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

Percentage Accurate: 99.5% → 99.5%

Time: 10.7s

Alternatives: 14

Speedup: 1.2×

• 21.6% 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: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $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. Final simplification 99.6%

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

Alternative 2: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-119}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-232}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-250}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-58}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+108} \lor \neg \left(z \leq 5 \cdot 10^{+233}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -350000000.0)
     t_0
     (if (<= z -5e-119)
       (* x -3.0)
       (if (<= z -1.1e-232)
         (* y 4.0)
         (if (<= z 5.2e-250)
           (* x -3.0)
           (if (<= z 4.2e-58)
             (* y 4.0)
             (if (<= z 1860.0)
               (* x -3.0)
               (if (or (<= z 8.6e+108) (not (<= z 5e+233)))
                 (* 6.0 (* x z))
                 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -350000000.0) {
		tmp = t_0;
	} else if (z <= -5e-119) {
		tmp = x * -3.0;
	} else if (z <= -1.1e-232) {
		tmp = y * 4.0;
	} else if (z <= 5.2e-250) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-58) {
		tmp = y * 4.0;
	} else if (z <= 1860.0) {
		tmp = x * -3.0;
	} else if ((z <= 8.6e+108) || !(z <= 5e+233)) {
		tmp = 6.0 * (x * 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) * (y * z)
    if (z <= (-350000000.0d0)) then
        tmp = t_0
    else if (z <= (-5d-119)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.1d-232)) then
        tmp = y * 4.0d0
    else if (z <= 5.2d-250) then
        tmp = x * (-3.0d0)
    else if (z <= 4.2d-58) then
        tmp = y * 4.0d0
    else if (z <= 1860.0d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 8.6d+108) .or. (.not. (z <= 5d+233))) then
        tmp = 6.0d0 * (x * 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 * (y * z);
	double tmp;
	if (z <= -350000000.0) {
		tmp = t_0;
	} else if (z <= -5e-119) {
		tmp = x * -3.0;
	} else if (z <= -1.1e-232) {
		tmp = y * 4.0;
	} else if (z <= 5.2e-250) {
		tmp = x * -3.0;
	} else if (z <= 4.2e-58) {
		tmp = y * 4.0;
	} else if (z <= 1860.0) {
		tmp = x * -3.0;
	} else if ((z <= 8.6e+108) || !(z <= 5e+233)) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -350000000.0:
		tmp = t_0
	elif z <= -5e-119:
		tmp = x * -3.0
	elif z <= -1.1e-232:
		tmp = y * 4.0
	elif z <= 5.2e-250:
		tmp = x * -3.0
	elif z <= 4.2e-58:
		tmp = y * 4.0
	elif z <= 1860.0:
		tmp = x * -3.0
	elif (z <= 8.6e+108) or not (z <= 5e+233):
		tmp = 6.0 * (x * z)
	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 <= -350000000.0)
		tmp = t_0;
	elseif (z <= -5e-119)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.1e-232)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.2e-250)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.2e-58)
		tmp = Float64(y * 4.0);
	elseif (z <= 1860.0)
		tmp = Float64(x * -3.0);
	elseif ((z <= 8.6e+108) || !(z <= 5e+233))
		tmp = Float64(6.0 * Float64(x * z));
	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 <= -350000000.0)
		tmp = t_0;
	elseif (z <= -5e-119)
		tmp = x * -3.0;
	elseif (z <= -1.1e-232)
		tmp = y * 4.0;
	elseif (z <= 5.2e-250)
		tmp = x * -3.0;
	elseif (z <= 4.2e-58)
		tmp = y * 4.0;
	elseif (z <= 1860.0)
		tmp = x * -3.0;
	elseif ((z <= 8.6e+108) || ~((z <= 5e+233)))
		tmp = 6.0 * (x * z);
	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, -350000000.0], t$95$0, If[LessEqual[z, -5e-119], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.1e-232], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.2e-250], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.2e-58], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1860.0], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 8.6e+108], N[Not[LessEqual[z, 5e+233]], $MachinePrecision]], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5e8 or 8.59999999999999993e108 < z < 5.00000000000000009e233

   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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 66.7%

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

   8. Taylor expanded in z around inf 66.3%

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

      1. *-commutative 66.3%

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

   10. Simplified 66.3%

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

   if -3.5e8 < z < -4.99999999999999993e-119 or -1.10000000000000001e-232 < z < 5.20000000000000016e-250 or 4.19999999999999975e-58 < z < 1860

   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 70.9%

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

      1. sub-neg 70.9%

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

      2. distribute-rgt-in 71.0%

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

      3. metadata-eval 71.0%

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

      4. distribute-lft-neg-in 71.0%

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

      5. associate-+r+ 71.0%

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

      6. metadata-eval 71.0%

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

      7. distribute-rgt-neg-in 71.0%

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

      8. metadata-eval 71.0%

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

   7. Simplified 71.0%

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

   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 -4.99999999999999993e-119 < z < -1.10000000000000001e-232 or 5.20000000000000016e-250 < z < 4.19999999999999975e-58

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 72.7%

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

   8. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   10. Simplified 72.9%

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

   if 1860 < z < 8.59999999999999993e108 or 5.00000000000000009e233 < 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 x around inf 70.2%

