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

Percentage Accurate: 99.5% → 99.7%

Time: 13.7s

Alternatives: 17

Speedup: 1.2×

• 20.8% 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

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

FPCore

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

C

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

Julia

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

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(z * -6.0 + 4.0), $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* 99.7%

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

   3. fma-define 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. +-commutative 99.7%

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

   6. distribute-lft-in 99.8%

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

   7. distribute-rgt-neg-out 99.8%

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

   8. *-commutative 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. fma-define 99.8%

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

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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* 99.7%

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

   3. fma-define 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 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Final simplification 99.8%

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

Alternative 3: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-236}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-306}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-37}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+101} \lor \neg \left(z \leq 8.5 \cdot 10^{+246}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -0.65)
     t_0
     (if (<= z -8.6e-184)
       (* y 4.0)
       (if (<= z -2.9e-236)
         (* x -3.0)
         (if (<= z -4.8e-306)
           (* y 4.0)
           (if (<= z 7e-231)
             (* x -3.0)
             (if (<= z 6.6e-177)
               (* y 4.0)
               (if (<= z 6e-37)
                 (* x -3.0)
                 (if (<= z 0.65)
                   (* y 4.0)
                   (if (or (<= z 7.5e+101) (not (<= z 8.5e+246)))
                     (* -6.0 (* y z))
                     t_0)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -8.6e-184) {
		tmp = y * 4.0;
	} else if (z <= -2.9e-236) {
		tmp = x * -3.0;
	} else if (z <= -4.8e-306) {
		tmp = y * 4.0;
	} else if (z <= 7e-231) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-177) {
		tmp = y * 4.0;
	} else if (z <= 6e-37) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if ((z <= 7.5e+101) || !(z <= 8.5e+246)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-0.65d0)) then
        tmp = t_0
    else if (z <= (-8.6d-184)) then
        tmp = y * 4.0d0
    else if (z <= (-2.9d-236)) then
        tmp = x * (-3.0d0)
    else if (z <= (-4.8d-306)) then
        tmp = y * 4.0d0
    else if (z <= 7d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 6.6d-177) then
        tmp = y * 4.0d0
    else if (z <= 6d-37) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if ((z <= 7.5d+101) .or. (.not. (z <= 8.5d+246))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -0.65) {
		tmp = t_0;
	} else if (z <= -8.6e-184) {
		tmp = y * 4.0;
	} else if (z <= -2.9e-236) {
		tmp = x * -3.0;
	} else if (z <= -4.8e-306) {
		tmp = y * 4.0;
	} else if (z <= 7e-231) {
		tmp = x * -3.0;
	} else if (z <= 6.6e-177) {
		tmp = y * 4.0;
	} else if (z <= 6e-37) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if ((z <= 7.5e+101) || !(z <= 8.5e+246)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -0.65:
		tmp = t_0
	elif z <= -8.6e-184:
		tmp = y * 4.0
	elif z <= -2.9e-236:
		tmp = x * -3.0
	elif z <= -4.8e-306:
		tmp = y * 4.0
	elif z <= 7e-231:
		tmp = x * -3.0
	elif z <= 6.6e-177:
		tmp = y * 4.0
	elif z <= 6e-37:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif (z <= 7.5e+101) or not (z <= 8.5e+246):
		tmp = -6.0 * (y * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -0.65)
		tmp = t_0;
	elseif (z <= -8.6e-184)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.9e-236)
		tmp = Float64(x * -3.0);
	elseif (z <= -4.8e-306)
		tmp = Float64(y * 4.0);
	elseif (z <= 7e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.6e-177)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e-37)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif ((z <= 7.5e+101) || !(z <= 8.5e+246))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -0.65)
		tmp = t_0;
	elseif (z <= -8.6e-184)
		tmp = y * 4.0;
	elseif (z <= -2.9e-236)
		tmp = x * -3.0;
	elseif (z <= -4.8e-306)
		tmp = y * 4.0;
	elseif (z <= 7e-231)
		tmp = x * -3.0;
	elseif (z <= 6.6e-177)
		tmp = y * 4.0;
	elseif (z <= 6e-37)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif ((z <= 7.5e+101) || ~((z <= 8.5e+246)))
		tmp = -6.0 * (y * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.65], t$95$0, If[LessEqual[z, -8.6e-184], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.9e-236], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -4.8e-306], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.6e-177], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e-37], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 7.5e+101], N[Not[LessEqual[z, 8.5e+246]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.650000000000000022 or 7.4999999999999995e101 < z < 8.49999999999999952e246

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around inf 59.4%

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

      1. sub-neg 59.4%

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

      2. distribute-rgt-in 59.4%

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

      3. metadata-eval 59.4%

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

      4. distribute-lft-neg-in 59.4%

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

      5. associate-+r+ 59.4%

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

      6. metadata-eval 59.4%

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

      7. *-commutative 59.4%

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

      8. distribute-lft-neg-in 59.4%

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

      9. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around inf 58.4%

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

      1. *-commutative 58.4%

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

   10. Simplified 58.4%

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

   if -0.650000000000000022 < z < -8.60000000000000013e-184 or -2.9e-236 < z < -4.7999999999999999e-306 or 7.0000000000000002e-231 < z < 6.5999999999999999e-177 or 6e-37 < z < 0.650000000000000022

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in z around 0 96.2%

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

      1. distribute-rgt-in 96.2%

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

      2. associate-+r+ 96.2%

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

      3. *-commutative 96.2%

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

      4. associate-*r* 96.3%

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

      5. metadata-eval 96.3%

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

      6. distribute-rgt1-in 96.3%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      7. metadata-eval 96.3%

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

      8. *-commutative 96.3%

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

      9. *-commutative 96.3%

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

      10. associate-*l* 96.5%

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

      11. metadata-eval 96.5%

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

   8. Simplified 96.5%

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

   9. Taylor expanded in x around 0 69.5%

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

       1. *-commutative 69.5%

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

   11. Simplified 69.5%

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

   if -8.60000000000000013e-184 < z < -2.9e-236 or -4.7999999999999999e-306 < z < 7.0000000000000002e-231 or 6.5999999999999999e-177 < z < 6e-37

