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

Percentage Accurate: 99.5% → 99.7%

Time: 11.5s

Alternatives: 14

Speedup: 1.2×

• 20.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in z around 0 99.8%

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

6. Final simplification 99.8%

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

Alternative 2: 49.3% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(z \cdot y\right)\\ t_2 := x \cdot \left(z \cdot 6\right)\\ t_3 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8 \cdot 10^{+129}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+86}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -0.0195:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-292}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-239}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+229}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+303}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0)))
        (t_1 (* -6.0 (* z y)))
        (t_2 (* x (* z 6.0)))
        (t_3 (* 6.0 (* x z))))
   (if (<= z -8e+129)
     t_1
     (if (<= z -1.7e+86)
       t_3
       (if (<= z -8.5e+68)
         (* z (* -6.0 y))
         (if (<= z -1.45e+41)
           t_2
           (if (<= z -0.0195)
             t_1
             (if (<= z -8.5e-292)
               t_0
               (if (<= z 1.85e-239)
                 (* x -3.0)
                 (if (<= z 6.1e-171)
                   t_0
                   (if (<= z 0.5)
                     (* x -3.0)
                     (if (<= z 9.5e+229)
                       t_2
                       (if (<= z 1.75e+303) t_1 t_3)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * (z * y);
	double t_2 = x * (z * 6.0);
	double t_3 = 6.0 * (x * z);
	double tmp;
	if (z <= -8e+129) {
		tmp = t_1;
	} else if (z <= -1.7e+86) {
		tmp = t_3;
	} else if (z <= -8.5e+68) {
		tmp = z * (-6.0 * y);
	} else if (z <= -1.45e+41) {
		tmp = t_2;
	} else if (z <= -0.0195) {
		tmp = t_1;
	} else if (z <= -8.5e-292) {
		tmp = t_0;
	} else if (z <= 1.85e-239) {
		tmp = x * -3.0;
	} else if (z <= 6.1e-171) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 9.5e+229) {
		tmp = t_2;
	} else if (z <= 1.75e+303) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: t_3
    real(8) :: tmp
    t_0 = x + (y * 4.0d0)
    t_1 = (-6.0d0) * (z * y)
    t_2 = x * (z * 6.0d0)
    t_3 = 6.0d0 * (x * z)
    if (z <= (-8d+129)) then
        tmp = t_1
    else if (z <= (-1.7d+86)) then
        tmp = t_3
    else if (z <= (-8.5d+68)) then
        tmp = z * ((-6.0d0) * y)
    else if (z <= (-1.45d+41)) then
        tmp = t_2
    else if (z <= (-0.0195d0)) then
        tmp = t_1
    else if (z <= (-8.5d-292)) then
        tmp = t_0
    else if (z <= 1.85d-239) then
        tmp = x * (-3.0d0)
    else if (z <= 6.1d-171) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 9.5d+229) then
        tmp = t_2
    else if (z <= 1.75d+303) then
        tmp = t_1
    else
        tmp = t_3
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * (z * y);
	double t_2 = x * (z * 6.0);
	double t_3 = 6.0 * (x * z);
	double tmp;
	if (z <= -8e+129) {
		tmp = t_1;
	} else if (z <= -1.7e+86) {
		tmp = t_3;
	} else if (z <= -8.5e+68) {
		tmp = z * (-6.0 * y);
	} else if (z <= -1.45e+41) {
		tmp = t_2;
	} else if (z <= -0.0195) {
		tmp = t_1;
	} else if (z <= -8.5e-292) {
		tmp = t_0;
	} else if (z <= 1.85e-239) {
		tmp = x * -3.0;
	} else if (z <= 6.1e-171) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 9.5e+229) {
		tmp = t_2;
	} else if (z <= 1.75e+303) {
		tmp = t_1;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	t_1 = -6.0 * (z * y)
	t_2 = x * (z * 6.0)
	t_3 = 6.0 * (x * z)
	tmp = 0
	if z <= -8e+129:
		tmp = t_1
	elif z <= -1.7e+86:
		tmp = t_3
	elif z <= -8.5e+68:
		tmp = z * (-6.0 * y)
	elif z <= -1.45e+41:
		tmp = t_2
	elif z <= -0.0195:
		tmp = t_1
	elif z <= -8.5e-292:
		tmp = t_0
	elif z <= 1.85e-239:
		tmp = x * -3.0
	elif z <= 6.1e-171:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 9.5e+229:
		tmp = t_2
	elif z <= 1.75e+303:
		tmp = t_1
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	t_1 = Float64(-6.0 * Float64(z * y))
	t_2 = Float64(x * Float64(z * 6.0))
	t_3 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -8e+129)
		tmp = t_1;
	elseif (z <= -1.7e+86)
		tmp = t_3;
	elseif (z <= -8.5e+68)
		tmp = Float64(z * Float64(-6.0 * y));
	elseif (z <= -1.45e+41)
		tmp = t_2;
	elseif (z <= -0.0195)
		tmp = t_1;
	elseif (z <= -8.5e-292)
		tmp = t_0;
	elseif (z <= 1.85e-239)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.1e-171)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 9.5e+229)
		tmp = t_2;
	elseif (z <= 1.75e+303)
		tmp = t_1;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 4.0);
	t_1 = -6.0 * (z * y);
	t_2 = x * (z * 6.0);
	t_3 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -8e+129)
		tmp = t_1;
	elseif (z <= -1.7e+86)
		tmp = t_3;
	elseif (z <= -8.5e+68)
		tmp = z * (-6.0 * y);
	elseif (z <= -1.45e+41)
		tmp = t_2;
	elseif (z <= -0.0195)
		tmp = t_1;
	elseif (z <= -8.5e-292)
		tmp = t_0;
	elseif (z <= 1.85e-239)
		tmp = x * -3.0;
	elseif (z <= 6.1e-171)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 9.5e+229)
		tmp = t_2;
	elseif (z <= 1.75e+303)
		tmp = t_1;
	else
		tmp = t_3;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$3 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8e+129], t$95$1, If[LessEqual[z, -1.7e+86], t$95$3, If[LessEqual[z, -8.5e+68], N[(z * N[(-6.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.45e+41], t$95$2, If[LessEqual[z, -0.0195], t$95$1, If[LessEqual[z, -8.5e-292], t$95$0, If[LessEqual[z, 1.85e-239], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.1e-171], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9.5e+229], t$95$2, If[LessEqual[z, 1.75e+303], t$95$1, t$95$3]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -8e129 or -1.44999999999999994e41 < z < -0.0195 or 9.5e229 < z < 1.75000000000000008e303