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

      1. sub-neg 70.2%

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

      2. distribute-rgt-in 70.2%

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

      3. metadata-eval 70.2%

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

      4. distribute-lft-neg-in 70.2%

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

      5. associate-+r+ 70.2%

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

      6. metadata-eval 70.2%

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

      7. distribute-rgt-neg-in 70.2%

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

      8. metadata-eval 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around inf 70.8%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-119}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{-232}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-250}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.2 \cdot 10^{-58}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.6 \cdot 10^{+108} \lor \neg \left(z \leq 5 \cdot 10^{+233}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-118}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-231}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-58}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+108} \lor \neg \left(z \leq 4.3 \cdot 10^{+234}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -350000000.0)
   (* y (* z -6.0))
   (if (<= z -2.2e-118)
     (* x -3.0)
     (if (<= z -1.95e-231)
       (* y 4.0)
       (if (<= z 1e-253)
         (* x -3.0)
         (if (<= z 5.4e-58)
           (* y 4.0)
           (if (<= z 1860.0)
             (* x -3.0)
             (if (or (<= z 2.1e+108) (not (<= z 4.3e+234)))
               (* 6.0 (* x z))
               (* -6.0 (* y z))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -350000000.0) {
		tmp = y * (z * -6.0);
	} else if (z <= -2.2e-118) {
		tmp = x * -3.0;
	} else if (z <= -1.95e-231) {
		tmp = y * 4.0;
	} else if (z <= 1e-253) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-58) {
		tmp = y * 4.0;
	} else if (z <= 1860.0) {
		tmp = x * -3.0;
	} else if ((z <= 2.1e+108) || !(z <= 4.3e+234)) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-350000000.0d0)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-2.2d-118)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.95d-231)) then
        tmp = y * 4.0d0
    else if (z <= 1d-253) then
        tmp = x * (-3.0d0)
    else if (z <= 5.4d-58) then
        tmp = y * 4.0d0
    else if (z <= 1860.0d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 2.1d+108) .or. (.not. (z <= 4.3d+234))) then
        tmp = 6.0d0 * (x * z)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -350000000.0) {
		tmp = y * (z * -6.0);
	} else if (z <= -2.2e-118) {
		tmp = x * -3.0;
	} else if (z <= -1.95e-231) {
		tmp = y * 4.0;
	} else if (z <= 1e-253) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-58) {
		tmp = y * 4.0;
	} else if (z <= 1860.0) {
		tmp = x * -3.0;
	} else if ((z <= 2.1e+108) || !(z <= 4.3e+234)) {
		tmp = 6.0 * (x * z);
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -350000000.0:
		tmp = y * (z * -6.0)
	elif z <= -2.2e-118:
		tmp = x * -3.0
	elif z <= -1.95e-231:
		tmp = y * 4.0
	elif z <= 1e-253:
		tmp = x * -3.0
	elif z <= 5.4e-58:
		tmp = y * 4.0
	elif z <= 1860.0:
		tmp = x * -3.0
	elif (z <= 2.1e+108) or not (z <= 4.3e+234):
		tmp = 6.0 * (x * z)
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -350000000.0)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -2.2e-118)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.95e-231)
		tmp = Float64(y * 4.0);
	elseif (z <= 1e-253)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.4e-58)
		tmp = Float64(y * 4.0);
	elseif (z <= 1860.0)
		tmp = Float64(x * -3.0);
	elseif ((z <= 2.1e+108) || !(z <= 4.3e+234))
		tmp = Float64(6.0 * Float64(x * z));
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -350000000.0)
		tmp = y * (z * -6.0);
	elseif (z <= -2.2e-118)
		tmp = x * -3.0;
	elseif (z <= -1.95e-231)
		tmp = y * 4.0;
	elseif (z <= 1e-253)
		tmp = x * -3.0;
	elseif (z <= 5.4e-58)
		tmp = y * 4.0;
	elseif (z <= 1860.0)
		tmp = x * -3.0;
	elseif ((z <= 2.1e+108) || ~((z <= 4.3e+234)))
		tmp = 6.0 * (x * z);
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -350000000.0], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-118], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.95e-231], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1e-253], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.4e-58], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1860.0], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 2.1e+108], N[Not[LessEqual[z, 4.3e+234]], $MachinePrecision]], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.5e8

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 67.3%

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

   8. Taylor expanded in z around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-*r* 66.8%

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

   10. Simplified 66.8%

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

   if -3.5e8 < z < -2.19999999999999984e-118 or -1.9499999999999999e-231 < z < 1.0000000000000001e-253 or 5.3999999999999998e-58 < z < 1860

   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 70.9%

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

      1. sub-neg 70.9%

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

      2. distribute-rgt-in 71.0%

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

      3. metadata-eval 71.0%

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

      4. distribute-lft-neg-in 71.0%

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

      5. associate-+r+ 71.0%

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

      6. metadata-eval 71.0%

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

      7. distribute-rgt-neg-in 71.0%

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

      8. metadata-eval 71.0%

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

   7. Simplified 71.0%

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

   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 -2.19999999999999984e-118 < z < -1.9499999999999999e-231 or 1.0000000000000001e-253 < z < 5.3999999999999998e-58

