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

Percentage Accurate: 99.5% → 99.7%

Time: 13.6s

Alternatives: 16

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -5.8 \cdot 10^{+213}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-86}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+106} \lor \neg \left(z \leq 6.2 \cdot 10^{+204}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -5.8e+213)
     t_0
     (if (<= z -0.5)
       t_1
       (if (<= z -8e-68)
         (* x -3.0)
         (if (<= z -2.25e-268)
           (* y 4.0)
           (if (<= z 7.2e-86)
             (* x -3.0)
             (if (<= z 1.02e-53)
               (* y 4.0)
               (if (<= z 0.5)
                 (* x -3.0)
                 (if (or (<= z 2.6e+106) (not (<= z 6.2e+204)))
                   t_1
                   t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -5.8e+213) {
		tmp = t_0;
	} else if (z <= -0.5) {
		tmp = t_1;
	} else if (z <= -8e-68) {
		tmp = x * -3.0;
	} else if (z <= -2.25e-268) {
		tmp = y * 4.0;
	} else if (z <= 7.2e-86) {
		tmp = x * -3.0;
	} else if (z <= 1.02e-53) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 2.6e+106) || !(z <= 6.2e+204)) {
		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) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-5.8d+213)) then
        tmp = t_0
    else if (z <= (-0.5d0)) then
        tmp = t_1
    else if (z <= (-8d-68)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.25d-268)) then
        tmp = y * 4.0d0
    else if (z <= 7.2d-86) then
        tmp = x * (-3.0d0)
    else if (z <= 1.02d-53) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 2.6d+106) .or. (.not. (z <= 6.2d+204))) 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 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -5.8e+213) {
		tmp = t_0;
	} else if (z <= -0.5) {
		tmp = t_1;
	} else if (z <= -8e-68) {
		tmp = x * -3.0;
	} else if (z <= -2.25e-268) {
		tmp = y * 4.0;
	} else if (z <= 7.2e-86) {
		tmp = x * -3.0;
	} else if (z <= 1.02e-53) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 2.6e+106) || !(z <= 6.2e+204)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -5.8e+213:
		tmp = t_0
	elif z <= -0.5:
		tmp = t_1
	elif z <= -8e-68:
		tmp = x * -3.0
	elif z <= -2.25e-268:
		tmp = y * 4.0
	elif z <= 7.2e-86:
		tmp = x * -3.0
	elif z <= 1.02e-53:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif (z <= 2.6e+106) or not (z <= 6.2e+204):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -5.8e+213)
		tmp = t_0;
	elseif (z <= -0.5)
		tmp = t_1;
	elseif (z <= -8e-68)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.25e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.2e-86)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.02e-53)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif ((z <= 2.6e+106) || !(z <= 6.2e+204))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -5.8e+213)
		tmp = t_0;
	elseif (z <= -0.5)
		tmp = t_1;
	elseif (z <= -8e-68)
		tmp = x * -3.0;
	elseif (z <= -2.25e-268)
		tmp = y * 4.0;
	elseif (z <= 7.2e-86)
		tmp = x * -3.0;
	elseif (z <= 1.02e-53)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif ((z <= 2.6e+106) || ~((z <= 6.2e+204)))
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.8e+213], t$95$0, If[LessEqual[z, -0.5], t$95$1, If[LessEqual[z, -8e-68], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.25e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.2e-86], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.02e-53], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 2.6e+106], N[Not[LessEqual[z, 6.2e+204]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.8000000000000006e213 or 2.6000000000000002e106 < z < 6.2000000000000003e204

   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. +-commutative 99.8%

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

      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. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 74.3%

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

   5. Taylor expanded in z around inf 74.3%

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

      1. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   if -5.8000000000000006e213 < z < -0.5 or 0.5 < z < 2.6000000000000002e106 or 6.2000000000000003e204 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 67.8%

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

      1. sub-neg 67.8%

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

      2. distribute-rgt-in 67.7%

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

      3. metadata-eval 67.7%

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

      4. neg-mul-1 67.7%

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

      5. associate-*r* 67.7%

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

      6. *-commutative 67.7%

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

      7. associate-+r+ 67.7%

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

      8. metadata-eval 67.7%

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

      9. associate-*r* 67.7%

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

      10. metadata-eval 67.7%

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

      11. *-commutative 67.7%

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

   6. Simplified 67.7%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-in 67.7%

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

      2. fma-def 67.7%

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

   8. Applied egg-rr 67.7%

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

      1. fma-udef 67.7%

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

      2. flip-+ 24.3%

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

      3. pow2 24.3%

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

      4. *-commutative 24.3%

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

      5. *-commutative 24.3%

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

   10. Applied egg-rr 24.3%

       \[\leadsto \color{blue}{\frac{\left(x \cdot -3\right) \cdot \left(x \cdot -3\right) - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)}} \]
   11. Step-by-step derivation

       1. swap-sqr 24.3%

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

       2. metadata-eval 24.3%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot \color{blue}{9} - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       3. *-commutative 24.3%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \color{blue}{\left(z \cdot 6\right)}\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       4. distribute-lft-out-- 24.3%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{\color{blue}{x \cdot \left(-3 - 6 \cdot z\right)}} \]

       5. *-commutative 24.3%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - \color{blue}{z \cdot 6}\right)} \]

   12. Simplified 24.3%

       \[\leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - z \cdot 6\right)}} \]

   13. Taylor expanded in z around inf 65.7%

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

       1. *-commutative 65.7%

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

   15. Simplified 65.7%

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

   if -0.5 < z < -8.00000000000000053e-68 or -2.2500000000000001e-268 < z < 7.19999999999999932e-86 or 1.02000000000000002e-53 < 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 x around inf 65.7%

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

      1. sub-neg 65.7%

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

      2. distribute-rgt-in 65.7%

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

      3. metadata-eval 65.7%

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

      4. neg-mul-1 65.7%

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

      5. associate-*r* 65.7%

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

      6. *-commutative 65.7%

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

      7. associate-+r+ 65.7%

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

      8. metadata-eval 65.7%

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

      9. associate-*r* 65.7%

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

      10. metadata-eval 65.7%

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

      11. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   9. Simplified 63.0%

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

   if -8.00000000000000053e-68 < z < -2.2500000000000001e-268 or 7.19999999999999932e-86 < z < 1.02000000000000002e-53