   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 z around 0 99.9%

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

   6. Taylor expanded in z around inf 96.8%

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

      1. associate-*r* 96.6%

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

      2. *-commutative 96.6%

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

   8. Simplified 96.6%

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

   9. Taylor expanded in y around inf 67.0%

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

   if -8e129 < z < -1.6999999999999999e86 or 1.75000000000000008e303 < 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 z around 0 100.0%

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

   6. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + \left(4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, y \cdot z, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]

      2. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, \color{blue}{z \cdot y}, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right) \]

      3. +-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{x \cdot \left(6 \cdot z - 3\right) + 4 \cdot y}\right) \]

      4. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \left(\color{blue}{z \cdot 6} - 3\right) + 4 \cdot y\right) \]

      5. fma-neg 82.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \color{blue}{\mathsf{fma}\left(z, 6, -3\right)} + 4 \cdot y\right) \]

      6. metadata-eval 82.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \mathsf{fma}\left(z, 6, \color{blue}{-3}\right) + 4 \cdot y\right) \]

      7. fma-def 82.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(z, 6, -3\right), 4 \cdot y\right)}\right) \]

      8. fma-udef 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{z \cdot 6 + -3}, 4 \cdot y\right)\right) \]

      9. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{6 \cdot z} + -3, 4 \cdot y\right)\right) \]

      10. fma-udef 82.8%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(6, z, -3\right)}, 4 \cdot y\right)\right) \]

      11. *-commutative 82.8%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), \color{blue}{y \cdot 4}\right)\right) \]

   8. Simplified 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), y \cdot 4\right)\right)} \]

   9. Taylor expanded in z around inf 100.0%

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

       1. distribute-lft-in 83.3%

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

       2. associate-*r* 83.1%

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

       3. *-commutative 83.1%

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

       4. metadata-eval 83.1%

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

       5. distribute-lft-neg-in 83.1%

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

       6. distribute-lft-neg-in 83.1%

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

       7. distribute-rgt-neg-out 83.1%

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

       8. *-commutative 83.1%

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

       9. *-commutative 83.1%

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

       10. associate-*r* 83.3%

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

       11. distribute-rgt-out 100.0%

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

       12. *-commutative 100.0%

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

       13. distribute-rgt-in 100.0%

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

       14. sub-neg 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in y around 0 100.0%

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

       1. *-commutative 100.0%

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

   14. Simplified 100.0%

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

   if -1.6999999999999999e86 < z < -8.49999999999999966e68

   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 z around 0 99.8%

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

   6. Taylor expanded in x around 0 85.5%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + \left(4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 85.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, y \cdot z, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]

      2. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(-6, \color{blue}{z \cdot y}, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right) \]

      3. +-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{x \cdot \left(6 \cdot z - 3\right) + 4 \cdot y}\right) \]

      4. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \left(\color{blue}{z \cdot 6} - 3\right) + 4 \cdot y\right) \]

      5. fma-neg 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \color{blue}{\mathsf{fma}\left(z, 6, -3\right)} + 4 \cdot y\right) \]

      6. metadata-eval 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \mathsf{fma}\left(z, 6, \color{blue}{-3}\right) + 4 \cdot y\right) \]

      7. fma-def 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(z, 6, -3\right), 4 \cdot y\right)}\right) \]

      8. fma-udef 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{z \cdot 6 + -3}, 4 \cdot y\right)\right) \]

      9. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{6 \cdot z} + -3, 4 \cdot y\right)\right) \]

      10. fma-udef 85.3%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(6, z, -3\right)}, 4 \cdot y\right)\right) \]

      11. *-commutative 85.3%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), \color{blue}{y \cdot 4}\right)\right) \]