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 67.7%

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

      1. sub-neg 67.7%

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

      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. distribute-lft-neg-in 67.7%

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

      5. associate-+r+ 67.7%

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

      6. metadata-eval 67.7%

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

      7. *-commutative 67.7%

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

      8. distribute-lft-neg-in 67.7%

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

      9. metadata-eval 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   10. Simplified 67.7%

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

   if 0.650000000000000022 < z < 7.4999999999999995e101 or 8.49999999999999952e246 < 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. Add Preprocessing

   5. Taylor expanded in y around inf 89.7%

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

   6. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in z around inf 70.3%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -8.6 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-236}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4.8 \cdot 10^{-306}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-37}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+101} \lor \neg \left(z \leq 8.5 \cdot 10^{+246}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.34:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-234}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-299}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-39}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+97} \lor \neg \left(z \leq 4 \cdot 10^{+245}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.34)
   (* 6.0 (* x z))
   (if (<= z -3e-181)
     (* y 4.0)
     (if (<= z -3.4e-234)
       (* x -3.0)
       (if (<= z -4e-299)
         (* y 4.0)
         (if (<= z 6e-229)
           (* x -3.0)
           (if (<= z 5e-176)
             (* y 4.0)
             (if (<= z 3.6e-39)
               (* x -3.0)
               (if (<= z 0.65)
                 (* y 4.0)
                 (if (or (<= z 8.5e+97) (not (<= z 4e+245)))
                   (* -6.0 (* y z))
                   (* x (* z 6.0))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.34) {
		tmp = 6.0 * (x * z);
	} else if (z <= -3e-181) {
		tmp = y * 4.0;
	} else if (z <= -3.4e-234) {
		tmp = x * -3.0;
	} else if (z <= -4e-299) {
		tmp = y * 4.0;
	} else if (z <= 6e-229) {
		tmp = x * -3.0;
	} else if (z <= 5e-176) {
		tmp = y * 4.0;
	} else if (z <= 3.6e-39) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if ((z <= 8.5e+97) || !(z <= 4e+245)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.34d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-3d-181)) then
        tmp = y * 4.0d0
    else if (z <= (-3.4d-234)) then
        tmp = x * (-3.0d0)
    else if (z <= (-4d-299)) then
        tmp = y * 4.0d0
    else if (z <= 6d-229) then
        tmp = x * (-3.0d0)
    else if (z <= 5d-176) then
        tmp = y * 4.0d0
    else if (z <= 3.6d-39) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if ((z <= 8.5d+97) .or. (.not. (z <= 4d+245))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.34) {
		tmp = 6.0 * (x * z);
	} else if (z <= -3e-181) {
		tmp = y * 4.0;
	} else if (z <= -3.4e-234) {
		tmp = x * -3.0;
	} else if (z <= -4e-299) {
		tmp = y * 4.0;
	} else if (z <= 6e-229) {
		tmp = x * -3.0;
	} else if (z <= 5e-176) {
		tmp = y * 4.0;
	} else if (z <= 3.6e-39) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if ((z <= 8.5e+97) || !(z <= 4e+245)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.34:
		tmp = 6.0 * (x * z)
	elif z <= -3e-181:
		tmp = y * 4.0
	elif z <= -3.4e-234:
		tmp = x * -3.0
	elif z <= -4e-299:
		tmp = y * 4.0
	elif z <= 6e-229:
		tmp = x * -3.0
	elif z <= 5e-176:
		tmp = y * 4.0
	elif z <= 3.6e-39:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif (z <= 8.5e+97) or not (z <= 4e+245):
		tmp = -6.0 * (y * z)
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.34)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -3e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.4e-234)
		tmp = Float64(x * -3.0);
	elseif (z <= -4e-299)
		tmp = Float64(y * 4.0);
	elseif (z <= 6e-229)
		tmp = Float64(x * -3.0);
	elseif (z <= 5e-176)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.6e-39)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif ((z <= 8.5e+97) || !(z <= 4e+245))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.34)
		tmp = 6.0 * (x * z);
	elseif (z <= -3e-181)
		tmp = y * 4.0;
	elseif (z <= -3.4e-234)
		tmp = x * -3.0;
	elseif (z <= -4e-299)
		tmp = y * 4.0;
	elseif (z <= 6e-229)
		tmp = x * -3.0;
	elseif (z <= 5e-176)
		tmp = y * 4.0;
	elseif (z <= 3.6e-39)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif ((z <= 8.5e+97) || ~((z <= 4e+245)))
		tmp = -6.0 * (y * z);
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.34], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.4e-234], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -4e-299], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6e-229], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5e-176], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.6e-39], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[Or[LessEqual[z, 8.5e+97], N[Not[LessEqual[z, 4e+245]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -0.340000000000000024

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 59.4%

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

      1. sub-neg 59.4%

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

      2. distribute-rgt-in 59.4%

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

      3. metadata-eval 59.4%

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

      4. distribute-lft-neg-in 59.4%

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

      5. associate-+r+ 59.4%

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

      6. metadata-eval 59.4%

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

      7. *-commutative 59.4%

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

      8. distribute-lft-neg-in 59.4%

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

      9. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around inf 58.1%

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

      1. *-commutative 58.1%

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

   10. Simplified 58.1%

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

   if -0.340000000000000024 < z < -2.99999999999999974e-181 or -3.39999999999999986e-234 < z < -3.99999999999999997e-299 or 6.00000000000000005e-229 < z < 5e-176 or 3.6000000000000001e-39 < z < 0.650000000000000022

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in z around 0 96.2%

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

      1. distribute-rgt-in 96.2%

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

      2. associate-+r+ 96.2%

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

      3. *-commutative 96.2%

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

      4. associate-*r* 96.3%

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

      5. metadata-eval 96.3%

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

      6. distribute-rgt1-in 96.3%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      7. metadata-eval 96.3%