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 72.7%

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

   8. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   10. Simplified 72.9%

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

   if 1860 < z < 2.1000000000000001e108 or 4.2999999999999998e234 < 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 x around inf 70.2%

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

      1. sub-neg 70.2%

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

      2. distribute-rgt-in 70.2%

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

      3. metadata-eval 70.2%

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

      4. distribute-lft-neg-in 70.2%

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

      5. associate-+r+ 70.2%

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

      6. metadata-eval 70.2%

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

      7. distribute-rgt-neg-in 70.2%

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

      8. metadata-eval 70.2%

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

   7. Simplified 70.2%

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

   8. Taylor expanded in z around inf 70.8%

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

   if 2.1000000000000001e108 < z < 4.2999999999999998e234

   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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 65.2%

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

   8. Taylor expanded in z around inf 65.2%

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

      1. *-commutative 65.2%

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

   10. Simplified 65.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-118}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.95 \cdot 10^{-231}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-58}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{+108} \lor \neg \left(z \leq 4.3 \cdot 10^{+234}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-118}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-232}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-254}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+231}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -350000000.0)
   (* y (* z -6.0))
   (if (<= z -1.32e-118)
     (* x -3.0)
     (if (<= z -1.5e-232)
       (* y 4.0)
       (if (<= z 2.25e-254)
         (* x -3.0)
         (if (<= z 1.6e-57)
           (* y 4.0)
           (if (<= z 1860.0)
             (* x -3.0)
             (if (<= z 1.9e+109)
               (* z (* x 6.0))
               (if (<= z 1.4e+231) (* -6.0 (* y z)) (* 6.0 (* x z)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -350000000.0) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.32e-118) {
		tmp = x * -3.0;
	} else if (z <= -1.5e-232) {
		tmp = y * 4.0;
	} else if (z <= 2.25e-254) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-57) {
		tmp = y * 4.0;
	} else if (z <= 1860.0) {
		tmp = x * -3.0;
	} else if (z <= 1.9e+109) {
		tmp = z * (x * 6.0);
	} else if (z <= 1.4e+231) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-350000000.0d0)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-1.32d-118)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.5d-232)) then
        tmp = y * 4.0d0
    else if (z <= 2.25d-254) then
        tmp = x * (-3.0d0)
    else if (z <= 1.6d-57) then
        tmp = y * 4.0d0
    else if (z <= 1860.0d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1.9d+109) then
        tmp = z * (x * 6.0d0)
    else if (z <= 1.4d+231) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -350000000.0) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.32e-118) {
		tmp = x * -3.0;
	} else if (z <= -1.5e-232) {
		tmp = y * 4.0;
	} else if (z <= 2.25e-254) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-57) {
		tmp = y * 4.0;
	} else if (z <= 1860.0) {
		tmp = x * -3.0;
	} else if (z <= 1.9e+109) {
		tmp = z * (x * 6.0);
	} else if (z <= 1.4e+231) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -350000000.0:
		tmp = y * (z * -6.0)
	elif z <= -1.32e-118:
		tmp = x * -3.0
	elif z <= -1.5e-232:
		tmp = y * 4.0
	elif z <= 2.25e-254:
		tmp = x * -3.0
	elif z <= 1.6e-57:
		tmp = y * 4.0
	elif z <= 1860.0:
		tmp = x * -3.0
	elif z <= 1.9e+109:
		tmp = z * (x * 6.0)
	elif z <= 1.4e+231:
		tmp = -6.0 * (y * z)
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -350000000.0)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -1.32e-118)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.5e-232)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.25e-254)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.6e-57)
		tmp = Float64(y * 4.0);
	elseif (z <= 1860.0)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.9e+109)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= 1.4e+231)
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -350000000.0)
		tmp = y * (z * -6.0);
	elseif (z <= -1.32e-118)
		tmp = x * -3.0;
	elseif (z <= -1.5e-232)
		tmp = y * 4.0;
	elseif (z <= 2.25e-254)
		tmp = x * -3.0;
	elseif (z <= 1.6e-57)
		tmp = y * 4.0;
	elseif (z <= 1860.0)
		tmp = x * -3.0;
	elseif (z <= 1.9e+109)
		tmp = z * (x * 6.0);
	elseif (z <= 1.4e+231)
		tmp = -6.0 * (y * z);
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -350000000.0], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.32e-118], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.5e-232], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.25e-254], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.6e-57], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1860.0], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.9e+109], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.4e+231], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.5e8

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 67.3%

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

   8. Taylor expanded in z around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-*r* 66.8%

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

   10. Simplified 66.8%

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

   if -3.5e8 < z < -1.32000000000000003e-118 or -1.49999999999999995e-232 < z < 2.25e-254 or 1.6e-57 < z < 1860

   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 70.9%

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

      1. sub-neg 70.9%

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

      2. distribute-rgt-in 71.0%

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

      3. metadata-eval 71.0%

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

      4. distribute-lft-neg-in 71.0%

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

      5. associate-+r+ 71.0%

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

      6. metadata-eval 71.0%

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

      7. distribute-rgt-neg-in 71.0%

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

      8. metadata-eval 71.0%

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

   7. Simplified 71.0%

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

   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 -1.32000000000000003e-118 < z < -1.49999999999999995e-232 or 2.25e-254 < z < 1.6e-57