   8. Simplified 85.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), y \cdot 4\right)\right)} \]

   9. Taylor expanded in z around inf 100.0%

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

       1. distribute-lft-in 85.7%

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

       2. associate-*r* 85.7%

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

       3. *-commutative 85.7%

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

       4. metadata-eval 85.7%

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

       5. distribute-lft-neg-in 85.7%

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

       6. distribute-lft-neg-in 85.7%

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

       7. distribute-rgt-neg-out 85.7%

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

       8. *-commutative 85.7%

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

       9. *-commutative 85.7%

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

       10. associate-*r* 85.7%

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

       11. distribute-rgt-out 100.0%

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

       12. *-commutative 100.0%

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

       13. distribute-rgt-in 100.0%

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

       14. sub-neg 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in y around inf 86.3%

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

   if -8.49999999999999966e68 < z < -1.44999999999999994e41 or 0.5 < z < 9.5e229

   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 61.6%

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

      1. sub-neg 61.6%

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

      2. distribute-rgt-in 61.6%

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

      3. metadata-eval 61.6%

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

      4. metadata-eval 61.6%

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

      5. distribute-lft-neg-in 61.6%

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

      6. associate-+r+ 61.6%

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

      7. metadata-eval 61.6%

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

      8. metadata-eval 61.6%

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

      9. distribute-rgt-neg-in 61.6%

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

      10. metadata-eval 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in z around inf 61.6%

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

   if -0.0195 < z < -8.50000000000000066e-292 or 1.85000000000000008e-239 < z < 6.1e-171

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 58.7%

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

      1. associate-*r* 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in z around 0 57.1%

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

      1. *-commutative 57.1%

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

   10. Simplified 57.1%

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

   if -8.50000000000000066e-292 < z < 1.85000000000000008e-239 or 6.1e-171 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 65.6%

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

      1. sub-neg 65.6%

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

      2. distribute-rgt-in 65.7%

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

      3. metadata-eval 65.7%

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

      4. metadata-eval 65.7%

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

      5. distribute-lft-neg-in 65.7%

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

      6. associate-+r+ 65.7%

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

      7. metadata-eval 65.7%

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

      8. metadata-eval 65.7%

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

      9. distribute-rgt-neg-in 65.7%

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

      10. metadata-eval 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

   10. Simplified 64.1%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 6 regimes into one program.

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8 \cdot 10^{+129}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{+86}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{+68}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{elif}\;z \leq -1.45 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -0.0195:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-292}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-239}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.1 \cdot 10^{-171}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9.5 \cdot 10^{+229}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+303}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 49.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.3 \cdot 10^{+128}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{+69}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -900:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+229} \lor \neg \left(z \leq 2.7 \cdot 10^{+296}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -1.3e+128)
     t_0
     (if (<= z -1.26e+85)
       t_1
       (if (<= z -1.36e+69)
         t_0
         (if (<= z -3.5e+37)
           t_1
           (if (<= z -900.0)
             t_0
             (if (<= z 0.5)
               (* x -3.0)
               (if (or (<= z 8.8e+229) (not (<= z 2.7e+296))) t_1 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.3e+128) {
		tmp = t_0;
	} else if (z <= -1.26e+85) {
		tmp = t_1;
	} else if (z <= -1.36e+69) {
		tmp = t_0;
	} else if (z <= -3.5e+37) {
		tmp = t_1;
	} else if (z <= -900.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 8.8e+229) || !(z <= 2.7e+296)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-1.3d+128)) then
        tmp = t_0
    else if (z <= (-1.26d+85)) then
        tmp = t_1
    else if (z <= (-1.36d+69)) then
        tmp = t_0
    else if (z <= (-3.5d+37)) then
        tmp = t_1
    else if (z <= (-900.0d0)) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 8.8d+229) .or. (.not. (z <= 2.7d+296))) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.3e+128) {
		tmp = t_0;
	} else if (z <= -1.26e+85) {
		tmp = t_1;
	} else if (z <= -1.36e+69) {
		tmp = t_0;
	} else if (z <= -3.5e+37) {
		tmp = t_1;
	} else if (z <= -900.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 8.8e+229) || !(z <= 2.7e+296)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -1.3e+128:
		tmp = t_0
	elif z <= -1.26e+85:
		tmp = t_1
	elif z <= -1.36e+69:
		tmp = t_0
	elif z <= -3.5e+37:
		tmp = t_1
	elif z <= -900.0:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	elif (z <= 8.8e+229) or not (z <= 2.7e+296):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.3e+128)
		tmp = t_0;
	elseif (z <= -1.26e+85)
		tmp = t_1;
	elseif (z <= -1.36e+69)
		tmp = t_0;
	elseif (z <= -3.5e+37)
		tmp = t_1;
	elseif (z <= -900.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif ((z <= 8.8e+229) || !(z <= 2.7e+296))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.3e+128)
		tmp = t_0;
	elseif (z <= -1.26e+85)
		tmp = t_1;
	elseif (z <= -1.36e+69)
		tmp = t_0;
	elseif (z <= -3.5e+37)
		tmp = t_1;
	elseif (z <= -900.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif ((z <= 8.8e+229) || ~((z <= 2.7e+296)))
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.3e+128], t$95$0, If[LessEqual[z, -1.26e+85], t$95$1, If[LessEqual[z, -1.36e+69], t$95$0, If[LessEqual[z, -3.5e+37], t$95$1, If[LessEqual[z, -900.0], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 8.8e+229], N[Not[LessEqual[z, 2.7e+296]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.3e128 or -1.26000000000000003e85 < z < -1.36000000000000006e69 or -3.5e37 < z < -900 or 8.80000000000000014e229 < z < 2.69999999999999986e296

