

   6. Simplified 62.9%

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

   if -1.5500000000000001e-295 < z < 2.7000000000000001e-103

   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. Step-by-step derivation

      1. add-cbrt-cube 46.1%

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

      2. pow3 45.9%

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

      3. +-commutative 45.9%

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

      4. associate-*l* 46.1%

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

      5. fma-udef 46.1%

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

   5. Applied egg-rr 46.1%

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

   6. Taylor expanded in z around 0 99.8%

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

      1. *-commutative 99.8%

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

   8. Simplified 99.8%

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

   9. Taylor expanded in x around 0 66.2%

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

       1. *-commutative 66.2%

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

   11. Simplified 66.2%

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

   if 2.7000000000000001e-103 < z < 8.4e-72

   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. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in x around inf 78.3%

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

      1. sub-neg 78.3%

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

      2. distribute-rgt-in 78.3%

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

      3. metadata-eval 78.3%

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

      4. metadata-eval 78.3%

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

      5. neg-mul-1 78.3%

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

      6. associate-*r* 78.3%

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

      7. *-commutative 78.3%

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

      8. associate-+r+ 78.3%

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

      9. metadata-eval 78.3%

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

      10. metadata-eval 78.3%

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

      11. associate-*r* 78.3%

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

      12. metadata-eval 78.3%

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

      13. *-commutative 78.3%

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

   6. Simplified 78.3%

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

   7. Taylor expanded in z around 0 78.3%

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

      1. *-commutative 78.3%

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

   9. Simplified 78.3%

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

   if 8.4e-72 < z < 4.2e15

   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* 99.9%

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

      3. fma-def 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-lft-in 99.9%

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

      7. distribute-rgt-neg-out 99.9%

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

      8. distribute-lft-neg-in 99.9%

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

      9. *-commutative 99.9%

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

      10. fma-def 99.8%

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

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 74.0%

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

   if 4.2e15 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

4. Final simplification 81.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -420000000:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-295}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-103}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.4 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 9: 50.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.36:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.36)
     t_0
     (if (<= z -2.5e-295)
       (* x -3.0)
       (if (<= z 8e-101)
         (* y 4.0)
         (if (<= z 8.8e-72) (* x -3.0) (if (<= z 0.68) (* 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 <= -0.36) {
		tmp = t_0;
	} else if (z <= -2.5e-295) {
		tmp = x * -3.0;
	} else if (z <= 8e-101) {
		tmp = y * 4.0;
	} else if (z <= 8.8e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		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 <= (-0.36d0)) then
        tmp = t_0
    else if (z <= (-2.5d-295)) then
        tmp = x * (-3.0d0)
    else if (z <= 8d-101) then
        tmp = y * 4.0d0
    else if (z <= 8.8d-72) then
        tmp = x * (-3.0d0)
    else if (z <= 0.68d0) 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 <= -0.36) {
		tmp = t_0;
	} else if (z <= -2.5e-295) {
		tmp = x * -3.0;
	} else if (z <= 8e-101) {
		tmp = y * 4.0;
	} else if (z <= 8.8e-72) {
		tmp = x * -3.0;
	} else if (z <= 0.68) {
		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 <= -0.36:
		tmp = t_0
	elif z <= -2.5e-295:
		tmp = x * -3.0
	elif z <= 8e-101:
		tmp = y * 4.0
	elif z <= 8.8e-72:
		tmp = x * -3.0
	elif z <= 0.68:
		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 <= -0.36)
		tmp = t_0;
	elseif (z <= -2.5e-295)
		tmp = Float64(x * -3.0);
	elseif (z <= 8e-101)
		tmp = Float64(y * 4.0);
	elseif (z <= 8.8e-72)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.68)
		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 <= -0.36)
		tmp = t_0;
	elseif (z <= -2.5e-295)
		tmp = x * -3.0;
	elseif (z <= 8e-101)
		tmp = y * 4.0;
	elseif (z <= 8.8e-72)
		tmp = x * -3.0;
	elseif (z <= 0.68)
		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, -0.36], t$95$0, If[LessEqual[z, -2.5e-295], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8e-101], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 8.8e-72], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.35999999999999999 or 0.680000000000000049 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 98.2%