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 72.7%

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

   8. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   10. Simplified 72.9%

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

   if 1860 < z < 1.90000000000000019e109

   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 70.1%

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

      1. sub-neg 70.1%

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

      2. distribute-rgt-in 70.1%

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

      3. metadata-eval 70.1%

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

      4. distribute-lft-neg-in 70.1%

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

      5. associate-+r+ 70.1%

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

      6. metadata-eval 70.1%

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

      7. distribute-rgt-neg-in 70.1%

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

      8. metadata-eval 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*r* 66.8%

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

   10. Simplified 66.8%

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

   11. Taylor expanded in x around 0 66.9%

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

       1. associate-*r* 66.9%

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

       2. *-commutative 66.9%

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

       3. *-commutative 66.9%

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

   13. Simplified 66.9%

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

   if 1.90000000000000019e109 < z < 1.4e231

   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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around inf 65.2%

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

   8. Taylor expanded in z around inf 65.2%

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

      1. *-commutative 65.2%

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

   10. Simplified 65.2%

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

   if 1.4e231 < z

   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 70.4%

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

      1. sub-neg 70.4%

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

      2. distribute-rgt-in 70.4%

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

      3. metadata-eval 70.4%

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

      4. distribute-lft-neg-in 70.4%

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

      5. associate-+r+ 70.4%

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

      6. metadata-eval 70.4%

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

      7. distribute-rgt-neg-in 70.4%

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

      8. metadata-eval 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in z around inf 75.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.32 \cdot 10^{-118}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-232}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.25 \cdot 10^{-254}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.9 \cdot 10^{+109}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{+231}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-119}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-232}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-250}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+233}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -350000000.0)
   (* y (* z -6.0))
   (if (<= z -2.2e-119)
     (* x -3.0)
     (if (<= z -2.8e-232)
       (* y 4.0)
       (if (<= z 1.8e-250)
         (* x -3.0)
         (if (<= z 2e-57)
           (* y 4.0)
           (if (<= z 1860.0)
             (* x -3.0)
             (if (<= z 2.45e+107)
               (* z (* x 6.0))
               (if (<= z 3.9e+233) (* z (* y -6.0)) (* 6.0 (* x z)))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -350000000.0) {
		tmp = y * (z * -6.0);
	} else if (z <= -2.2e-119) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-232) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-250) {
		tmp = x * -3.0;
	} else if (z <= 2e-57) {
		tmp = y * 4.0;
	} else if (z <= 1860.0) {
		tmp = x * -3.0;
	} else if (z <= 2.45e+107) {
		tmp = z * (x * 6.0);
	} else if (z <= 3.9e+233) {
		tmp = z * (y * -6.0);
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-350000000.0d0)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-2.2d-119)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.8d-232)) then
        tmp = y * 4.0d0
    else if (z <= 1.8d-250) then
        tmp = x * (-3.0d0)
    else if (z <= 2d-57) then
        tmp = y * 4.0d0
    else if (z <= 1860.0d0) then
        tmp = x * (-3.0d0)
    else if (z <= 2.45d+107) then
        tmp = z * (x * 6.0d0)
    else if (z <= 3.9d+233) then
        tmp = z * (y * (-6.0d0))
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -350000000.0) {
		tmp = y * (z * -6.0);
	} else if (z <= -2.2e-119) {
		tmp = x * -3.0;
	} else if (z <= -2.8e-232) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-250) {
		tmp = x * -3.0;
	} else if (z <= 2e-57) {
		tmp = y * 4.0;
	} else if (z <= 1860.0) {
		tmp = x * -3.0;
	} else if (z <= 2.45e+107) {
		tmp = z * (x * 6.0);
	} else if (z <= 3.9e+233) {
		tmp = z * (y * -6.0);
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -350000000.0:
		tmp = y * (z * -6.0)
	elif z <= -2.2e-119:
		tmp = x * -3.0
	elif z <= -2.8e-232:
		tmp = y * 4.0
	elif z <= 1.8e-250:
		tmp = x * -3.0
	elif z <= 2e-57:
		tmp = y * 4.0
	elif z <= 1860.0:
		tmp = x * -3.0
	elif z <= 2.45e+107:
		tmp = z * (x * 6.0)
	elif z <= 3.9e+233:
		tmp = z * (y * -6.0)
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -350000000.0)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -2.2e-119)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.8e-232)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.8e-250)
		tmp = Float64(x * -3.0);
	elseif (z <= 2e-57)
		tmp = Float64(y * 4.0);
	elseif (z <= 1860.0)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.45e+107)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= 3.9e+233)
		tmp = Float64(z * Float64(y * -6.0));
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -350000000.0)
		tmp = y * (z * -6.0);
	elseif (z <= -2.2e-119)
		tmp = x * -3.0;
	elseif (z <= -2.8e-232)
		tmp = y * 4.0;
	elseif (z <= 1.8e-250)
		tmp = x * -3.0;
	elseif (z <= 2e-57)
		tmp = y * 4.0;
	elseif (z <= 1860.0)
		tmp = x * -3.0;
	elseif (z <= 2.45e+107)
		tmp = z * (x * 6.0);
	elseif (z <= 3.9e+233)
		tmp = z * (y * -6.0);
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -350000000.0], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.2e-119], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.8e-232], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.8e-250], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2e-57], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1860.0], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.45e+107], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 3.9e+233], N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.5e8