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

      8. *-commutative 96.3%

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

      9. *-commutative 96.3%

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

      10. associate-*l* 96.5%

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

      11. metadata-eval 96.5%

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

   8. Simplified 96.5%

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

   9. Taylor expanded in x around 0 69.5%

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

       1. *-commutative 69.5%

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

   11. Simplified 69.5%

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

   if -2.99999999999999974e-181 < z < -3.39999999999999986e-234 or -3.99999999999999997e-299 < z < 6.00000000000000005e-229 or 5e-176 < z < 3.6000000000000001e-39

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 67.7%

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

      1. sub-neg 67.7%

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

      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. distribute-lft-neg-in 67.7%

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

      5. associate-+r+ 67.7%

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

      6. metadata-eval 67.7%

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

      7. *-commutative 67.7%

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

      8. distribute-lft-neg-in 67.7%

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

      9. metadata-eval 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   10. Simplified 67.7%

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

   if 0.650000000000000022 < z < 8.4999999999999993e97 or 4.00000000000000018e245 < 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. Add Preprocessing

   5. Taylor expanded in y around inf 89.7%

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

   6. Taylor expanded in y around inf 74.7%

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

      1. *-commutative 74.7%

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

   8. Simplified 74.7%

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

   9. Taylor expanded in z around inf 70.3%

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

   if 8.4999999999999993e97 < z < 4.00000000000000018e245

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 59.5%

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

      1. sub-neg 59.5%

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

      2. distribute-rgt-in 59.5%

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

      3. metadata-eval 59.5%

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

      4. distribute-lft-neg-in 59.5%

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

      5. associate-+r+ 59.5%

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

      6. metadata-eval 59.5%

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

      7. *-commutative 59.5%

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

      8. distribute-lft-neg-in 59.5%

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

      9. metadata-eval 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in z around inf 59.5%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.34:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-234}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-299}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-39}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+97} \lor \neg \left(z \leq 4 \cdot 10^{+245}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.15:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-300}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-38}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+99}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.15)
   (* 6.0 (* x z))
   (if (<= z -7.5e-181)
     (* y 4.0)
     (if (<= z -2e-233)
       (* x -3.0)
       (if (<= z -1.1e-300)
         (* y 4.0)
         (if (<= z 1.1e-229)
           (* x -3.0)
           (if (<= z 4.8e-176)
             (* y 4.0)
             (if (<= z 4.3e-38)
               (* x -3.0)
               (if (<= z 0.65)
                 (* y 4.0)
                 (if (<= z 1.75e+99)
                   (* -6.0 (* y z))
                   (if (<= z 7.8e+244)
                     (* x (* z 6.0))
                     (* y (* z -6.0)))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.15) {
		tmp = 6.0 * (x * z);
	} else if (z <= -7.5e-181) {
		tmp = y * 4.0;
	} else if (z <= -2e-233) {
		tmp = x * -3.0;
	} else if (z <= -1.1e-300) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-229) {
		tmp = x * -3.0;
	} else if (z <= 4.8e-176) {
		tmp = y * 4.0;
	} else if (z <= 4.3e-38) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 1.75e+99) {
		tmp = -6.0 * (y * z);
	} else if (z <= 7.8e+244) {
		tmp = x * (z * 6.0);
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.15d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-7.5d-181)) then
        tmp = y * 4.0d0
    else if (z <= (-2d-233)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.1d-300)) then
        tmp = y * 4.0d0
    else if (z <= 1.1d-229) then
        tmp = x * (-3.0d0)
    else if (z <= 4.8d-176) then
        tmp = y * 4.0d0
    else if (z <= 4.3d-38) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if (z <= 1.75d+99) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= 7.8d+244) then
        tmp = x * (z * 6.0d0)
    else
        tmp = y * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.15) {
		tmp = 6.0 * (x * z);
	} else if (z <= -7.5e-181) {
		tmp = y * 4.0;
	} else if (z <= -2e-233) {
		tmp = x * -3.0;
	} else if (z <= -1.1e-300) {
		tmp = y * 4.0;
	} else if (z <= 1.1e-229) {
		tmp = x * -3.0;
	} else if (z <= 4.8e-176) {
		tmp = y * 4.0;
	} else if (z <= 4.3e-38) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 1.75e+99) {
		tmp = -6.0 * (y * z);
	} else if (z <= 7.8e+244) {
		tmp = x * (z * 6.0);
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.15:
		tmp = 6.0 * (x * z)
	elif z <= -7.5e-181:
		tmp = y * 4.0
	elif z <= -2e-233:
		tmp = x * -3.0
	elif z <= -1.1e-300:
		tmp = y * 4.0
	elif z <= 1.1e-229:
		tmp = x * -3.0
	elif z <= 4.8e-176:
		tmp = y * 4.0
	elif z <= 4.3e-38:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif z <= 1.75e+99:
		tmp = -6.0 * (y * z)
	elif z <= 7.8e+244:
		tmp = x * (z * 6.0)
	else:
		tmp = y * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.15)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -7.5e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= -2e-233)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.1e-300)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.1e-229)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.8e-176)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.3e-38)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.75e+99)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= 7.8e+244)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = Float64(y * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.15)
		tmp = 6.0 * (x * z);
	elseif (z <= -7.5e-181)
		tmp = y * 4.0;
	elseif (z <= -2e-233)
		tmp = x * -3.0;
	elseif (z <= -1.1e-300)
		tmp = y * 4.0;
	elseif (z <= 1.1e-229)
		tmp = x * -3.0;
	elseif (z <= 4.8e-176)
		tmp = y * 4.0;
	elseif (z <= 4.3e-38)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif (z <= 1.75e+99)
		tmp = -6.0 * (y * z);
	elseif (z <= 7.8e+244)
		tmp = x * (z * 6.0);
	else
		tmp = y * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.15], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.5e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2e-233], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.1e-300], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.1e-229], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.8e-176], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.3e-38], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.75e+99], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.8e+244], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -0.149999999999999994