   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 0 99.9%

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

   6. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 71.9%

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

   if -1.3e128 < z < -1.26000000000000003e85 or -1.36000000000000006e69 < z < -3.5e37 or 0.5 < z < 8.80000000000000014e229 or 2.69999999999999986e296 < z

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in x around 0 96.5%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + \left(4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 96.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, y \cdot z, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]

      2. *-commutative 96.5%

         \[\leadsto \mathsf{fma}\left(-6, \color{blue}{z \cdot y}, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right) \]

      3. +-commutative 96.5%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{x \cdot \left(6 \cdot z - 3\right) + 4 \cdot y}\right) \]

      4. *-commutative 96.5%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \left(\color{blue}{z \cdot 6} - 3\right) + 4 \cdot y\right) \]

      5. fma-neg 96.6%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \color{blue}{\mathsf{fma}\left(z, 6, -3\right)} + 4 \cdot y\right) \]

      6. metadata-eval 96.6%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \mathsf{fma}\left(z, 6, \color{blue}{-3}\right) + 4 \cdot y\right) \]

      7. fma-def 96.6%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(z, 6, -3\right), 4 \cdot y\right)}\right) \]

      8. fma-udef 96.5%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{z \cdot 6 + -3}, 4 \cdot y\right)\right) \]

      9. *-commutative 96.5%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{6 \cdot z} + -3, 4 \cdot y\right)\right) \]

      10. fma-udef 96.6%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(6, z, -3\right)}, 4 \cdot y\right)\right) \]

      11. *-commutative 96.6%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), \color{blue}{y \cdot 4}\right)\right) \]

   8. Simplified 96.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), y \cdot 4\right)\right)} \]

   9. Taylor expanded in z around inf 99.6%

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

       1. distribute-lft-in 96.4%

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

       2. associate-*r* 96.5%

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

       3. *-commutative 96.5%

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

       4. metadata-eval 96.5%

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

       5. distribute-lft-neg-in 96.5%

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

       6. distribute-lft-neg-in 96.5%

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

       7. distribute-rgt-neg-out 96.5%

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

       8. *-commutative 96.5%

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

       9. *-commutative 96.5%

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

       10. associate-*r* 96.4%

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

       11. distribute-rgt-out 99.6%

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

       12. *-commutative 99.6%

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

       13. distribute-rgt-in 99.6%

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

       14. sub-neg 99.6%

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

   11. Simplified 99.6%

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

   12. Taylor expanded in y around 0 65.2%

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

       1. *-commutative 65.2%

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

   14. Simplified 65.2%

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

   if -900 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. sub-neg 50.2%

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

      2. distribute-rgt-in 50.2%

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

      3. metadata-eval 50.2%

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

      4. metadata-eval 50.2%

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

      5. distribute-lft-neg-in 50.2%

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

      6. associate-+r+ 50.2%

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

      7. metadata-eval 50.2%

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

      8. metadata-eval 50.2%

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

      9. distribute-rgt-neg-in 50.2%

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

      10. metadata-eval 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in z around 0 48.2%

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

      1. *-commutative 48.2%

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

   10. Simplified 48.2%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.3 \cdot 10^{+128}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.26 \cdot 10^{+85}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{+69}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{+37}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -900:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{+229} \lor \neg \left(z \leq 2.7 \cdot 10^{+296}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 49.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ t_2 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.95 \cdot 10^{+127}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+67}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+37}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -900:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+227}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+295}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* x (* z 6.0))) (t_2 (* 6.0 (* x z))))
   (if (<= z -1.95e+127)
     t_0
     (if (<= z -5.2e+93)
       t_2
       (if (<= z -5.5e+67)
         t_0
         (if (<= z -2.6e+37)
           t_1
           (if (<= z -900.0)
             t_0
             (if (<= z 0.5)
               (* x -3.0)
               (if (<= z 1.75e+227) t_1 (if (<= z 4.5e+295) t_0 t_2))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = x * (z * 6.0);
	double t_2 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.95e+127) {
		tmp = t_0;
	} else if (z <= -5.2e+93) {
		tmp = t_2;
	} else if (z <= -5.5e+67) {
		tmp = t_0;
	} else if (z <= -2.6e+37) {
		tmp = t_1;
	} else if (z <= -900.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 1.75e+227) {
		tmp = t_1;
	} else if (z <= 4.5e+295) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * y)
    t_1 = x * (z * 6.0d0)
    t_2 = 6.0d0 * (x * z)
    if (z <= (-1.95d+127)) then
        tmp = t_0
    else if (z <= (-5.2d+93)) then
        tmp = t_2
    else if (z <= (-5.5d+67)) then
        tmp = t_0
    else if (z <= (-2.6d+37)) then
        tmp = t_1
    else if (z <= (-900.0d0)) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1.75d+227) then
        tmp = t_1
    else if (z <= 4.5d+295) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = x * (z * 6.0);
	double t_2 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.95e+127) {
		tmp = t_0;
	} else if (z <= -5.2e+93) {
		tmp = t_2;
	} else if (z <= -5.5e+67) {
		tmp = t_0;
	} else if (z <= -2.6e+37) {
		tmp = t_1;
	} else if (z <= -900.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 1.75e+227) {
		tmp = t_1;
	} else if (z <= 4.5e+295) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = x * (z * 6.0)
	t_2 = 6.0 * (x * z)
	tmp = 0
	if z <= -1.95e+127:
		tmp = t_0
	elif z <= -5.2e+93:
		tmp = t_2
	elif z <= -5.5e+67:
		tmp = t_0
	elif z <= -2.6e+37:
		tmp = t_1
	elif z <= -900.0:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 1.75e+227:
		tmp = t_1
	elif z <= 4.5e+295:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(x * Float64(z * 6.0))
	t_2 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.95e+127)
		tmp = t_0;
	elseif (z <= -5.2e+93)
		tmp = t_2;
	elseif (z <= -5.5e+67)
		tmp = t_0;
	elseif (z <= -2.6e+37)
		tmp = t_1;
	elseif (z <= -900.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.75e+227)
		tmp = t_1;
	elseif (z <= 4.5e+295)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = x * (z * 6.0);
	t_2 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.95e+127)
		tmp = t_0;
	elseif (z <= -5.2e+93)
		tmp = t_2;
	elseif (z <= -5.5e+67)
		tmp = t_0;
	elseif (z <= -2.6e+37)
		tmp = t_1;
	elseif (z <= -900.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 1.75e+227)
		tmp = t_1;
	elseif (z <= 4.5e+295)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.95e+127], t$95$0, If[LessEqual[z, -5.2e+93], t$95$2, If[LessEqual[z, -5.5e+67], t$95$0, If[LessEqual[z, -2.6e+37], t$95$1, If[LessEqual[z, -900.0], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.75e+227], t$95$1, If[LessEqual[z, 4.5e+295], t$95$0, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.94999999999999991e127 or -5.19999999999999999e93 < z < -5.49999999999999968e67 or -2.5999999999999999e37 < z < -900 or 1.75e227 < z < 4.5000000000000004e295