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 67.3%

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

   8. Taylor expanded in z around inf 66.7%

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

      1. *-commutative 66.7%

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

      2. associate-*r* 66.8%

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

   10. Simplified 66.8%

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

   if -3.5e8 < z < -2.2000000000000001e-119 or -2.79999999999999993e-232 < z < 1.79999999999999991e-250 or 1.99999999999999991e-57 < z < 1860

   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 70.9%

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

      1. sub-neg 70.9%

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

      2. distribute-rgt-in 71.0%

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

      3. metadata-eval 71.0%

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

      4. distribute-lft-neg-in 71.0%

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

      5. associate-+r+ 71.0%

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

      6. metadata-eval 71.0%

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

      7. distribute-rgt-neg-in 71.0%

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

      8. metadata-eval 71.0%

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

   7. Simplified 71.0%

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

   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 -2.2000000000000001e-119 < z < -2.79999999999999993e-232 or 1.79999999999999991e-250 < z < 1.99999999999999991e-57

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 72.7%

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

   8. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   10. Simplified 72.9%

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

   if 1860 < z < 2.4500000000000001e107

   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 70.1%

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

      1. sub-neg 70.1%

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

      2. distribute-rgt-in 70.1%

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

      3. metadata-eval 70.1%

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

      4. distribute-lft-neg-in 70.1%

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

      5. associate-+r+ 70.1%

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

      6. metadata-eval 70.1%

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

      7. distribute-rgt-neg-in 70.1%

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

      8. metadata-eval 70.1%

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

   7. Simplified 70.1%

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

   8. Taylor expanded in z around inf 66.9%

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

      1. *-commutative 66.9%

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

      2. associate-*r* 66.8%

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

   10. Simplified 66.8%

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

   11. Taylor expanded in x around 0 66.9%

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

       1. associate-*r* 66.9%

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

       2. *-commutative 66.9%

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

       3. *-commutative 66.9%

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

   13. Simplified 66.9%

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

   if 2.4500000000000001e107 < z < 3.8999999999999999e233

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

   6. Taylor expanded in z around inf 99.8%

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

   7. Taylor expanded in y around inf 65.3%

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

      1. *-commutative 65.3%

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

   9. Simplified 65.3%

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

   if 3.8999999999999999e233 < z

   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 70.4%

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

      1. sub-neg 70.4%

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

      2. distribute-rgt-in 70.4%

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

      3. metadata-eval 70.4%

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

      4. distribute-lft-neg-in 70.4%

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

      5. associate-+r+ 70.4%

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

      6. metadata-eval 70.4%

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

      7. distribute-rgt-neg-in 70.4%

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

      8. metadata-eval 70.4%

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

   7. Simplified 70.4%

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

   8. Taylor expanded in z around inf 75.2%

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

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.2 \cdot 10^{-119}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-232}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-250}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1860:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.45 \cdot 10^{+107}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 3.9 \cdot 10^{+233}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -5.4 \cdot 10^{-12}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-120}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-231}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -5.4e-12)
     t_0
     (if (<= z -1.8e-120)
       (* x -3.0)
       (if (<= z -1.4e-231)
         (* y 4.0)
         (if (<= z 9.2e-253)
           (* x -3.0)
           (if (<= z 1.6e-57) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -5.4e-12) {
		tmp = t_0;
	} else if (z <= -1.8e-120) {
		tmp = x * -3.0;
	} else if (z <= -1.4e-231) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-253) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-57) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-5.4d-12)) then
        tmp = t_0
    else if (z <= (-1.8d-120)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.4d-231)) then
        tmp = y * 4.0d0
    else if (z <= 9.2d-253) then
        tmp = x * (-3.0d0)
    else if (z <= 1.6d-57) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -5.4e-12) {
		tmp = t_0;
	} else if (z <= -1.8e-120) {
		tmp = x * -3.0;
	} else if (z <= -1.4e-231) {
		tmp = y * 4.0;
	} else if (z <= 9.2e-253) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-57) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -5.4e-12:
		tmp = t_0
	elif z <= -1.8e-120:
		tmp = x * -3.0
	elif z <= -1.4e-231:
		tmp = y * 4.0
	elif z <= 9.2e-253:
		tmp = x * -3.0
	elif z <= 1.6e-57:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -5.4e-12)
		tmp = t_0;
	elseif (z <= -1.8e-120)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.4e-231)
		tmp = Float64(y * 4.0);
	elseif (z <= 9.2e-253)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.6e-57)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -5.4e-12)
		tmp = t_0;
	elseif (z <= -1.8e-120)
		tmp = x * -3.0;
	elseif (z <= -1.4e-231)
		tmp = y * 4.0;
	elseif (z <= 9.2e-253)
		tmp = x * -3.0;
	elseif (z <= 1.6e-57)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.4e-12], t$95$0, If[LessEqual[z, -1.8e-120], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.4e-231], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 9.2e-253], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.6e-57], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -5.39999999999999961e-12 or 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 97.0%