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

   5. Taylor expanded in z around inf 98.2%

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

   6. Taylor expanded in y around inf 49.3%

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

   if -0.35999999999999999 < z < -2.50000000000000004e-295 or 8.00000000000000041e-101 < z < 8.8000000000000001e-72

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 64.4%

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

      1. sub-neg 64.4%

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

      2. distribute-rgt-in 64.4%

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

      3. metadata-eval 64.4%

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

      4. metadata-eval 64.4%

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

      5. neg-mul-1 64.4%

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

      6. associate-*r* 64.4%

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

      7. *-commutative 64.4%

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

      8. associate-+r+ 64.4%

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

      9. metadata-eval 64.4%

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

      10. metadata-eval 64.4%

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

      11. associate-*r* 64.4%

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

      12. metadata-eval 64.4%

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

      13. *-commutative 64.4%

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

   6. Simplified 64.4%

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

   7. Taylor expanded in z around 0 63.2%

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

      1. *-commutative 63.2%

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

   9. Simplified 63.2%

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

   if -2.50000000000000004e-295 < z < 8.00000000000000041e-101 or 8.8000000000000001e-72 < z < 0.680000000000000049

   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. Step-by-step derivation

      1. add-cbrt-cube 47.0%

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

      2. pow3 46.9%

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

      3. +-commutative 46.9%

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

      4. associate-*l* 47.0%

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

      5. fma-udef 47.0%

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

   5. Applied egg-rr 47.0%

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

   6. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in x around 0 66.3%

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

       1. *-commutative 66.3%

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

   11. Simplified 66.3%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.36:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-295}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8 \cdot 10^{-101}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-72}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 10: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* z (* (- y x) -6.0))
   (if (<= z 0.5) (+ x (* (- y x) 4.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = -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 <= (-0.6d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.5d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = (-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 <= -0.6) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.5:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.5)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = 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 <= -0.6)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.5)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   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. Taylor expanded in z around inf 97.1%

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

   5. Taylor expanded in z around inf 97.1%

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

      1. associate-*r* 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l* 97.2%

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

   7. Simplified 97.2%

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

   if -0.599999999999999978 < 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. Taylor expanded in z around 0 98.5%

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

   if 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 99.4%

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

   5. Taylor expanded in z around inf 99.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 11: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* z (* (- y x) -6.0))
   (if (<= z 0.55) (+ (* y 4.0) (* x -3.0)) (* -6.0 (* (- y x) z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.55) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = -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 <= (-0.55d0)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if (z <= 0.55d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = (-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 <= -0.55) {
		tmp = z * ((y - x) * -6.0);
	} else if (z <= 0.55) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = -6.0 * ((y - x) * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = z * ((y - x) * -6.0)
	elif z <= 0.55:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = -6.0 * ((y - x) * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif (z <= 0.55)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = 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 <= -0.55)
		tmp = z * ((y - x) * -6.0);
	elseif (z <= 0.55)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = -6.0 * ((y - x) * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.55], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   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. Taylor expanded in z around inf 97.1%

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

   5. Taylor expanded in z around inf 97.1%

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

      1. associate-*r* 97.1%

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

      2. *-commutative 97.1%

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

      3. associate-*l* 97.2%

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

   7. Simplified 97.2%

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

   if -0.55000000000000004 < z < 0.55000000000000004

   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. Step-by-step derivation

      1. add-cbrt-cube 42.6%

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

      2. pow3 42.5%

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

      3. +-commutative 42.5%

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

      4. associate-*l* 42.6%

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

      5. fma-udef 42.7%

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

   5. Applied egg-rr 42.7%

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

   6. Taylor expanded in z around 0 98.5%

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

      1. *-commutative 98.5%

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

   8. Simplified 98.5%

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

   9. Taylor expanded in x around 0 98.6%

      \[\leadsto \color{blue}{-3 \cdot x + 4 \cdot y} \]

   if 0.55000000000000004 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in z around inf 99.4%