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 67.2%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.8 \cdot 10^{+213}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-68}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-86}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.02 \cdot 10^{-53}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{+106} \lor \neg \left(z \leq 6.2 \cdot 10^{+204}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 3: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -6 \cdot 10^{+213}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-66}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{-85}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+99}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+199}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -6e+213)
     t_0
     (if (<= z -0.5)
       t_1
       (if (<= z -1.3e-66)
         (* x -3.0)
         (if (<= z -1.45e-268)
           (* y 4.0)
           (if (<= z 1.04e-85)
             (* x -3.0)
             (if (<= z 2.5e-55)
               (* y 4.0)
               (if (<= z 0.5)
                 (* x -3.0)
                 (if (<= z 9.2e+99)
                   t_1
                   (if (<= z 4.5e+199) t_0 (* x (* 6.0 z)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -6e+213) {
		tmp = t_0;
	} else if (z <= -0.5) {
		tmp = t_1;
	} else if (z <= -1.3e-66) {
		tmp = x * -3.0;
	} else if (z <= -1.45e-268) {
		tmp = y * 4.0;
	} else if (z <= 1.04e-85) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-55) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 9.2e+99) {
		tmp = t_1;
	} else if (z <= 4.5e+199) {
		tmp = t_0;
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-6d+213)) then
        tmp = t_0
    else if (z <= (-0.5d0)) then
        tmp = t_1
    else if (z <= (-1.3d-66)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.45d-268)) then
        tmp = y * 4.0d0
    else if (z <= 1.04d-85) then
        tmp = x * (-3.0d0)
    else if (z <= 2.5d-55) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 9.2d+99) then
        tmp = t_1
    else if (z <= 4.5d+199) then
        tmp = t_0
    else
        tmp = x * (6.0d0 * 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 t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -6e+213) {
		tmp = t_0;
	} else if (z <= -0.5) {
		tmp = t_1;
	} else if (z <= -1.3e-66) {
		tmp = x * -3.0;
	} else if (z <= -1.45e-268) {
		tmp = y * 4.0;
	} else if (z <= 1.04e-85) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-55) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 9.2e+99) {
		tmp = t_1;
	} else if (z <= 4.5e+199) {
		tmp = t_0;
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -6e+213:
		tmp = t_0
	elif z <= -0.5:
		tmp = t_1
	elif z <= -1.3e-66:
		tmp = x * -3.0
	elif z <= -1.45e-268:
		tmp = y * 4.0
	elif z <= 1.04e-85:
		tmp = x * -3.0
	elif z <= 2.5e-55:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 9.2e+99:
		tmp = t_1
	elif z <= 4.5e+199:
		tmp = t_0
	else:
		tmp = x * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -6e+213)
		tmp = t_0;
	elseif (z <= -0.5)
		tmp = t_1;
	elseif (z <= -1.3e-66)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.45e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.04e-85)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.5e-55)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.2e+99)
		tmp = t_1;
	elseif (z <= 4.5e+199)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -6e+213)
		tmp = t_0;
	elseif (z <= -0.5)
		tmp = t_1;
	elseif (z <= -1.3e-66)
		tmp = x * -3.0;
	elseif (z <= -1.45e-268)
		tmp = y * 4.0;
	elseif (z <= 1.04e-85)
		tmp = x * -3.0;
	elseif (z <= 2.5e-55)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 9.2e+99)
		tmp = t_1;
	elseif (z <= 4.5e+199)
		tmp = t_0;
	else
		tmp = x * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -6e+213], t$95$0, If[LessEqual[z, -0.5], t$95$1, If[LessEqual[z, -1.3e-66], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.45e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.04e-85], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.5e-55], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.2e+99], t$95$1, If[LessEqual[z, 4.5e+199], t$95$0, N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -6.0000000000000002e213 or 9.20000000000000077e99 < z < 4.4999999999999997e199

   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. +-commutative 99.8%

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

      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. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 74.3%

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

   5. Taylor expanded in z around inf 74.3%

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

      1. *-commutative 74.3%

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

   7. Simplified 74.3%

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

   if -6.0000000000000002e213 < z < -0.5 or 0.5 < z < 9.20000000000000077e99

   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 68.8%

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

      1. sub-neg 68.8%

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

      2. distribute-rgt-in 68.8%

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

      3. metadata-eval 68.8%

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

      4. neg-mul-1 68.8%

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

      5. associate-*r* 68.8%

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

      6. *-commutative 68.8%

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

      7. associate-+r+ 68.8%

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

      8. metadata-eval 68.8%

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

      9. associate-*r* 68.8%

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

      10. metadata-eval 68.8%

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

      11. *-commutative 68.8%

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

   6. Simplified 68.8%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-in 68.8%

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

      2. fma-def 68.8%

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

   8. Applied egg-rr 68.8%

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

      1. fma-udef 68.8%

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

      2. flip-+ 27.5%

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

      3. pow2 27.5%

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

      4. *-commutative 27.5%

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

      5. *-commutative 27.5%

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

   10. Applied egg-rr 27.5%

       \[\leadsto \color{blue}{\frac{\left(x \cdot -3\right) \cdot \left(x \cdot -3\right) - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)}} \]
   11. Step-by-step derivation

       1. swap-sqr 27.5%

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

       2. metadata-eval 27.5%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot \color{blue}{9} - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       3. *-commutative 27.5%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \color{blue}{\left(z \cdot 6\right)}\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       4. distribute-lft-out-- 27.5%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{\color{blue}{x \cdot \left(-3 - 6 \cdot z\right)}} \]

       5. *-commutative 27.5%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - \color{blue}{z \cdot 6}\right)} \]

   12. Simplified 27.5%

       \[\leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - z \cdot 6\right)}} \]