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

   if -5.39999999999999961e-12 < z < -1.8000000000000001e-120 or -1.3999999999999999e-231 < z < 9.2000000000000001e-253 or 1.6e-57 < z < 0.5

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 74.6%

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

      1. sub-neg 74.6%

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

      2. distribute-rgt-in 74.6%

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

      3. metadata-eval 74.6%

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

      4. distribute-lft-neg-in 74.6%

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

      5. associate-+r+ 74.6%

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

      6. metadata-eval 74.6%

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

      7. distribute-rgt-neg-in 74.6%

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

      8. metadata-eval 74.6%

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

   7. Simplified 74.6%

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

   8. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   10. Simplified 72.9%

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

   if -1.8000000000000001e-120 < z < -1.3999999999999999e-231 or 9.2000000000000001e-253 < z < 1.6e-57

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 72.7%

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

   8. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   10. Simplified 72.9%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.4 \cdot 10^{-12}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-120}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-231}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 9.2 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-57}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 49.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-119}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-232}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-58}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -350000000.0)
     t_0
     (if (<= z -1.02e-119)
       (* x -3.0)
       (if (<= z -1.52e-232)
         (* y 4.0)
         (if (<= z 1.22e-253)
           (* x -3.0)
           (if (<= z 5.9e-58) (* y 4.0) (if (<= z 0.58) (* x -3.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -350000000.0) {
		tmp = t_0;
	} else if (z <= -1.02e-119) {
		tmp = x * -3.0;
	} else if (z <= -1.52e-232) {
		tmp = y * 4.0;
	} else if (z <= 1.22e-253) {
		tmp = x * -3.0;
	} else if (z <= 5.9e-58) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-350000000.0d0)) then
        tmp = t_0
    else if (z <= (-1.02d-119)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.52d-232)) then
        tmp = y * 4.0d0
    else if (z <= 1.22d-253) then
        tmp = x * (-3.0d0)
    else if (z <= 5.9d-58) then
        tmp = y * 4.0d0
    else if (z <= 0.58d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -350000000.0) {
		tmp = t_0;
	} else if (z <= -1.02e-119) {
		tmp = x * -3.0;
	} else if (z <= -1.52e-232) {
		tmp = y * 4.0;
	} else if (z <= 1.22e-253) {
		tmp = x * -3.0;
	} else if (z <= 5.9e-58) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -350000000.0:
		tmp = t_0
	elif z <= -1.02e-119:
		tmp = x * -3.0
	elif z <= -1.52e-232:
		tmp = y * 4.0
	elif z <= 1.22e-253:
		tmp = x * -3.0
	elif z <= 5.9e-58:
		tmp = y * 4.0
	elif z <= 0.58:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -350000000.0)
		tmp = t_0;
	elseif (z <= -1.02e-119)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.52e-232)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.22e-253)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.9e-58)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.58)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -350000000.0)
		tmp = t_0;
	elseif (z <= -1.02e-119)
		tmp = x * -3.0;
	elseif (z <= -1.52e-232)
		tmp = y * 4.0;
	elseif (z <= 1.22e-253)
		tmp = x * -3.0;
	elseif (z <= 5.9e-58)
		tmp = y * 4.0;
	elseif (z <= 0.58)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -350000000.0], t$95$0, If[LessEqual[z, -1.02e-119], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.52e-232], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.22e-253], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.9e-58], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.58], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.5e8 or 0.57999999999999996 < 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. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.8%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 57.2%

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

   8. Taylor expanded in z around inf 55.8%

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

      1. *-commutative 55.8%

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

   10. Simplified 55.8%

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

   if -3.5e8 < z < -1.02e-119 or -1.52e-232 < z < 1.22e-253 or 5.9e-58 < z < 0.57999999999999996

   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 73.6%

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

      1. sub-neg 73.6%

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

      2. distribute-rgt-in 73.7%

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

      3. metadata-eval 73.7%

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

      4. distribute-lft-neg-in 73.7%

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

      5. associate-+r+ 73.7%

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

      6. metadata-eval 73.7%

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

      7. distribute-rgt-neg-in 73.7%

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

      8. metadata-eval 73.7%

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

   7. Simplified 73.7%

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

   8. Taylor expanded in z around 0 70.3%

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

      1. *-commutative 70.3%

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

   10. Simplified 70.3%

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

   if -1.02e-119 < z < -1.52e-232 or 1.22e-253 < z < 5.9e-58

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*r* 99.5%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 72.7%