   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 0 99.9%

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

   6. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 71.9%

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

   if -1.94999999999999991e127 < z < -5.19999999999999999e93 or 4.5000000000000004e295 < 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 z around 0 100.0%

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

   6. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + \left(4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, y \cdot z, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]

      2. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, \color{blue}{z \cdot y}, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right) \]

      3. +-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{x \cdot \left(6 \cdot z - 3\right) + 4 \cdot y}\right) \]

      4. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \left(\color{blue}{z \cdot 6} - 3\right) + 4 \cdot y\right) \]

      5. fma-neg 82.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \color{blue}{\mathsf{fma}\left(z, 6, -3\right)} + 4 \cdot y\right) \]

      6. metadata-eval 82.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \mathsf{fma}\left(z, 6, \color{blue}{-3}\right) + 4 \cdot y\right) \]

      7. fma-def 82.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(z, 6, -3\right), 4 \cdot y\right)}\right) \]

      8. fma-udef 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{z \cdot 6 + -3}, 4 \cdot y\right)\right) \]

      9. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{6 \cdot z} + -3, 4 \cdot y\right)\right) \]

      10. fma-udef 82.8%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(6, z, -3\right)}, 4 \cdot y\right)\right) \]

      11. *-commutative 82.8%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), \color{blue}{y \cdot 4}\right)\right) \]

   8. Simplified 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), y \cdot 4\right)\right)} \]

   9. Taylor expanded in z around inf 100.0%

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

       1. distribute-lft-in 83.3%

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

       2. associate-*r* 83.1%

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

       3. *-commutative 83.1%

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

       4. metadata-eval 83.1%

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

       5. distribute-lft-neg-in 83.1%

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

       6. distribute-lft-neg-in 83.1%

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

       7. distribute-rgt-neg-out 83.1%

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

       8. *-commutative 83.1%

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

       9. *-commutative 83.1%

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

       10. associate-*r* 83.3%

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

       11. distribute-rgt-out 100.0%

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

       12. *-commutative 100.0%

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

       13. distribute-rgt-in 100.0%

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

       14. sub-neg 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in y around 0 100.0%

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

       1. *-commutative 100.0%

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

   14. Simplified 100.0%

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

   if -5.49999999999999968e67 < z < -2.5999999999999999e37 or 0.5 < z < 1.75e227

   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 61.6%

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

      1. sub-neg 61.6%

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

      2. distribute-rgt-in 61.6%

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

      3. metadata-eval 61.6%

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

      4. metadata-eval 61.6%

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

      5. distribute-lft-neg-in 61.6%

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

      6. associate-+r+ 61.6%

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

      7. metadata-eval 61.6%

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

      8. metadata-eval 61.6%

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

      9. distribute-rgt-neg-in 61.6%

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

      10. metadata-eval 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in z around inf 61.6%

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

   if -900 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. sub-neg 50.2%

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

      2. distribute-rgt-in 50.2%

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

      3. metadata-eval 50.2%

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

      4. metadata-eval 50.2%

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

      5. distribute-lft-neg-in 50.2%

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

      6. associate-+r+ 50.2%

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

      7. metadata-eval 50.2%

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

      8. metadata-eval 50.2%

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

      9. distribute-rgt-neg-in 50.2%

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

      10. metadata-eval 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in z around 0 48.2%