   13. Taylor expanded in z around inf 66.2%

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

       1. *-commutative 66.2%

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

   15. Simplified 66.2%

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

   if -0.5 < z < -1.2999999999999999e-66 or -1.4500000000000001e-268 < z < 1.04e-85 or 2.5000000000000001e-55 < 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 x around inf 65.7%

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

      1. sub-neg 65.7%

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

      2. distribute-rgt-in 65.7%

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

      3. metadata-eval 65.7%

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

      4. neg-mul-1 65.7%

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

      5. associate-*r* 65.7%

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

      6. *-commutative 65.7%

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

      7. associate-+r+ 65.7%

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

      8. metadata-eval 65.7%

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

      9. associate-*r* 65.7%

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

      10. metadata-eval 65.7%

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

      11. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   9. Simplified 63.0%

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

   if -1.2999999999999999e-66 < z < -1.4500000000000001e-268 or 1.04e-85 < z < 2.5000000000000001e-55

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 67.2%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 4.4999999999999997e199 < z

   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 64.5%

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

      1. sub-neg 64.5%

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

      2. distribute-rgt-in 64.5%

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

      3. metadata-eval 64.5%

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

      4. neg-mul-1 64.5%

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

      5. associate-*r* 64.5%

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

      6. *-commutative 64.5%

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

      7. associate-+r+ 64.5%

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

      8. metadata-eval 64.5%

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

      9. associate-*r* 64.5%

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

      10. metadata-eval 64.5%

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

      11. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in z around inf 64.5%

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

4. Final simplification 66.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -6 \cdot 10^{+213}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-66}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.04 \cdot 10^{-85}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-55}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{+99}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+199}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 4: 50.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+213}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-70}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-87}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+199}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -4.5e+213)
     (* -6.0 (* y z))
     (if (<= z -0.5)
       t_0
       (if (<= z -8.6e-70)
         (* x -3.0)
         (if (<= z -2.2e-268)
           (* y 4.0)
           (if (<= z 1.05e-87)
             (* x -3.0)
             (if (<= z 1.4e-56)
               (* y 4.0)
               (if (<= z 0.5)
                 (* x -3.0)
                 (if (<= z 2.8e+101)
                   t_0
                   (if (<= z 1.7e+199)
                     (* y (* z -6.0))
                     (* x (* 6.0 z)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -4.5e+213) {
		tmp = -6.0 * (y * z);
	} else if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -8.6e-70) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-268) {
		tmp = y * 4.0;
	} else if (z <= 1.05e-87) {
		tmp = x * -3.0;
	} else if (z <= 1.4e-56) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 2.8e+101) {
		tmp = t_0;
	} else if (z <= 1.7e+199) {
		tmp = y * (z * -6.0);
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-4.5d+213)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-0.5d0)) then
        tmp = t_0
    else if (z <= (-8.6d-70)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.2d-268)) then
        tmp = y * 4.0d0
    else if (z <= 1.05d-87) then
        tmp = x * (-3.0d0)
    else if (z <= 1.4d-56) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 2.8d+101) then
        tmp = t_0
    else if (z <= 1.7d+199) then
        tmp = y * (z * (-6.0d0))
    else
        tmp = x * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -4.5e+213) {
		tmp = -6.0 * (y * z);
	} else if (z <= -0.5) {
		tmp = t_0;
	} else if (z <= -8.6e-70) {
		tmp = x * -3.0;
	} else if (z <= -2.2e-268) {
		tmp = y * 4.0;
	} else if (z <= 1.05e-87) {
		tmp = x * -3.0;
	} else if (z <= 1.4e-56) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 2.8e+101) {
		tmp = t_0;
	} else if (z <= 1.7e+199) {
		tmp = y * (z * -6.0);
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -4.5e+213:
		tmp = -6.0 * (y * z)
	elif z <= -0.5:
		tmp = t_0
	elif z <= -8.6e-70:
		tmp = x * -3.0
	elif z <= -2.2e-268:
		tmp = y * 4.0
	elif z <= 1.05e-87:
		tmp = x * -3.0
	elif z <= 1.4e-56:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 2.8e+101:
		tmp = t_0
	elif z <= 1.7e+199:
		tmp = y * (z * -6.0)
	else:
		tmp = x * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -4.5e+213)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -0.5)
		tmp = t_0;
	elseif (z <= -8.6e-70)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.2e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.05e-87)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.4e-56)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.8e+101)
		tmp = t_0;
	elseif (z <= 1.7e+199)
		tmp = Float64(y * Float64(z * -6.0));
	else
		tmp = Float64(x * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -4.5e+213)
		tmp = -6.0 * (y * z);
	elseif (z <= -0.5)
		tmp = t_0;
	elseif (z <= -8.6e-70)
		tmp = x * -3.0;
	elseif (z <= -2.2e-268)
		tmp = y * 4.0;
	elseif (z <= 1.05e-87)
		tmp = x * -3.0;
	elseif (z <= 1.4e-56)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 2.8e+101)
		tmp = t_0;
	elseif (z <= 1.7e+199)
		tmp = y * (z * -6.0);
	else
		tmp = x * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+213], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.5], t$95$0, If[LessEqual[z, -8.6e-70], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.2e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.05e-87], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.4e-56], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.8e+101], t$95$0, If[LessEqual[z, 1.7e+199], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -4.5000000000000002e213

   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. +-commutative 99.9%

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

      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. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 71.6%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if -4.5000000000000002e213 < z < -0.5 or 0.5 < z < 2.79999999999999981e101