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 59.4%

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

      1. sub-neg 59.4%

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

      2. distribute-rgt-in 59.4%

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

      3. metadata-eval 59.4%

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

      4. distribute-lft-neg-in 59.4%

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

      5. associate-+r+ 59.4%

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

      6. metadata-eval 59.4%

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

      7. *-commutative 59.4%

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

      8. distribute-lft-neg-in 59.4%

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

      9. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around inf 58.1%

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

      1. *-commutative 58.1%

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

   10. Simplified 58.1%

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

   if -0.149999999999999994 < z < -7.5000000000000002e-181 or -1.99999999999999992e-233 < z < -1.10000000000000001e-300 or 1.0999999999999999e-229 < z < 4.80000000000000012e-176 or 4.3000000000000002e-38 < z < 0.650000000000000022

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in z around 0 96.2%

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

      1. distribute-rgt-in 96.2%

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

      2. associate-+r+ 96.2%

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

      3. *-commutative 96.2%

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

      4. associate-*r* 96.3%

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

      5. metadata-eval 96.3%

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

      6. distribute-rgt1-in 96.3%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      7. metadata-eval 96.3%

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

      8. *-commutative 96.3%

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

      9. *-commutative 96.3%

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

      10. associate-*l* 96.5%

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

      11. metadata-eval 96.5%

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

   8. Simplified 96.5%

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

   9. Taylor expanded in x around 0 69.5%

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

       1. *-commutative 69.5%

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

   11. Simplified 69.5%

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

   if -7.5000000000000002e-181 < z < -1.99999999999999992e-233 or -1.10000000000000001e-300 < z < 1.0999999999999999e-229 or 4.80000000000000012e-176 < z < 4.3000000000000002e-38

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 67.7%

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

      1. sub-neg 67.7%

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

      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. distribute-lft-neg-in 67.7%

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

      5. associate-+r+ 67.7%

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

      6. metadata-eval 67.7%

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

      7. *-commutative 67.7%

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

      8. distribute-lft-neg-in 67.7%

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

      9. metadata-eval 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   10. Simplified 67.7%

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

   if 0.650000000000000022 < z < 1.7499999999999999e99

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 94.8%

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

   6. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

   8. Simplified 84.7%

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

   9. Taylor expanded in z around inf 76.4%

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

   if 1.7499999999999999e99 < z < 7.8000000000000001e244

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 59.5%

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

      1. sub-neg 59.5%

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

      2. distribute-rgt-in 59.5%

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

      3. metadata-eval 59.5%

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

      4. distribute-lft-neg-in 59.5%

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

      5. associate-+r+ 59.5%

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

      6. metadata-eval 59.5%

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

      7. *-commutative 59.5%

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

      8. distribute-lft-neg-in 59.5%

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

      9. metadata-eval 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in z around inf 59.5%

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

   if 7.8000000000000001e244 < 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. Add Preprocessing

   5. Taylor expanded in y around inf 84.0%

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

   6. Taylor expanded in y around inf 63.6%

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

      1. *-commutative 63.6%

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

   8. Simplified 63.6%

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

   9. Taylor expanded in z around inf 63.6%

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

       1. *-commutative 63.6%

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

       2. associate-*r* 63.7%

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

   11. Simplified 63.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.15:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.5 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-300}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-38}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+99}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-238}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-302}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-37}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.75)
   (* 6.0 (* x z))
   (if (<= z -6.6e-182)
     (* y 4.0)
     (if (<= z -2.4e-238)
       (* x -3.0)
       (if (<= z -3e-302)
         (* y 4.0)
         (if (<= z 2.4e-231)
           (* x -3.0)
           (if (<= z 4.5e-176)
             (* y 4.0)
             (if (<= z 7.6e-37)
               (* x -3.0)
               (if (<= z 0.65)
                 (* y 4.0)
                 (if (<= z 5.4e+97)
                   (* z (* y -6.0))
                   (if (<= z 3.5e+245)
                     (* x (* z 6.0))
                     (* y (* z -6.0)))))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.75) {
		tmp = 6.0 * (x * z);
	} else if (z <= -6.6e-182) {
		tmp = y * 4.0;
	} else if (z <= -2.4e-238) {
		tmp = x * -3.0;
	} else if (z <= -3e-302) {
		tmp = y * 4.0;
	} else if (z <= 2.4e-231) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-176) {
		tmp = y * 4.0;
	} else if (z <= 7.6e-37) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 5.4e+97) {
		tmp = z * (y * -6.0);
	} else if (z <= 3.5e+245) {
		tmp = x * (z * 6.0);
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.75d0)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-6.6d-182)) then
        tmp = y * 4.0d0
    else if (z <= (-2.4d-238)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3d-302)) then
        tmp = y * 4.0d0
    else if (z <= 2.4d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 4.5d-176) then
        tmp = y * 4.0d0
    else if (z <= 7.6d-37) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else if (z <= 5.4d+97) then
        tmp = z * (y * (-6.0d0))
    else if (z <= 3.5d+245) then
        tmp = x * (z * 6.0d0)
    else
        tmp = y * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.75) {
		tmp = 6.0 * (x * z);
	} else if (z <= -6.6e-182) {
		tmp = y * 4.0;
	} else if (z <= -2.4e-238) {
		tmp = x * -3.0;
	} else if (z <= -3e-302) {
		tmp = y * 4.0;
	} else if (z <= 2.4e-231) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-176) {
		tmp = y * 4.0;
	} else if (z <= 7.6e-37) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else if (z <= 5.4e+97) {
		tmp = z * (y * -6.0);
	} else if (z <= 3.5e+245) {
		tmp = x * (z * 6.0);
	} else {
		tmp = y * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.75:
		tmp = 6.0 * (x * z)
	elif z <= -6.6e-182:
		tmp = y * 4.0
	elif z <= -2.4e-238:
		tmp = x * -3.0
	elif z <= -3e-302:
		tmp = y * 4.0
	elif z <= 2.4e-231:
		tmp = x * -3.0
	elif z <= 4.5e-176:
		tmp = y * 4.0
	elif z <= 7.6e-37:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	elif z <= 5.4e+97:
		tmp = z * (y * -6.0)
	elif z <= 3.5e+245:
		tmp = x * (z * 6.0)
	else:
		tmp = y * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.75)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -6.6e-182)
		tmp = Float64(y * 4.0);
	elseif (z <= -2.4e-238)
		tmp = Float64(x * -3.0);
	elseif (z <= -3e-302)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.4e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.5e-176)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.6e-37)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.4e+97)
		tmp = Float64(z * Float64(y * -6.0));
	elseif (z <= 3.5e+245)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = Float64(y * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.75)
		tmp = 6.0 * (x * z);
	elseif (z <= -6.6e-182)
		tmp = y * 4.0;
	elseif (z <= -2.4e-238)
		tmp = x * -3.0;
	elseif (z <= -3e-302)
		tmp = y * 4.0;
	elseif (z <= 2.4e-231)
		tmp = x * -3.0;
	elseif (z <= 4.5e-176)
		tmp = y * 4.0;
	elseif (z <= 7.6e-37)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	elseif (z <= 5.4e+97)
		tmp = z * (y * -6.0);
	elseif (z <= 3.5e+245)
		tmp = x * (z * 6.0);
	else
		tmp = y * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.75], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.6e-182], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -2.4e-238], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3e-302], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.4e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.5e-176], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.6e-37], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.4e+97], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.5e+245], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -0.75