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

      1. *-commutative 48.2%

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

   10. Simplified 48.2%

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

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.95 \cdot 10^{+127}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -5.2 \cdot 10^{+93}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+67}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+37}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -900:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+227}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{+295}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 49.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := x \cdot \left(z \cdot 6\right)\\ t_2 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+129}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+91}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+38}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -900:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.25 \cdot 10^{+226}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+291}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* x (* z 6.0))) (t_2 (* 6.0 (* x z))))
   (if (<= z -2.1e+129)
     t_0
     (if (<= z -2.1e+91)
       t_2
       (if (<= z -2.25e+70)
         (* z (* -6.0 y))
         (if (<= z -2.1e+38)
           t_1
           (if (<= z -900.0)
             t_0
             (if (<= z 0.5)
               (* x -3.0)
               (if (<= z 4.25e+226) t_1 (if (<= z 1.1e+291) t_0 t_2))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = x * (z * 6.0);
	double t_2 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.1e+129) {
		tmp = t_0;
	} else if (z <= -2.1e+91) {
		tmp = t_2;
	} else if (z <= -2.25e+70) {
		tmp = z * (-6.0 * y);
	} else if (z <= -2.1e+38) {
		tmp = t_1;
	} else if (z <= -900.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 4.25e+226) {
		tmp = t_1;
	} else if (z <= 1.1e+291) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = (-6.0d0) * (z * y)
    t_1 = x * (z * 6.0d0)
    t_2 = 6.0d0 * (x * z)
    if (z <= (-2.1d+129)) then
        tmp = t_0
    else if (z <= (-2.1d+91)) then
        tmp = t_2
    else if (z <= (-2.25d+70)) then
        tmp = z * ((-6.0d0) * y)
    else if (z <= (-2.1d+38)) then
        tmp = t_1
    else if (z <= (-900.0d0)) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 4.25d+226) then
        tmp = t_1
    else if (z <= 1.1d+291) then
        tmp = t_0
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = x * (z * 6.0);
	double t_2 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.1e+129) {
		tmp = t_0;
	} else if (z <= -2.1e+91) {
		tmp = t_2;
	} else if (z <= -2.25e+70) {
		tmp = z * (-6.0 * y);
	} else if (z <= -2.1e+38) {
		tmp = t_1;
	} else if (z <= -900.0) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 4.25e+226) {
		tmp = t_1;
	} else if (z <= 1.1e+291) {
		tmp = t_0;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = x * (z * 6.0)
	t_2 = 6.0 * (x * z)
	tmp = 0
	if z <= -2.1e+129:
		tmp = t_0
	elif z <= -2.1e+91:
		tmp = t_2
	elif z <= -2.25e+70:
		tmp = z * (-6.0 * y)
	elif z <= -2.1e+38:
		tmp = t_1
	elif z <= -900.0:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 4.25e+226:
		tmp = t_1
	elif z <= 1.1e+291:
		tmp = t_0
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(x * Float64(z * 6.0))
	t_2 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.1e+129)
		tmp = t_0;
	elseif (z <= -2.1e+91)
		tmp = t_2;
	elseif (z <= -2.25e+70)
		tmp = Float64(z * Float64(-6.0 * y));
	elseif (z <= -2.1e+38)
		tmp = t_1;
	elseif (z <= -900.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.25e+226)
		tmp = t_1;
	elseif (z <= 1.1e+291)
		tmp = t_0;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = x * (z * 6.0);
	t_2 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.1e+129)
		tmp = t_0;
	elseif (z <= -2.1e+91)
		tmp = t_2;
	elseif (z <= -2.25e+70)
		tmp = z * (-6.0 * y);
	elseif (z <= -2.1e+38)
		tmp = t_1;
	elseif (z <= -900.0)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 4.25e+226)
		tmp = t_1;
	elseif (z <= 1.1e+291)
		tmp = t_0;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+129], t$95$0, If[LessEqual[z, -2.1e+91], t$95$2, If[LessEqual[z, -2.25e+70], N[(z * N[(-6.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e+38], t$95$1, If[LessEqual[z, -900.0], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.25e+226], t$95$1, If[LessEqual[z, 1.1e+291], t$95$0, t$95$2]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.09999999999999997e129 or -2.1e38 < z < -900 or 4.24999999999999987e226 < z < 1.1e291

   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 0 99.9%

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

   6. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

   8. Simplified 99.7%

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

   9. Taylor expanded in y around inf 69.8%

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

   if -2.09999999999999997e129 < z < -2.10000000000000008e91 or 1.1e291 < 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 z around 0 100.0%

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

   6. Taylor expanded in x around 0 83.1%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + \left(4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 83.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, y \cdot z, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]

      2. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, \color{blue}{z \cdot y}, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right) \]

      3. +-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{x \cdot \left(6 \cdot z - 3\right) + 4 \cdot y}\right) \]

      4. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \left(\color{blue}{z \cdot 6} - 3\right) + 4 \cdot y\right) \]

      5. fma-neg 82.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \color{blue}{\mathsf{fma}\left(z, 6, -3\right)} + 4 \cdot y\right) \]

      6. metadata-eval 82.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \mathsf{fma}\left(z, 6, \color{blue}{-3}\right) + 4 \cdot y\right) \]

      7. fma-def 82.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(z, 6, -3\right), 4 \cdot y\right)}\right) \]