   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 68.8%

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

      1. sub-neg 68.8%

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

      2. distribute-rgt-in 68.8%

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

      3. metadata-eval 68.8%

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

      4. neg-mul-1 68.8%

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

      5. associate-*r* 68.8%

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

      6. *-commutative 68.8%

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

      7. associate-+r+ 68.8%

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

      8. metadata-eval 68.8%

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

      9. associate-*r* 68.8%

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

      10. metadata-eval 68.8%

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

      11. *-commutative 68.8%

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

   6. Simplified 68.8%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-in 68.8%

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

      2. fma-def 68.8%

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

   8. Applied egg-rr 68.8%

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

      1. fma-udef 68.8%

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

      2. flip-+ 27.5%

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

      3. pow2 27.5%

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

      4. *-commutative 27.5%

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

      5. *-commutative 27.5%

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

   10. Applied egg-rr 27.5%

       \[\leadsto \color{blue}{\frac{\left(x \cdot -3\right) \cdot \left(x \cdot -3\right) - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)}} \]
   11. Step-by-step derivation

       1. swap-sqr 27.5%

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

       2. metadata-eval 27.5%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot \color{blue}{9} - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       3. *-commutative 27.5%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \color{blue}{\left(z \cdot 6\right)}\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       4. distribute-lft-out-- 27.5%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{\color{blue}{x \cdot \left(-3 - 6 \cdot z\right)}} \]

       5. *-commutative 27.5%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - \color{blue}{z \cdot 6}\right)} \]

   12. Simplified 27.5%

       \[\leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - z \cdot 6\right)}} \]

   13. Taylor expanded in z around inf 66.2%

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

       1. *-commutative 66.2%

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

   15. Simplified 66.2%

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

   if -0.5 < z < -8.6e-70 or -2.20000000000000004e-268 < z < 1.05000000000000004e-87 or 1.39999999999999997e-56 < 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 x around inf 65.7%

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

      1. sub-neg 65.7%

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

      2. distribute-rgt-in 65.7%

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

      3. metadata-eval 65.7%

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

      4. neg-mul-1 65.7%

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

      5. associate-*r* 65.7%

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

      6. *-commutative 65.7%

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

      7. associate-+r+ 65.7%

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

      8. metadata-eval 65.7%

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

      9. associate-*r* 65.7%

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

      10. metadata-eval 65.7%

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

      11. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   9. Simplified 63.0%

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

   if -8.6e-70 < z < -2.20000000000000004e-268 or 1.05000000000000004e-87 < z < 1.39999999999999997e-56

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 67.2%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 2.79999999999999981e101 < z < 1.7e199

   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. +-commutative 99.8%

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

      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. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 79.0%

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

   5. Taylor expanded in z around inf 79.0%

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

   if 1.7e199 < z

   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 64.5%

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

      1. sub-neg 64.5%

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

      2. distribute-rgt-in 64.5%

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

      3. metadata-eval 64.5%

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

      4. neg-mul-1 64.5%

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

      5. associate-*r* 64.5%

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

      6. *-commutative 64.5%

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

      7. associate-+r+ 64.5%

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

      8. metadata-eval 64.5%

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

      9. associate-*r* 64.5%

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

      10. metadata-eval 64.5%

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

      11. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in z around inf 64.5%

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

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+213}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-70}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-87}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.8 \cdot 10^{+101}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{+199}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 5: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+213}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-69}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-87}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+202}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5e+213)
   (* -6.0 (* y z))
   (if (<= z -0.5)
     (* 6.0 (* x z))
     (if (<= z -1.08e-69)
       (* x -3.0)
       (if (<= z -2.8e-268)
         (* y 4.0)
         (if (<= z 9.8e-87)
           (* x -3.0)
           (if (<= z 2.9e-56)
             (* y 4.0)
             (if (<= z 0.5)
               (* x -3.0)
               (if (<= z 1.05e+99)
                 (* z (* x 6.0))
                 (if (<= z 1.25e+202)
                   (* y (* z -6.0))
                   (* x (* 6.0 z))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+213) {
		tmp = -6.0 * (y * z);
	} else if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-69) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-268) {
		tmp = y * 4.0;
	} else if (z <= 9.8e-87) {
		tmp = x * -3.0;
	} else if (z <= 2.9e-56) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 1.05e+99) {
		tmp = z * (x * 6.0);
	} else if (z <= 1.25e+202) {
		tmp = y * (z * -6.0);
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5d+213)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-0.5d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-1.08d-69)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.8d-268)) then
        tmp = y * 4.0d0
    else if (z <= 9.8d-87) then
        tmp = x * (-3.0d0)
    else if (z <= 2.9d-56) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1.05d+99) then
        tmp = z * (x * 6.0d0)
    else if (z <= 1.25d+202) then
        tmp = y * (z * (-6.0d0))
    else
        tmp = x * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5e+213) {
		tmp = -6.0 * (y * z);
	} else if (z <= -0.5) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-69) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-268) {
		tmp = y * 4.0;
	} else if (z <= 9.8e-87) {
		tmp = x * -3.0;
	} else if (z <= 2.9e-56) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 1.05e+99) {
		tmp = z * (x * 6.0);
	} else if (z <= 1.25e+202) {
		tmp = y * (z * -6.0);
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5e+213:
		tmp = -6.0 * (y * z)
	elif z <= -0.5:
		tmp = 6.0 * (x * z)
	elif z <= -1.08e-69:
		tmp = x * -3.0
	elif z <= -2.8e-268:
		tmp = y * 4.0
	elif z <= 9.8e-87:
		tmp = x * -3.0
	elif z <= 2.9e-56:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 1.05e+99:
		tmp = z * (x * 6.0)
	elif z <= 1.25e+202:
		tmp = y * (z * -6.0)
	else:
		tmp = x * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5e+213)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -0.5)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -1.08e-69)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.8e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.8e-87)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.9e-56)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.05e+99)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= 1.25e+202)
		tmp = Float64(y * Float64(z * -6.0));
	else
		tmp = Float64(x * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5e+213)
		tmp = -6.0 * (y * z);
	elseif (z <= -0.5)
		tmp = 6.0 * (x * z);
	elseif (z <= -1.08e-69)
		tmp = x * -3.0;
	elseif (z <= -2.8e-268)
		tmp = y * 4.0;
	elseif (z <= 9.8e-87)
		tmp = x * -3.0;
	elseif (z <= 2.9e-56)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 1.05e+99)
		tmp = z * (x * 6.0);
	elseif (z <= 1.25e+202)
		tmp = y * (z * -6.0);
	else
		tmp = x * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5e+213], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -0.5], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-69], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.8e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.8e-87], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.9e-56], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.05e+99], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.25e+202], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -4.9999999999999998e213