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

   8. Taylor expanded in z around 0 72.9%

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

      1. *-commutative 72.9%

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

   10. Simplified 72.9%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -350000000:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.02 \cdot 10^{-119}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.52 \cdot 10^{-232}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.22 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.9 \cdot 10^{-58}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -63000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-231}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-58}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -63000.0)
     t_0
     (if (<= z -5.6e-231)
       (* 6.0 (* y (- 0.6666666666666666 z)))
       (if (<= z 1.28e-253)
         (* x -3.0)
         (if (<= z 6.8e-58) (* y 4.0) (if (<= z 0.5) (* x -3.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -63000.0) {
		tmp = t_0;
	} else if (z <= -5.6e-231) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= 1.28e-253) {
		tmp = x * -3.0;
	} else if (z <= 6.8e-58) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-63000.0d0)) then
        tmp = t_0
    else if (z <= (-5.6d-231)) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else if (z <= 1.28d-253) then
        tmp = x * (-3.0d0)
    else if (z <= 6.8d-58) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -63000.0) {
		tmp = t_0;
	} else if (z <= -5.6e-231) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= 1.28e-253) {
		tmp = x * -3.0;
	} else if (z <= 6.8e-58) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -63000.0:
		tmp = t_0
	elif z <= -5.6e-231:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	elif z <= 1.28e-253:
		tmp = x * -3.0
	elif z <= 6.8e-58:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -63000.0)
		tmp = t_0;
	elseif (z <= -5.6e-231)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	elseif (z <= 1.28e-253)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.8e-58)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -63000.0)
		tmp = t_0;
	elseif (z <= -5.6e-231)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	elseif (z <= 1.28e-253)
		tmp = x * -3.0;
	elseif (z <= 6.8e-58)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -63000.0], t$95$0, If[LessEqual[z, -5.6e-231], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.28e-253], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.8e-58], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -63000 or 0.5 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

      1. +-commutative 99.8%

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

      2. *-commutative 99.8%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in z around inf 97.6%

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

   if -63000 < z < -5.5999999999999997e-231

   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. Step-by-step derivation

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.4%

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

      4. fma-define 99.3%

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

   6. Applied egg-rr 99.3%

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

   7. Taylor expanded in y around inf 62.5%

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

   if -5.5999999999999997e-231 < z < 1.28e-253 or 6.79999999999999947e-58 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 79.2%

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

      1. sub-neg 79.2%

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

      2. distribute-rgt-in 79.2%

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

      3. metadata-eval 79.2%

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

      4. distribute-lft-neg-in 79.2%

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

      5. associate-+r+ 79.2%

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

      6. metadata-eval 79.2%

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

      7. distribute-rgt-neg-in 79.2%

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

      8. metadata-eval 79.2%

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

   7. Simplified 79.2%

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

   8. Taylor expanded in z around 0 76.8%

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

      1. *-commutative 76.8%

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

   10. Simplified 76.8%

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

   if 1.28e-253 < z < 6.79999999999999947e-58

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. +-commutative 99.5%

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

      2. *-commutative 99.5%

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

      3. associate-*r* 99.6%

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

      4. fma-define 99.5%

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

   6. Applied egg-rr 99.5%

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

   7. Taylor expanded in y around inf 68.6%

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

   8. Taylor expanded in z around 0 68.9%

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

      1. *-commutative 68.9%

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

   10. Simplified 68.9%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -63000:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-231}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq 1.28 \cdot 10^{-253}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-58}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+46} \lor \neg \left(x \leq 2.6 \cdot 10^{-53}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.02e+46) (not (<= x 2.6e-53)))
   (* x (+ -3.0 (* 6.0 z)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.02e+46) || !(x <= 2.6e-53)) {
		tmp = x * (-3.0 + (6.0 * z));
	} 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 <= (-1.02d+46)) .or. (.not. (x <= 2.6d-53))) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    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 <= -1.02e+46) || !(x <= 2.6e-53)) {
		tmp = x * (-3.0 + (6.0 * z));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.02e+46) or not (x <= 2.6e-53):
		tmp = x * (-3.0 + (6.0 * z))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.02e+46) || !(x <= 2.6e-53))
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	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 <= -1.02e+46) || ~((x <= 2.6e-53)))
		tmp = x * (-3.0 + (6.0 * z));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.02e+46], N[Not[LessEqual[x, 2.6e-53]], $MachinePrecision]], N[(x * N[(-3.0 + N[(6.0 * z), $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 < -1.0199999999999999e46 or 2.59999999999999996e-53 < x

   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 81.4%

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

      1. sub-neg 81.4%

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

      2. distribute-rgt-in 81.4%

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

      3. metadata-eval 81.4%

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

      4. distribute-lft-neg-in 81.4%

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

      5. associate-+r+ 81.4%

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

      6. metadata-eval 81.4%

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

      7. distribute-rgt-neg-in 81.4%

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

      8. metadata-eval 81.4%

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

   7. Simplified 81.4%

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

   if -1.0199999999999999e46 < x < 2.59999999999999996e-53

   1. Initial program 99.6%

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

      1. 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. Step-by-step derivation