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in x around inf 59.4%

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

      1. sub-neg 59.4%

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

      2. distribute-rgt-in 59.4%

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

      3. metadata-eval 59.4%

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

      4. distribute-lft-neg-in 59.4%

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

      5. associate-+r+ 59.4%

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

      6. metadata-eval 59.4%

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

      7. *-commutative 59.4%

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

      8. distribute-lft-neg-in 59.4%

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

      9. metadata-eval 59.4%

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

   7. Simplified 59.4%

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

   8. Taylor expanded in z around inf 58.1%

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

      1. *-commutative 58.1%

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

   10. Simplified 58.1%

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

   if -0.75 < z < -6.59999999999999991e-182 or -2.3999999999999998e-238 < z < -2.99999999999999989e-302 or 2.39999999999999992e-231 < z < 4.5e-176 or 7.6000000000000008e-37 < z < 0.650000000000000022

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in z around 0 96.2%

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

      1. distribute-rgt-in 96.2%

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

      2. associate-+r+ 96.2%

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

      3. *-commutative 96.2%

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

      4. associate-*r* 96.3%

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

      5. metadata-eval 96.3%

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

      6. distribute-rgt1-in 96.3%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      7. metadata-eval 96.3%

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

      8. *-commutative 96.3%

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

      9. *-commutative 96.3%

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

      10. associate-*l* 96.5%

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

      11. metadata-eval 96.5%

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

   8. Simplified 96.5%

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

   9. Taylor expanded in x around 0 69.5%

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

       1. *-commutative 69.5%

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

   11. Simplified 69.5%

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

   if -6.59999999999999991e-182 < z < -2.3999999999999998e-238 or -2.99999999999999989e-302 < z < 2.39999999999999992e-231 or 4.5e-176 < z < 7.6000000000000008e-37

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 67.7%

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

      1. sub-neg 67.7%

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

      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. distribute-lft-neg-in 67.7%

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

      5. associate-+r+ 67.7%

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

      6. metadata-eval 67.7%

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

      7. *-commutative 67.7%

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

      8. distribute-lft-neg-in 67.7%

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

      9. metadata-eval 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   10. Simplified 67.7%

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

   if 0.650000000000000022 < z < 5.39999999999999987e97

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 94.8%

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

   6. Taylor expanded in y around inf 84.7%

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

      1. *-commutative 84.7%

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

   8. Simplified 84.7%

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

   9. Taylor expanded in z around inf 76.4%

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

       1. associate-*r* 76.4%

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

       2. *-commutative 76.4%

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

   11. Simplified 76.4%

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

   if 5.39999999999999987e97 < z < 3.49999999999999985e245

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around inf 59.5%

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

      1. sub-neg 59.5%

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

      2. distribute-rgt-in 59.5%

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

      3. metadata-eval 59.5%

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

      4. distribute-lft-neg-in 59.5%

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

      5. associate-+r+ 59.5%

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

      6. metadata-eval 59.5%

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

      7. *-commutative 59.5%

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

      8. distribute-lft-neg-in 59.5%

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

      9. metadata-eval 59.5%

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

   7. Simplified 59.5%

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

   8. Taylor expanded in z around inf 59.5%

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

   if 3.49999999999999985e245 < 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. Add Preprocessing