   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. +-commutative 99.9%

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

      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. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 71.6%

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

   5. Taylor expanded in z around inf 71.6%

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

      1. *-commutative 71.6%

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

   7. Simplified 71.6%

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

   if -4.9999999999999998e213 < z < -0.5

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 68.6%

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

      1. sub-neg 68.6%

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

      2. distribute-rgt-in 68.6%

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

      3. metadata-eval 68.6%

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

      4. neg-mul-1 68.6%

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

      5. associate-*r* 68.6%

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

      6. *-commutative 68.6%

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

      7. associate-+r+ 68.6%

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

      8. metadata-eval 68.6%

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

      9. associate-*r* 68.6%

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

      10. metadata-eval 68.6%

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

      11. *-commutative 68.6%

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

   6. Simplified 68.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-in 68.6%

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

      2. fma-def 68.6%

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

   8. Applied egg-rr 68.6%

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

      1. fma-udef 68.6%

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

      2. flip-+ 22.6%

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

      3. pow2 22.6%

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

      4. *-commutative 22.6%

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

      5. *-commutative 22.6%

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

   10. Applied egg-rr 22.6%

       \[\leadsto \color{blue}{\frac{\left(x \cdot -3\right) \cdot \left(x \cdot -3\right) - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)}} \]
   11. Step-by-step derivation

       1. swap-sqr 22.6%

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

       2. metadata-eval 22.6%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot \color{blue}{9} - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       3. *-commutative 22.6%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \color{blue}{\left(z \cdot 6\right)}\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       4. distribute-lft-out-- 22.6%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{\color{blue}{x \cdot \left(-3 - 6 \cdot z\right)}} \]

       5. *-commutative 22.6%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - \color{blue}{z \cdot 6}\right)} \]

   12. Simplified 22.6%

       \[\leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - z \cdot 6\right)}} \]

   13. Taylor expanded in z around inf 67.0%

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

       1. *-commutative 67.0%

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

   15. Simplified 67.0%

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

   if -0.5 < z < -1.0800000000000001e-69 or -2.80000000000000015e-268 < z < 9.7999999999999994e-87 or 2.89999999999999991e-56 < 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 x around inf 65.7%

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

      1. sub-neg 65.7%

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

      2. distribute-rgt-in 65.7%

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

      3. metadata-eval 65.7%

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

      4. neg-mul-1 65.7%

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

      5. associate-*r* 65.7%

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

      6. *-commutative 65.7%

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

      7. associate-+r+ 65.7%

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

      8. metadata-eval 65.7%

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

      9. associate-*r* 65.7%

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

      10. metadata-eval 65.7%

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

      11. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   9. Simplified 63.0%

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

   if -1.0800000000000001e-69 < z < -2.80000000000000015e-268 or 9.7999999999999994e-87 < z < 2.89999999999999991e-56

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 67.2%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if 0.5 < z < 1.05000000000000005e99

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around inf 69.4%

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

      1. sub-neg 69.4%

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

      2. distribute-rgt-in 69.4%

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

      3. metadata-eval 69.4%

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

      4. neg-mul-1 69.4%

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

      5. associate-*r* 69.4%

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

      6. *-commutative 69.4%

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

      7. associate-+r+ 69.4%

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

      8. metadata-eval 69.4%

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

      9. associate-*r* 69.4%

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

      10. metadata-eval 69.4%

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

      11. *-commutative 69.4%

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

   6. Simplified 69.4%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   7. Step-by-step derivation

      1. distribute-lft-in 69.4%

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

      2. fma-def 69.4%

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

   8. Applied egg-rr 69.4%

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

      1. fma-udef 69.4%

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

      2. flip-+ 37.4%

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

      3. pow2 37.4%

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

      4. *-commutative 37.4%

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

      5. *-commutative 37.4%

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

   10. Applied egg-rr 37.4%

       \[\leadsto \color{blue}{\frac{\left(x \cdot -3\right) \cdot \left(x \cdot -3\right) - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)}} \]
   11. Step-by-step derivation

       1. swap-sqr 37.4%

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

       2. metadata-eval 37.4%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot \color{blue}{9} - {\left(x \cdot \left(6 \cdot z\right)\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       3. *-commutative 37.4%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \color{blue}{\left(z \cdot 6\right)}\right)}^{2}}{x \cdot -3 - x \cdot \left(6 \cdot z\right)} \]

       4. distribute-lft-out-- 37.3%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{\color{blue}{x \cdot \left(-3 - 6 \cdot z\right)}} \]

       5. *-commutative 37.3%

          \[\leadsto \frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - \color{blue}{z \cdot 6}\right)} \]

   12. Simplified 37.3%

       \[\leadsto \color{blue}{\frac{\left(x \cdot x\right) \cdot 9 - {\left(x \cdot \left(z \cdot 6\right)\right)}^{2}}{x \cdot \left(-3 - z \cdot 6\right)}} \]

   13. Taylor expanded in z around inf 64.5%

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

       1. *-commutative 64.5%

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

       2. associate-*r* 64.5%

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

       3. *-commutative 64.5%

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

       4. associate-*l* 64.5%

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

   15. Simplified 64.5%

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

   if 1.05000000000000005e99 < z < 1.25e202

   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. +-commutative 99.8%

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

      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. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 79.0%

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

   5. Taylor expanded in z around inf 79.0%

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

   if 1.25e202 < z

   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 64.5%

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

      1. sub-neg 64.5%

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

      2. distribute-rgt-in 64.5%

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

      3. metadata-eval 64.5%

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

      4. neg-mul-1 64.5%

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

      5. associate-*r* 64.5%

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

      6. *-commutative 64.5%

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

      7. associate-+r+ 64.5%

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

      8. metadata-eval 64.5%

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

      9. associate-*r* 64.5%

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

      10. metadata-eval 64.5%

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

      11. *-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in z around inf 64.5%

      \[\leadsto x \cdot \color{blue}{\left(6 \cdot z\right)} \]
3. Recombined 7 regimes into one program.