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.6%

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

      4. fma-define 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 81.1%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.02 \cdot 10^{+46} \lor \neg \left(x \leq 2.6 \cdot 10^{-53}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+50} \lor \neg \left(x \leq 8.2 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6 + 4\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -9.2e+50) (not (<= x 8.2e-56)))
   (* x (+ -3.0 (* 6.0 z)))
   (* y (+ (* z -6.0) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.2e+50) || !(x <= 8.2e-56)) {
		tmp = x * (-3.0 + (6.0 * z));
	} else {
		tmp = y * ((z * -6.0) + 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-9.2d+50)) .or. (.not. (x <= 8.2d-56))) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else
        tmp = y * ((z * (-6.0d0)) + 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -9.2e+50) || !(x <= 8.2e-56)) {
		tmp = x * (-3.0 + (6.0 * z));
	} else {
		tmp = y * ((z * -6.0) + 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -9.2e+50) or not (x <= 8.2e-56):
		tmp = x * (-3.0 + (6.0 * z))
	else:
		tmp = y * ((z * -6.0) + 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -9.2e+50) || !(x <= 8.2e-56))
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	else
		tmp = Float64(y * Float64(Float64(z * -6.0) + 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -9.2e+50) || ~((x <= 8.2e-56)))
		tmp = x * (-3.0 + (6.0 * z));
	else
		tmp = y * ((z * -6.0) + 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -9.2e+50], N[Not[LessEqual[x, 8.2e-56]], $MachinePrecision]], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(z * -6.0), $MachinePrecision] + 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -9.19999999999999987e50 or 8.2000000000000003e-56 < x

   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 81.4%

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

      1. sub-neg 81.4%

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

      2. distribute-rgt-in 81.4%

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

      3. metadata-eval 81.4%

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

      4. distribute-lft-neg-in 81.4%

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

      5. associate-+r+ 81.4%

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

      6. metadata-eval 81.4%

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

      7. distribute-rgt-neg-in 81.4%

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

      8. metadata-eval 81.4%

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

   7. Simplified 81.4%

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

   if -9.19999999999999987e50 < x < 8.2000000000000003e-56

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.1%

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

      3. fma-define 99.1%

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

      4. sub-neg 99.1%

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

      5. distribute-rgt-in 99.1%

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

      6. metadata-eval 99.1%

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

      7. metadata-eval 99.1%

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

      8. distribute-lft-neg-out 99.1%

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

      9. distribute-rgt-neg-in 99.1%

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

      10. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around inf 81.3%

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

4. Final simplification 81.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{+50} \lor \neg \left(x \leq 8.2 \cdot 10^{-56}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(z \cdot -6 + 4\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* (- y x) (* z -6.0))
   (if (<= z 0.52) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.52d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.52) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.52:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.52)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.52)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.52], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

      1. +-commutative 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r* 99.7%

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

      4. fma-define 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in z around inf 98.6%

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

      1. *-commutative 98.6%

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

      2. associate-*r* 98.6%

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

      3. *-commutative 98.6%

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

      4. associate-*l* 98.6%

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

   9. Simplified 98.6%

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

   if -0.57999999999999996 < 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 z around 0 98.6%

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

   if 0.52000000000000002 < 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 z around inf 99.9%

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

   6. Taylor expanded in z around inf 96.8%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 38.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+43} \lor \neg \left(x \leq 3.3 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.05e+43) (not (<= x 3.3e-41))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.05e+43) || !(x <= 3.3e-41)) {
		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 <= (-2.05d+43)) .or. (.not. (x <= 3.3d-41))) 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 <= -2.05e+43) || !(x <= 3.3e-41)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.05e+43) or not (x <= 3.3e-41):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.05e+43) || !(x <= 3.3e-41))
		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 <= -2.05e+43) || ~((x <= 3.3e-41)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.05e+43], N[Not[LessEqual[x, 3.3e-41]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.05e43 or 3.30000000000000024e-41 < x

   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 81.4%

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

      1. sub-neg 81.4%

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

      2. distribute-rgt-in 81.4%

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

      3. metadata-eval 81.4%

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

      4. distribute-lft-neg-in 81.4%

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

      5. associate-+r+ 81.4%

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

      6. metadata-eval 81.4%

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

      7. distribute-rgt-neg-in 81.4%

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

      8. metadata-eval 81.4%

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

   7. Simplified 81.4%

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

   8. Taylor expanded in z around 0 40.8%

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

      1. *-commutative 40.8%

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

   10. Simplified 40.8%

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

   if -2.05e43 < x < 3.30000000000000024e-41

   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. Step-by-step derivation

      1. +-commutative 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.6%

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

      4. fma-define 99.6%

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

   6. Applied egg-rr 99.6%

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

   7. Taylor expanded in y around inf 81.1%

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

   8. Taylor expanded in z around 0 37.3%

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

      1. *-commutative 37.3%

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

   10. Simplified 37.3%

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

4. Final simplification 38.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{+43} \lor \neg \left(x \leq 3.3 \cdot 10^{-41}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 26.5% 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 46.7%

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

   1. sub-neg 46.7%

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

   2. distribute-rgt-in 46.7%

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

   3. metadata-eval 46.7%

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

   4. distribute-lft-neg-in 46.7%

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

   5. associate-+r+ 46.7%

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

   6. metadata-eval 46.7%

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

   7. distribute-rgt-neg-in 46.7%

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

   8. metadata-eval 46.7%

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

7. Simplified 46.7%

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

8. Taylor expanded in z around 0 22.8%

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

   1. *-commutative 22.8%

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

10. Simplified 22.8%

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

11. Final simplification 22.8%

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

Alternative 14: 2.5% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around inf 54.8%

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

   1. associate-*r* 54.8%

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

7. Simplified 54.8%

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

8. Taylor expanded in x around inf 2.7%

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

9. Final simplification 2.7%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(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))))