   5. Taylor expanded in y around inf 84.0%

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

   6. Taylor expanded in y around inf 63.6%

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

      1. *-commutative 63.6%

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

   8. Simplified 63.6%

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

   9. Taylor expanded in z around inf 63.6%

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

       1. *-commutative 63.6%

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

       2. associate-*r* 63.7%

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

   11. Simplified 63.7%

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

4. Final simplification 65.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.75:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-238}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-302}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.4 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-37}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{+97}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq 3.5 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 50.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -25500:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-304}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-40}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -25500.0)
     t_0
     (if (<= z -5e-184)
       (* y 4.0)
       (if (<= z -3.7e-233)
         (* x -3.0)
         (if (<= z -2.6e-304)
           (* y 4.0)
           (if (<= z 3.9e-231)
             (* x -3.0)
             (if (<= z 6.5e-177)
               (* y 4.0)
               (if (<= z 1.8e-40)
                 (* x -3.0)
                 (if (<= z 0.65) (* y 4.0) t_0))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -25500.0) {
		tmp = t_0;
	} else if (z <= -5e-184) {
		tmp = y * 4.0;
	} else if (z <= -3.7e-233) {
		tmp = x * -3.0;
	} else if (z <= -2.6e-304) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-231) {
		tmp = x * -3.0;
	} else if (z <= 6.5e-177) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-40) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-25500.0d0)) then
        tmp = t_0
    else if (z <= (-5d-184)) then
        tmp = y * 4.0d0
    else if (z <= (-3.7d-233)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.6d-304)) then
        tmp = y * 4.0d0
    else if (z <= 3.9d-231) then
        tmp = x * (-3.0d0)
    else if (z <= 6.5d-177) then
        tmp = y * 4.0d0
    else if (z <= 1.8d-40) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -25500.0) {
		tmp = t_0;
	} else if (z <= -5e-184) {
		tmp = y * 4.0;
	} else if (z <= -3.7e-233) {
		tmp = x * -3.0;
	} else if (z <= -2.6e-304) {
		tmp = y * 4.0;
	} else if (z <= 3.9e-231) {
		tmp = x * -3.0;
	} else if (z <= 6.5e-177) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-40) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -25500.0:
		tmp = t_0
	elif z <= -5e-184:
		tmp = y * 4.0
	elif z <= -3.7e-233:
		tmp = x * -3.0
	elif z <= -2.6e-304:
		tmp = y * 4.0
	elif z <= 3.9e-231:
		tmp = x * -3.0
	elif z <= 6.5e-177:
		tmp = y * 4.0
	elif z <= 1.8e-40:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -25500.0)
		tmp = t_0;
	elseif (z <= -5e-184)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.7e-233)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.6e-304)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.9e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.5e-177)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.8e-40)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -25500.0)
		tmp = t_0;
	elseif (z <= -5e-184)
		tmp = y * 4.0;
	elseif (z <= -3.7e-233)
		tmp = x * -3.0;
	elseif (z <= -2.6e-304)
		tmp = y * 4.0;
	elseif (z <= 3.9e-231)
		tmp = x * -3.0;
	elseif (z <= 6.5e-177)
		tmp = y * 4.0;
	elseif (z <= 1.8e-40)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -25500.0], t$95$0, If[LessEqual[z, -5e-184], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.7e-233], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.6e-304], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.9e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.5e-177], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.8e-40], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -25500 or 0.650000000000000022 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 81.9%

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

   6. Taylor expanded in y around inf 52.8%

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

      1. *-commutative 52.8%

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

   8. Simplified 52.8%

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

   9. Taylor expanded in z around inf 51.5%

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

   if -25500 < z < -5.00000000000000003e-184 or -3.6999999999999998e-233 < z < -2.59999999999999997e-304 or 3.8999999999999998e-231 < z < 6.4999999999999998e-177 or 1.8e-40 < z < 0.650000000000000022

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in z around 0 95.1%

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

      1. distribute-rgt-in 95.1%

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

      2. associate-+r+ 95.1%

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

      3. *-commutative 95.1%

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

      4. associate-*r* 95.2%

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

      5. metadata-eval 95.2%

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

      6. distribute-rgt1-in 95.2%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      7. metadata-eval 95.2%

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

      8. *-commutative 95.2%

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

      9. *-commutative 95.2%

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

      10. associate-*l* 95.4%

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

      11. metadata-eval 95.4%

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

   8. Simplified 95.4%

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

   9. Taylor expanded in x around 0 68.6%

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

       1. *-commutative 68.6%

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

   11. Simplified 68.6%

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

   if -5.00000000000000003e-184 < z < -3.6999999999999998e-233 or -2.59999999999999997e-304 < z < 3.8999999999999998e-231 or 6.4999999999999998e-177 < z < 1.8e-40

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 67.7%

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

      1. sub-neg 67.7%

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

      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. distribute-lft-neg-in 67.7%

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

      5. associate-+r+ 67.7%

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

      6. metadata-eval 67.7%

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

      7. *-commutative 67.7%

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

      8. distribute-lft-neg-in 67.7%

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

      9. metadata-eval 67.7%

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

   7. Simplified 67.7%

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

   8. Taylor expanded in z around 0 67.7%

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

      1. *-commutative 67.7%

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

   10. Simplified 67.7%

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

4. Final simplification 60.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -25500:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-184}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-233}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-304}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-40}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 57.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+200}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+77} \lor \neg \left(x \leq 2.2 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.4e+247)
   (* x -3.0)
   (if (<= x -3.2e+200)
     (* 6.0 (* x z))
     (if (or (<= x -1.3e+77) (not (<= x 2.2e+35)))
       (* x -3.0)
       (* 6.0 (* y (- 0.6666666666666666 z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e+247) {
		tmp = x * -3.0;
	} else if (x <= -3.2e+200) {
		tmp = 6.0 * (x * z);
	} else if ((x <= -1.3e+77) || !(x <= 2.2e+35)) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.4d+247)) then
        tmp = x * (-3.0d0)
    else if (x <= (-3.2d+200)) then
        tmp = 6.0d0 * (x * z)
    else if ((x <= (-1.3d+77)) .or. (.not. (x <= 2.2d+35))) then
        tmp = x * (-3.0d0)
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.4e+247) {
		tmp = x * -3.0;
	} else if (x <= -3.2e+200) {
		tmp = 6.0 * (x * z);
	} else if ((x <= -1.3e+77) || !(x <= 2.2e+35)) {
		tmp = x * -3.0;
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.4e+247:
		tmp = x * -3.0
	elif x <= -3.2e+200:
		tmp = 6.0 * (x * z)
	elif (x <= -1.3e+77) or not (x <= 2.2e+35):
		tmp = x * -3.0
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.4e+247)
		tmp = Float64(x * -3.0);
	elseif (x <= -3.2e+200)
		tmp = Float64(6.0 * Float64(x * z));
	elseif ((x <= -1.3e+77) || !(x <= 2.2e+35))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.4e+247)
		tmp = x * -3.0;
	elseif (x <= -3.2e+200)
		tmp = 6.0 * (x * z);
	elseif ((x <= -1.3e+77) || ~((x <= 2.2e+35)))
		tmp = x * -3.0;
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.4e+247], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, -3.2e+200], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -1.3e+77], N[Not[LessEqual[x, 2.2e+35]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.40000000000000022e247 or -3.20000000000000031e200 < x < -1.3000000000000001e77 or 2.1999999999999999e35 < x