4. Final simplification 66.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5 \cdot 10^{+213}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -0.5:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-69}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.8 \cdot 10^{-87}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.9 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{+99}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{+202}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \]

Alternative 6: 73.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.011:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-69}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-86}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.011)
     t_0
     (if (<= z -1.8e-69)
       (* x -3.0)
       (if (<= z -2.4e-268)
         (* y 4.0)
         (if (<= z 1.25e-86)
           (* x -3.0)
           (if (<= z 5.4e-56) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.011) {
		tmp = t_0;
	} else if (z <= -1.8e-69) {
		tmp = x * -3.0;
	} else if (z <= -2.4e-268) {
		tmp = y * 4.0;
	} else if (z <= 1.25e-86) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-56) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.011d0)) then
        tmp = t_0
    else if (z <= (-1.8d-69)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.4d-268)) then
        tmp = y * 4.0d0
    else if (z <= 1.25d-86) then
        tmp = x * (-3.0d0)
    else if (z <= 5.4d-56) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.011) {
		tmp = t_0;
	} else if (z <= -1.8e-69) {
		tmp = x * -3.0;
	} else if (z <= -2.4e-268) {
		tmp = y * 4.0;
	} else if (z <= 1.25e-86) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-56) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.011:
		tmp = t_0
	elif z <= -1.8e-69:
		tmp = x * -3.0
	elif z <= -2.4e-268:
		tmp = y * 4.0
	elif z <= 1.25e-86:
		tmp = x * -3.0
	elif z <= 5.4e-56:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.011)
		tmp = t_0;
	elseif (z <= -1.8e-69)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.4e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.25e-86)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.4e-56)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.011)
		tmp = t_0;
	elseif (z <= -1.8e-69)
		tmp = x * -3.0;
	elseif (z <= -2.4e-268)
		tmp = y * 4.0;
	elseif (z <= 1.25e-86)
		tmp = x * -3.0;
	elseif (z <= 5.4e-56)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.011], t$95$0, If[LessEqual[z, -1.8e-69], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.4e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.25e-86], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.4e-56], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.010999999999999999 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 97.7%

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

   if -0.010999999999999999 < z < -1.80000000000000009e-69 or -2.3999999999999999e-268 < z < 1.25e-86 or 5.3999999999999999e-56 < 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 x around inf 65.7%

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

      1. sub-neg 65.7%

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

      2. distribute-rgt-in 65.7%

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

      3. metadata-eval 65.7%

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

      4. neg-mul-1 65.7%

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

      5. associate-*r* 65.7%

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

      6. *-commutative 65.7%

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

      7. associate-+r+ 65.7%

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

      8. metadata-eval 65.7%

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

      9. associate-*r* 65.7%

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

      10. metadata-eval 65.7%

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

      11. *-commutative 65.7%

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

   6. Simplified 65.7%

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

   7. Taylor expanded in z around 0 63.0%

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

      1. *-commutative 63.0%

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

   9. Simplified 63.0%

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

   if -1.80000000000000009e-69 < z < -2.3999999999999999e-268 or 1.25e-86 < z < 5.3999999999999999e-56

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 67.2%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.011:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-69}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.25 \cdot 10^{-86}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 7: 74.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + 6 \cdot z\right)\\ t_1 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -54000:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1450000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* 6.0 z)))) (t_1 (* -6.0 (* (- y x) z))))
   (if (<= z -54000.0)
     t_1
     (if (<= z -4.2e-69)
       t_0
       (if (<= z -2.5e-268)
         (* y 4.0)
         (if (<= z 7.8e-88)
           (* x -3.0)
           (if (<= z 1.7e-56) (* y 4.0) (if (<= z 1450000000.0) t_0 t_1))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (6.0 * z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -54000.0) {
		tmp = t_1;
	} else if (z <= -4.2e-69) {
		tmp = t_0;
	} else if (z <= -2.5e-268) {
		tmp = y * 4.0;
	} else if (z <= 7.8e-88) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-56) {
		tmp = y * 4.0;
	} else if (z <= 1450000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (6.0d0 * z))
    t_1 = (-6.0d0) * ((y - x) * z)
    if (z <= (-54000.0d0)) then
        tmp = t_1
    else if (z <= (-4.2d-69)) then
        tmp = t_0
    else if (z <= (-2.5d-268)) then
        tmp = y * 4.0d0
    else if (z <= 7.8d-88) then
        tmp = x * (-3.0d0)
    else if (z <= 1.7d-56) then
        tmp = y * 4.0d0
    else if (z <= 1450000000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (6.0 * z));
	double t_1 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -54000.0) {
		tmp = t_1;
	} else if (z <= -4.2e-69) {
		tmp = t_0;
	} else if (z <= -2.5e-268) {
		tmp = y * 4.0;
	} else if (z <= 7.8e-88) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-56) {
		tmp = y * 4.0;
	} else if (z <= 1450000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (6.0 * z))
	t_1 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -54000.0:
		tmp = t_1
	elif z <= -4.2e-69:
		tmp = t_0
	elif z <= -2.5e-268:
		tmp = y * 4.0
	elif z <= 7.8e-88:
		tmp = x * -3.0
	elif z <= 1.7e-56:
		tmp = y * 4.0
	elif z <= 1450000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(6.0 * z)))
	t_1 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -54000.0)
		tmp = t_1;
	elseif (z <= -4.2e-69)
		tmp = t_0;
	elseif (z <= -2.5e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.8e-88)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.7e-56)
		tmp = Float64(y * 4.0);
	elseif (z <= 1450000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (6.0 * z));
	t_1 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -54000.0)
		tmp = t_1;
	elseif (z <= -4.2e-69)
		tmp = t_0;
	elseif (z <= -2.5e-268)
		tmp = y * 4.0;
	elseif (z <= 7.8e-88)
		tmp = x * -3.0;
	elseif (z <= 1.7e-56)
		tmp = y * 4.0;
	elseif (z <= 1450000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -54000.0], t$95$1, If[LessEqual[z, -4.2e-69], t$95$0, If[LessEqual[z, -2.5e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.8e-88], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.7e-56], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1450000000.0], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -54000 or 1.45e9 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 99.1%