      8. fma-udef 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{z \cdot 6 + -3}, 4 \cdot y\right)\right) \]

      9. *-commutative 83.1%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{6 \cdot z} + -3, 4 \cdot y\right)\right) \]

      10. fma-udef 82.8%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(6, z, -3\right)}, 4 \cdot y\right)\right) \]

      11. *-commutative 82.8%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), \color{blue}{y \cdot 4}\right)\right) \]

   8. Simplified 82.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), y \cdot 4\right)\right)} \]

   9. Taylor expanded in z around inf 100.0%

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

       1. distribute-lft-in 83.3%

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

       2. associate-*r* 83.1%

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

       3. *-commutative 83.1%

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

       4. metadata-eval 83.1%

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

       5. distribute-lft-neg-in 83.1%

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

       6. distribute-lft-neg-in 83.1%

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

       7. distribute-rgt-neg-out 83.1%

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

       8. *-commutative 83.1%

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

       9. *-commutative 83.1%

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

       10. associate-*r* 83.3%

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

       11. distribute-rgt-out 100.0%

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

       12. *-commutative 100.0%

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

       13. distribute-rgt-in 100.0%

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

       14. sub-neg 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in y around 0 100.0%

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

       1. *-commutative 100.0%

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

   14. Simplified 100.0%

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

   if -2.10000000000000008e91 < z < -2.25e70

   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 z around 0 99.8%

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

   6. Taylor expanded in x around 0 85.5%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + \left(4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 85.3%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, y \cdot z, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]

      2. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(-6, \color{blue}{z \cdot y}, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right) \]

      3. +-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{x \cdot \left(6 \cdot z - 3\right) + 4 \cdot y}\right) \]

      4. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \left(\color{blue}{z \cdot 6} - 3\right) + 4 \cdot y\right) \]

      5. fma-neg 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \color{blue}{\mathsf{fma}\left(z, 6, -3\right)} + 4 \cdot y\right) \]

      6. metadata-eval 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \mathsf{fma}\left(z, 6, \color{blue}{-3}\right) + 4 \cdot y\right) \]

      7. fma-def 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(z, 6, -3\right), 4 \cdot y\right)}\right) \]

      8. fma-udef 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{z \cdot 6 + -3}, 4 \cdot y\right)\right) \]

      9. *-commutative 85.3%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{6 \cdot z} + -3, 4 \cdot y\right)\right) \]

      10. fma-udef 85.3%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(6, z, -3\right)}, 4 \cdot y\right)\right) \]

      11. *-commutative 85.3%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), \color{blue}{y \cdot 4}\right)\right) \]

   8. Simplified 85.3%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), y \cdot 4\right)\right)} \]

   9. Taylor expanded in z around inf 100.0%

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

       1. distribute-lft-in 85.7%

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

       2. associate-*r* 85.7%

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

       3. *-commutative 85.7%

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

       4. metadata-eval 85.7%

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

       5. distribute-lft-neg-in 85.7%

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

       6. distribute-lft-neg-in 85.7%

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

       7. distribute-rgt-neg-out 85.7%

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

       8. *-commutative 85.7%

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

       9. *-commutative 85.7%

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

       10. associate-*r* 85.7%

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

       11. distribute-rgt-out 100.0%

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

       12. *-commutative 100.0%

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

       13. distribute-rgt-in 100.0%

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

       14. sub-neg 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in y around inf 86.3%

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

   if -2.25e70 < z < -2.1e38 or 0.5 < z < 4.24999999999999987e226

   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 61.6%

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

      1. sub-neg 61.6%

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

      2. distribute-rgt-in 61.6%

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

      3. metadata-eval 61.6%

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

      4. metadata-eval 61.6%

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

      5. distribute-lft-neg-in 61.6%

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

      6. associate-+r+ 61.6%

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

      7. metadata-eval 61.6%

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

      8. metadata-eval 61.6%

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

      9. distribute-rgt-neg-in 61.6%

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

      10. metadata-eval 61.6%

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

   7. Simplified 61.6%

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

   8. Taylor expanded in z around inf 61.6%

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

   if -900 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. sub-neg 50.2%

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

      2. distribute-rgt-in 50.2%

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

      3. metadata-eval 50.2%

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

      4. metadata-eval 50.2%

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

      5. distribute-lft-neg-in 50.2%

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

      6. associate-+r+ 50.2%

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

      7. metadata-eval 50.2%

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

      8. metadata-eval 50.2%

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

      9. distribute-rgt-neg-in 50.2%

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

      10. metadata-eval 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in z around 0 48.2%

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

      1. *-commutative 48.2%

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

   10. Simplified 48.2%

       \[\leadsto \color{blue}{x \cdot -3} \]
3. Recombined 5 regimes into one program.