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 84.1%

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

      1. sub-neg 84.1%

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

      2. distribute-rgt-in 84.1%

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

      3. metadata-eval 84.1%

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

      4. distribute-lft-neg-in 84.1%

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

      5. associate-+r+ 84.1%

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

      6. metadata-eval 84.1%

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

      7. *-commutative 84.1%

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

      8. distribute-lft-neg-in 84.1%

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

      9. metadata-eval 84.1%

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

   7. Simplified 84.1%

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

   8. Taylor expanded in z around 0 50.7%

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

      1. *-commutative 50.7%

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

   10. Simplified 50.7%

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

   if -4.40000000000000022e247 < x < -3.20000000000000031e200

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 93.2%

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

      1. sub-neg 93.2%

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

      2. distribute-rgt-in 93.2%

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

      3. metadata-eval 93.2%

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

      4. distribute-lft-neg-in 93.2%

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

      5. associate-+r+ 93.2%

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

      6. metadata-eval 93.2%

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

      7. *-commutative 93.2%

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

      8. distribute-lft-neg-in 93.2%

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

      9. metadata-eval 93.2%

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

   7. Simplified 93.2%

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

   8. Taylor expanded in z around inf 83.5%

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

      1. *-commutative 83.5%

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

   10. Simplified 83.5%

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

   if -1.3000000000000001e77 < x < 2.1999999999999999e35

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 95.5%

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

   6. Taylor expanded in y around inf 75.4%

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

      1. *-commutative 75.4%

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

   8. Simplified 75.4%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.4 \cdot 10^{+247}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq -3.2 \cdot 10^{+200}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq -1.3 \cdot 10^{+77} \lor \neg \left(x \leq 2.2 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.52)))
   (* z (+ (* y -6.0) (* x 6.0)))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.52)) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else {
		tmp = (x * -3.0) + (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 ((z <= (-0.6d0)) .or. (.not. (z <= 0.52d0))) then
        tmp = z * ((y * (-6.0d0)) + (x * 6.0d0))
    else
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.52)) {
		tmp = z * ((y * -6.0) + (x * 6.0));
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.52):
		tmp = z * ((y * -6.0) + (x * 6.0))
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.52))
		tmp = Float64(z * Float64(Float64(y * -6.0) + Float64(x * 6.0)));
	else
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.52)))
		tmp = z * ((y * -6.0) + (x * 6.0));
	else
		tmp = (x * -3.0) + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.52]], $MachinePrecision]], N[(z * N[(N[(y * -6.0), $MachinePrecision] + N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.52000000000000002 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 99.7%

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

   6. Taylor expanded in z around inf 97.6%

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

      1. mul-1-neg 97.6%

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

      2. fma-define 97.6%

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

      3. distribute-rgt-neg-in 97.6%

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

      4. fma-define 97.6%

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

      5. +-commutative 97.6%

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

      6. distribute-neg-in 97.6%

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

      7. distribute-lft-neg-in 97.6%

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

      8. metadata-eval 97.6%

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

      9. distribute-rgt-neg-in 97.6%

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

      10. mul-1-neg 97.6%

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

      11. distribute-lft-in 97.6%

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

      12. mul-1-neg 97.6%

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

      13. sub-neg 97.6%

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

   8. Simplified 97.6%

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

   9. Taylor expanded in y around 0 97.6%

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

   10. Taylor expanded in z around inf 97.7%

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

   if -0.599999999999999978 < z < 0.52000000000000002

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in z around 0 97.6%

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

      1. distribute-rgt-in 97.6%

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

      2. associate-+r+ 97.6%

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

      3. *-commutative 97.6%

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

      4. associate-*r* 97.8%

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

      5. metadata-eval 97.8%

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

      6. distribute-rgt1-in 97.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      7. metadata-eval 97.8%

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

      8. *-commutative 97.8%

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

      9. *-commutative 97.8%

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

      10. associate-*l* 98.0%

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

      11. metadata-eval 98.0%

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

   8. Simplified 98.0%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.5% accurate, 0.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + (-6.0 * ((y - x) * z));
	} else if (z <= 0.65) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * ((y * -6.0) + (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 <= (-0.65d0)) then
        tmp = x + ((-6.0d0) * ((y - x) * z))
    else if (z <= 0.65d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = z * ((y * (-6.0d0)) + (x * 6.0d0))
    end if
    code = tmp
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around inf 98.2%

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

   if -0.650000000000000022 < z < 0.650000000000000022

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in z around 0 97.6%

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

      1. distribute-rgt-in 97.6%

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

      2. associate-+r+ 97.6%

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

      3. *-commutative 97.6%

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

      4. associate-*r* 97.8%

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

      5. metadata-eval 97.8%

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

      6. distribute-rgt1-in 97.8%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      7. metadata-eval 97.8%

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

      8. *-commutative 97.8%

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

      9. *-commutative 97.8%

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

      10. associate-*l* 98.0%

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

      11. metadata-eval 98.0%

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

   8. Simplified 98.0%

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

   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. Add Preprocessing

   5. Taylor expanded in y around 0 99.8%

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

   6. Taylor expanded in z around inf 97.1%

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

      1. mul-1-neg 97.1%

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

      2. fma-define 97.1%

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

      3. distribute-rgt-neg-in 97.1%

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

      4. fma-define 97.1%

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

      5. +-commutative 97.1%

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

      6. distribute-neg-in 97.1%

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

      7. distribute-lft-neg-in 97.1%

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

      8. metadata-eval 97.1%

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

      9. distribute-rgt-neg-in 97.1%

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

      10. mul-1-neg 97.1%

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

      11. distribute-lft-in 97.1%

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

      12. mul-1-neg 97.1%

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

      13. sub-neg 97.1%

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

   8. Simplified 97.1%

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

   9. Taylor expanded in y around 0 97.1%

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

   10. Taylor expanded in z around inf 97.1%

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

4. Final simplification 97.8%

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

Alternative 11: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -310000000000 \lor \neg \left(x \leq 3 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -310000000000.0) (not (<= x 3e+32)))
   (* x (+ -3.0 (* z 6.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -310000000000.0) || !(x <= 3e+32)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-310000000000.0d0)) .or. (.not. (x <= 3d+32))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -310000000000.0) || !(x <= 3e+32)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -310000000000.0) or not (x <= 3e+32):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -310000000000.0) || !(x <= 3e+32))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -310000000000.0) || ~((x <= 3e+32)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -310000000000.0], N[Not[LessEqual[x, 3e+32]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e11 or 3e32 < 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. Add Preprocessing