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

   if -54000 < z < -4.1999999999999999e-69 or 1.69999999999999991e-56 < z < 1.45e9

   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 85.1%

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

      1. sub-neg 85.1%

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

      2. distribute-rgt-in 85.1%

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

      3. metadata-eval 85.1%

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

      4. neg-mul-1 85.1%

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

      5. associate-*r* 85.1%

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

      6. *-commutative 85.1%

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

      7. associate-+r+ 85.1%

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

      8. metadata-eval 85.1%

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

      9. associate-*r* 85.1%

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

      10. metadata-eval 85.1%

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

      11. *-commutative 85.1%

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

   6. Simplified 85.1%

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

   if -4.1999999999999999e-69 < z < -2.5e-268 or 7.79999999999999985e-88 < z < 1.69999999999999991e-56

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 67.2%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

   if -2.5e-268 < z < 7.79999999999999985e-88

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around inf 60.1%

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

      1. sub-neg 60.1%

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

      2. distribute-rgt-in 60.1%

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

      3. metadata-eval 60.1%

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

      4. neg-mul-1 60.1%

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

      5. associate-*r* 60.1%

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

      6. *-commutative 60.1%

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

      7. associate-+r+ 60.1%

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

      8. metadata-eval 60.1%

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

      9. associate-*r* 60.1%

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

      10. metadata-eval 60.1%

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

      11. *-commutative 60.1%

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

   6. Simplified 60.1%

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

   7. Taylor expanded in z around 0 60.1%

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

      1. *-commutative 60.1%

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

   9. Simplified 60.1%

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

4. Final simplification 82.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -54000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-69}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-88}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1450000000:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 8: 50.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -110:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-67}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-86}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -110.0)
     t_0
     (if (<= z -1.55e-67)
       (* x -3.0)
       (if (<= z -1.7e-268)
         (* y 4.0)
         (if (<= z 2.7e-86)
           (* x -3.0)
           (if (<= z 2e-56) (* y 4.0) (if (<= z 0.64) (* x -3.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -110.0) {
		tmp = t_0;
	} else if (z <= -1.55e-67) {
		tmp = x * -3.0;
	} else if (z <= -1.7e-268) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-86) {
		tmp = x * -3.0;
	} else if (z <= 2e-56) {
		tmp = y * 4.0;
	} else if (z <= 0.64) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-110.0d0)) then
        tmp = t_0
    else if (z <= (-1.55d-67)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.7d-268)) then
        tmp = y * 4.0d0
    else if (z <= 2.7d-86) then
        tmp = x * (-3.0d0)
    else if (z <= 2d-56) then
        tmp = y * 4.0d0
    else if (z <= 0.64d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -110.0) {
		tmp = t_0;
	} else if (z <= -1.55e-67) {
		tmp = x * -3.0;
	} else if (z <= -1.7e-268) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-86) {
		tmp = x * -3.0;
	} else if (z <= 2e-56) {
		tmp = y * 4.0;
	} else if (z <= 0.64) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -110.0:
		tmp = t_0
	elif z <= -1.55e-67:
		tmp = x * -3.0
	elif z <= -1.7e-268:
		tmp = y * 4.0
	elif z <= 2.7e-86:
		tmp = x * -3.0
	elif z <= 2e-56:
		tmp = y * 4.0
	elif z <= 0.64:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -110.0)
		tmp = t_0;
	elseif (z <= -1.55e-67)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.7e-268)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.7e-86)
		tmp = Float64(x * -3.0);
	elseif (z <= 2e-56)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.64)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -110.0)
		tmp = t_0;
	elseif (z <= -1.55e-67)
		tmp = x * -3.0;
	elseif (z <= -1.7e-268)
		tmp = y * 4.0;
	elseif (z <= 2.7e-86)
		tmp = x * -3.0;
	elseif (z <= 2e-56)
		tmp = y * 4.0;
	elseif (z <= 0.64)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -110.0], t$95$0, If[LessEqual[z, -1.55e-67], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.7e-268], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.7e-86], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2e-56], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.64], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -110 or 0.640000000000000013 < z

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 47.3%

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

   5. Taylor expanded in z around inf 46.7%

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

      1. *-commutative 46.7%

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

   7. Simplified 46.7%

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

   if -110 < z < -1.5500000000000001e-67 or -1.7e-268 < z < 2.69999999999999992e-86 or 2.0000000000000001e-56 < z < 0.640000000000000013

   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 66.1%

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

      1. sub-neg 66.1%

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

      2. distribute-rgt-in 66.1%

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

      3. metadata-eval 66.1%

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

      4. neg-mul-1 66.1%

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

      5. associate-*r* 66.1%

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

      6. *-commutative 66.1%

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

      7. associate-+r+ 66.1%

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

      8. metadata-eval 66.1%

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

      9. associate-*r* 66.1%

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

      10. metadata-eval 66.1%

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

      11. *-commutative 66.1%

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

   6. Simplified 66.1%

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

   7. Taylor expanded in z around 0 62.5%

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

      1. *-commutative 62.5%

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

   9. Simplified 62.5%

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

   if -1.5500000000000001e-67 < z < -1.7e-268 or 2.69999999999999992e-86 < z < 2.0000000000000001e-56

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 67.2%

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

   5. Taylor expanded in z around 0 67.2%

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

      1. *-commutative 67.2%

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

   7. Simplified 67.2%

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

4. Final simplification 55.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -110:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.55 \cdot 10^{-67}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-268}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-86}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-56}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.64:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 9: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((-6.0d0) * ((y - x) * z)) + ((y - x) * 4.0d0))
end function

Java

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

Python

def code(x, y, z):
	return x + ((-6.0 * ((y - x) * z)) + ((y - x) * 4.0))