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

   5. Taylor expanded in z around inf 99.4%

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

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 12: 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. Final simplification 99.6%

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

Alternative 13: 37.9% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+19}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+31}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e+19) (* y 4.0) (if (<= y 3.4e+31) (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e+19) {
		tmp = y * 4.0;
	} else if (y <= 3.4e+31) {
		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 (y <= (-4.5d+19)) then
        tmp = y * 4.0d0
    else if (y <= 3.4d+31) 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 (y <= -4.5e+19) {
		tmp = y * 4.0;
	} else if (y <= 3.4e+31) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e+19:
		tmp = y * 4.0
	elif y <= 3.4e+31:
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e+19)
		tmp = Float64(y * 4.0);
	elseif (y <= 3.4e+31)
		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 (y <= -4.5e+19)
		tmp = y * 4.0;
	elseif (y <= 3.4e+31)
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e+19], N[(y * 4.0), $MachinePrecision], If[LessEqual[y, 3.4e+31], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5e19 or 3.3999999999999998e31 < 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. Step-by-step derivation

      1. add-cbrt-cube 48.5%

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

      2. pow3 48.4%

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

      3. +-commutative 48.4%

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

      4. associate-*l* 48.5%

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

      5. fma-udef 48.5%

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

   5. Applied egg-rr 48.5%

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

   6. Taylor expanded in z around 0 56.4%

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

      1. *-commutative 56.4%

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

   8. Simplified 56.4%

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

   9. Taylor expanded in x around 0 44.7%

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

       1. *-commutative 44.7%

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

   11. Simplified 44.7%

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

   if -4.5e19 < y < 3.3999999999999998e31

   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. Taylor expanded in x around inf 74.9%

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

      1. sub-neg 74.9%

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

      2. distribute-rgt-in 74.9%

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

      3. metadata-eval 74.9%

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

      4. metadata-eval 74.9%

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

      5. neg-mul-1 74.9%

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

      6. associate-*r* 74.9%

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

      7. *-commutative 74.9%

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

      8. associate-+r+ 74.9%

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

      9. metadata-eval 74.9%

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

      10. metadata-eval 74.9%

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

      11. associate-*r* 74.9%

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

      12. metadata-eval 74.9%

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

      13. *-commutative 74.9%

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

   6. Simplified 74.9%

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

   7. Taylor expanded in z around 0 41.3%

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

      1. *-commutative 41.3%

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

   9. Simplified 41.3%

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

4. Final simplification 42.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{+19}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 3.4 \cdot 10^{+31}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]

Alternative 14: 26.4% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in x around inf 54.2%

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

   1. sub-neg 54.2%

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

   2. distribute-rgt-in 54.2%

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

   3. metadata-eval 54.2%

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

   4. metadata-eval 54.2%

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

   5. neg-mul-1 54.2%

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

   6. associate-*r* 54.2%

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

   7. *-commutative 54.2%

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

   8. associate-+r+ 54.2%

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

   9. metadata-eval 54.2%

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

   10. metadata-eval 54.2%

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

   11. associate-*r* 54.2%

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

   12. metadata-eval 54.2%

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

   13. *-commutative 54.2%

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

6. Simplified 54.2%

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

7. Taylor expanded in z around 0 29.0%

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

   1. *-commutative 29.0%

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

9. Simplified 29.0%

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

10. Final simplification 29.0%

    \[\leadsto x \cdot -3 \]

Alternative 15: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in z around inf 46.9%

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

5. Taylor expanded in z around 0 2.5%

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

6. Final simplification 2.5%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023279 
(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))))