   5. Taylor expanded in x around inf 81.9%

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

      1. sub-neg 81.9%

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

      2. distribute-rgt-in 81.9%

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

      3. metadata-eval 81.9%

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

      4. distribute-lft-neg-in 81.9%

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

      5. associate-+r+ 81.9%

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

      6. metadata-eval 81.9%

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

      7. *-commutative 81.9%

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

      8. distribute-lft-neg-in 81.9%

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

      9. metadata-eval 81.9%

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

   7. Simplified 81.9%

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

   if -3.1e11 < x < 3e32

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 97.7%

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

   6. Taylor expanded in y around inf 78.9%

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

      1. *-commutative 78.9%

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

   8. Simplified 78.9%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -310000000000 \lor \neg \left(x \leq 3 \cdot 10^{+32}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 76.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -310000000000 \lor \neg \left(x \leq 9.8 \cdot 10^{+27}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -310000000000.0) (not (<= x 9.8e+27)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -310000000000.0) || !(x <= 9.8e+27)) {
		tmp = x * (-3.0 + (z * 6.0));
	} 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 <= (-310000000000.0d0)) .or. (.not. (x <= 9.8d+27))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    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 <= -310000000000.0) || !(x <= 9.8e+27)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -310000000000.0) or not (x <= 9.8e+27):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -310000000000.0) || !(x <= 9.8e+27))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	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 <= -310000000000.0) || ~((x <= 9.8e+27)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -310000000000.0], N[Not[LessEqual[x, 9.8e+27]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $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 < -3.1e11 or 9.8000000000000003e27 < 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. Add Preprocessing

   5. Taylor expanded in x around inf 81.9%

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

      1. sub-neg 81.9%

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

      2. distribute-rgt-in 81.9%

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

      3. metadata-eval 81.9%

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

      4. distribute-lft-neg-in 81.9%

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

      5. associate-+r+ 81.9%

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

      6. metadata-eval 81.9%

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

      7. *-commutative 81.9%

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

      8. distribute-lft-neg-in 81.9%

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

      9. metadata-eval 81.9%

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

   7. Simplified 81.9%

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

   if -3.1e11 < x < 9.8000000000000003e27

   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* 99.7%

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

      3. fma-define 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. Add Preprocessing

   5. Taylor expanded in y around inf 79.2%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -310000000000 \lor \neg \left(x \leq 9.8 \cdot 10^{+27}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 38.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -310000000000 \lor \neg \left(x \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -310000000000.0) (not (<= x 2e+35))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -310000000000.0) || !(x <= 2e+35)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-310000000000.0d0)) .or. (.not. (x <= 2d+35))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -310000000000.0) || !(x <= 2e+35)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -310000000000.0) or not (x <= 2e+35):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -310000000000.0) || !(x <= 2e+35))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -310000000000.0) || ~((x <= 2e+35)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -310000000000.0], N[Not[LessEqual[x, 2e+35]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e11 or 1.9999999999999999e35 < 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. Add Preprocessing

   5. Taylor expanded in x around inf 81.8%

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

      1. sub-neg 81.8%

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

      2. distribute-rgt-in 81.8%

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

      3. metadata-eval 81.8%

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

      4. distribute-lft-neg-in 81.8%

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

      5. associate-+r+ 81.8%

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

      6. metadata-eval 81.8%

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

      7. *-commutative 81.8%

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

      8. distribute-lft-neg-in 81.8%

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

      9. metadata-eval 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in z around 0 44.7%

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

      1. *-commutative 44.7%

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

   10. Simplified 44.7%

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

   if -3.1e11 < x < 1.9999999999999999e35

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 99.6%

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

   6. Taylor expanded in z around 0 48.4%

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

      1. distribute-rgt-in 48.4%

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

      2. associate-+r+ 48.4%

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

      3. *-commutative 48.4%

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

      4. associate-*r* 48.4%

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

      5. metadata-eval 48.4%

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

      6. distribute-rgt1-in 48.4%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      7. metadata-eval 48.4%

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

      8. *-commutative 48.4%

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

      9. *-commutative 48.4%

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

      10. associate-*l* 48.6%

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

      11. metadata-eval 48.6%

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

   8. Simplified 48.6%

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

   9. Taylor expanded in x around 0 40.7%

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

       1. *-commutative 40.7%

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

   11. Simplified 40.7%

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

4. Final simplification 42.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -310000000000 \lor \neg \left(x \leq 2 \cdot 10^{+35}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around 0 99.6%

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

6. Final simplification 99.6%

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

Alternative 15: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 16: 26.4% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in x around inf 47.9%

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

   1. sub-neg 47.9%

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

   2. distribute-rgt-in 47.9%

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

   3. metadata-eval 47.9%

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

   4. distribute-lft-neg-in 47.9%

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

   5. associate-+r+ 47.9%

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

   6. metadata-eval 47.9%

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

   7. *-commutative 47.9%

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

   8. distribute-lft-neg-in 47.9%

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

   9. metadata-eval 47.9%

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

7. Simplified 47.9%

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

8. Taylor expanded in z around 0 25.3%

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

   1. *-commutative 25.3%

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

10. Simplified 25.3%

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

11. Final simplification 25.3%

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

Alternative 17: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around 0 99.6%

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

6. Taylor expanded in z around inf 49.4%

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

   1. mul-1-neg 49.4%

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

   2. fma-define 49.4%

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

   3. distribute-rgt-neg-in 49.4%

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

   4. fma-define 49.4%

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

   5. +-commutative 49.4%

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

   6. distribute-neg-in 49.4%

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

   7. distribute-lft-neg-in 49.4%

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

   8. metadata-eval 49.4%

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

   9. distribute-rgt-neg-in 49.4%

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

   10. mul-1-neg 49.4%

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

   11. distribute-lft-in 49.4%

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

   12. mul-1-neg 49.4%

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

   13. sub-neg 49.4%

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

8. Simplified 49.4%

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

9. Taylor expanded in z around 0 2.4%

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

10. Final simplification 2.4%

    \[\leadsto x \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024067 
(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))))