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((-6.0 * ((y - x) * z)) + ((y - x) * 4.0));
end

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

4. Taylor expanded in z around 0 99.8%

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

5. Final simplification 99.8%

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

Alternative 10: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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 y around 0 99.6%

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

5. Final simplification 99.6%

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

Alternative 11: 74.6% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-73} \lor \neg \left(x \leq 10500000000000\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3e-73) (not (<= x 10500000000000.0)))
   (* x (+ -3.0 (* 6.0 z)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e-73) || !(x <= 10500000000000.0)) {
		tmp = x * (-3.0 + (6.0 * z));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-3d-73)) .or. (.not. (x <= 10500000000000.0d0))) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3e-73) || !(x <= 10500000000000.0)) {
		tmp = x * (-3.0 + (6.0 * z));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3e-73) or not (x <= 10500000000000.0):
		tmp = x * (-3.0 + (6.0 * z))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3e-73) || !(x <= 10500000000000.0))
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -3e-73) || ~((x <= 10500000000000.0)))
		tmp = x * (-3.0 + (6.0 * z));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3e-73], N[Not[LessEqual[x, 10500000000000.0]], $MachinePrecision]], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3e-73 or 1.05e13 < x

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 77.0%

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

      1. sub-neg 77.0%

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

      2. distribute-rgt-in 77.0%

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

      3. metadata-eval 77.0%

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

      4. neg-mul-1 77.0%

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

      5. associate-*r* 77.0%

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

      6. *-commutative 77.0%

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

      7. associate-+r+ 77.0%

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

      8. metadata-eval 77.0%

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

      9. associate-*r* 77.0%

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

      10. metadata-eval 77.0%

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

      11. *-commutative 77.0%

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

   6. Simplified 77.0%

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

   if -3e-73 < x < 1.05e13

   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 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 79.5%

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

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{-73} \lor \neg \left(x \leq 10500000000000\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]

Alternative 12: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.52)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.5) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.52) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.52d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.5d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.52) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.52:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.5:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.52)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.5)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.52)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.5)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.52], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.52000000000000002

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 97.5%

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

   if -0.52000000000000002 < 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 97.6%

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

   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 0 99.7%

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

   5. Taylor expanded in z around inf 97.8%

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

      1. associate-*r* 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-*l* 97.9%

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

   7. Simplified 97.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.52:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 13: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.56)
   (* -6.0 (* (- y x) z))
   (if (<= z 0.65) (+ (* y 4.0) (* x -3.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.56) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.65) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.56d0)) then
        tmp = (-6.0d0) * ((y - x) * z)
    else if (z <= 0.65d0) then
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.56) {
		tmp = -6.0 * ((y - x) * z);
	} else if (z <= 0.65) {
		tmp = (y * 4.0) + (x * -3.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.56:
		tmp = -6.0 * ((y - x) * z)
	elif z <= 0.65:
		tmp = (y * 4.0) + (x * -3.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.56)
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 0.65)
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.56)
		tmp = -6.0 * ((y - x) * z);
	elseif (z <= 0.65)
		tmp = (y * 4.0) + (x * -3.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.56], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.56000000000000005

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 97.5%

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

   if -0.56000000000000005 < z < 0.650000000000000022

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in z around 0 97.6%

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

   5. Taylor expanded in x around 0 97.6%

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

   if 0.650000000000000022 < 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 0 99.7%

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

   5. Taylor expanded in z around inf 97.8%

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

      1. associate-*r* 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-*l* 97.9%

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

   7. Simplified 97.9%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]

Alternative 14: 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 15: 36.6% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-25}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -4.5e-25) (* y 4.0) (if (<= y 2.7e+150) (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -4.5e-25) {
		tmp = y * 4.0;
	} else if (y <= 2.7e+150) {
		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-25)) then
        tmp = y * 4.0d0
    else if (y <= 2.7d+150) 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-25) {
		tmp = y * 4.0;
	} else if (y <= 2.7e+150) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -4.5e-25:
		tmp = y * 4.0
	elif y <= 2.7e+150:
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -4.5e-25)
		tmp = Float64(y * 4.0);
	elseif (y <= 2.7e+150)
		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-25)
		tmp = y * 4.0;
	elseif (y <= 2.7e+150)
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -4.5e-25], N[(y * 4.0), $MachinePrecision], If[LessEqual[y, 2.7e+150], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -4.5000000000000001e-25 or 2.70000000000000008e150 < y

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 81.4%

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

   5. Taylor expanded in z around 0 45.8%

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

      1. *-commutative 45.8%

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

   7. Simplified 45.8%

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

   if -4.5000000000000001e-25 < y < 2.70000000000000008e150

   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 76.3%

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

      1. sub-neg 76.3%

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

      2. distribute-rgt-in 76.3%

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

      3. metadata-eval 76.3%

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

      4. neg-mul-1 76.3%

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

      5. associate-*r* 76.3%

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

      6. *-commutative 76.3%

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

      7. associate-+r+ 76.3%

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

      8. metadata-eval 76.3%

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

      9. associate-*r* 76.3%

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

      10. metadata-eval 76.3%

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

      11. *-commutative 76.3%

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

   6. Simplified 76.3%

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

   7. Taylor expanded in z around 0 40.9%

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

      1. *-commutative 40.9%

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

   9. Simplified 40.9%

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

4. Final simplification 42.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-25}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+150}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]

Alternative 16: 26.0% 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 56.8%

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

   1. sub-neg 56.8%

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

   2. distribute-rgt-in 56.8%

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

   3. metadata-eval 56.8%

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

   4. neg-mul-1 56.8%

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

   5. associate-*r* 56.8%

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

   6. *-commutative 56.8%

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

   7. associate-+r+ 56.8%

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

   8. metadata-eval 56.8%

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

   9. associate-*r* 56.8%

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

   10. metadata-eval 56.8%

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

   11. *-commutative 56.8%

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

6. Simplified 56.8%

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

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%

    \[\leadsto x \cdot -3 \]

Reproduce

herbie shell --seed 2023280 
(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))))