4. Final simplification 57.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+129}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+91}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.25 \cdot 10^{+70}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+38}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq -900:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.25 \cdot 10^{+226}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 1.1 \cdot 10^{+291}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 73.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.0048:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-290}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-239}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* -6.0 (* z (- y x)))))
   (if (<= z -0.0048)
     t_1
     (if (<= z -2e-290)
       t_0
       (if (<= z 2.6e-239)
         (* x -3.0)
         (if (<= z 7.2e-171) t_0 (if (<= z 0.5) (* x -3.0) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.0048) {
		tmp = t_1;
	} else if (z <= -2e-290) {
		tmp = t_0;
	} else if (z <= 2.6e-239) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-171) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y * 4.0d0)
    t_1 = (-6.0d0) * (z * (y - x))
    if (z <= (-0.0048d0)) then
        tmp = t_1
    else if (z <= (-2d-290)) then
        tmp = t_0
    else if (z <= 2.6d-239) then
        tmp = x * (-3.0d0)
    else if (z <= 7.2d-171) then
        tmp = t_0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.0048) {
		tmp = t_1;
	} else if (z <= -2e-290) {
		tmp = t_0;
	} else if (z <= 2.6e-239) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-171) {
		tmp = t_0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	t_1 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -0.0048:
		tmp = t_1
	elif z <= -2e-290:
		tmp = t_0
	elif z <= 2.6e-239:
		tmp = x * -3.0
	elif z <= 7.2e-171:
		tmp = t_0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	t_1 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.0048)
		tmp = t_1;
	elseif (z <= -2e-290)
		tmp = t_0;
	elseif (z <= 2.6e-239)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.2e-171)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 4.0);
	t_1 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.0048)
		tmp = t_1;
	elseif (z <= -2e-290)
		tmp = t_0;
	elseif (z <= 2.6e-239)
		tmp = x * -3.0;
	elseif (z <= 7.2e-171)
		tmp = t_0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0048], t$95$1, If[LessEqual[z, -2e-290], t$95$0, If[LessEqual[z, 2.6e-239], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.2e-171], t$95$0, If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00479999999999999958 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 98.5%

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

   if -0.00479999999999999958 < z < -2.0000000000000001e-290 or 2.60000000000000003e-239 < z < 7.20000000000000006e-171

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 58.7%

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

      1. associate-*r* 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in z around 0 57.1%

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

      1. *-commutative 57.1%

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

   10. Simplified 57.1%

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

   if -2.0000000000000001e-290 < z < 2.60000000000000003e-239 or 7.20000000000000006e-171 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 65.6%

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

      1. sub-neg 65.6%

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

      2. distribute-rgt-in 65.7%

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

      3. metadata-eval 65.7%

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

      4. metadata-eval 65.7%

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

      5. distribute-lft-neg-in 65.7%

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

      6. associate-+r+ 65.7%

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

      7. metadata-eval 65.7%

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

      8. metadata-eval 65.7%

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

      9. distribute-rgt-neg-in 65.7%

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

      10. metadata-eval 65.7%

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

   7. Simplified 65.7%

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

   8. Taylor expanded in z around 0 64.1%

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

      1. *-commutative 64.1%

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

   10. Simplified 64.1%

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

4. Final simplification 77.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0048:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -2 \cdot 10^{-290}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-239}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-171}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 73.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + y \cdot 4\\ t_1 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -0.0028:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-291}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-239}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-171}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* y 4.0))) (t_1 (* -6.0 (* z (- y x)))))
   (if (<= z -0.0028)
     t_1
     (if (<= z -7.8e-291)
       t_0
       (if (<= z 2.2e-239)
         (* x -3.0)
         (if (<= z 8.5e-171)
           t_0
           (if (<= z 1.75e+15) (* x (+ -3.0 (* z 6.0))) t_1)))))))

C

double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.0028) {
		tmp = t_1;
	} else if (z <= -7.8e-291) {
		tmp = t_0;
	} else if (z <= 2.2e-239) {
		tmp = x * -3.0;
	} else if (z <= 8.5e-171) {
		tmp = t_0;
	} else if (z <= 1.75e+15) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = x + (y * 4.0d0)
    t_1 = (-6.0d0) * (z * (y - x))
    if (z <= (-0.0028d0)) then
        tmp = t_1
    else if (z <= (-7.8d-291)) then
        tmp = t_0
    else if (z <= 2.2d-239) then
        tmp = x * (-3.0d0)
    else if (z <= 8.5d-171) then
        tmp = t_0
    else if (z <= 1.75d+15) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x + (y * 4.0);
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -0.0028) {
		tmp = t_1;
	} else if (z <= -7.8e-291) {
		tmp = t_0;
	} else if (z <= 2.2e-239) {
		tmp = x * -3.0;
	} else if (z <= 8.5e-171) {
		tmp = t_0;
	} else if (z <= 1.75e+15) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (y * 4.0)
	t_1 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -0.0028:
		tmp = t_1
	elif z <= -7.8e-291:
		tmp = t_0
	elif z <= 2.2e-239:
		tmp = x * -3.0
	elif z <= 8.5e-171:
		tmp = t_0
	elif z <= 1.75e+15:
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(y * 4.0))
	t_1 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -0.0028)
		tmp = t_1;
	elseif (z <= -7.8e-291)
		tmp = t_0;
	elseif (z <= 2.2e-239)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.5e-171)
		tmp = t_0;
	elseif (z <= 1.75e+15)
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x + (y * 4.0);
	t_1 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -0.0028)
		tmp = t_1;
	elseif (z <= -7.8e-291)
		tmp = t_0;
	elseif (z <= 2.2e-239)
		tmp = x * -3.0;
	elseif (z <= 8.5e-171)
		tmp = t_0;
	elseif (z <= 1.75e+15)
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0028], t$95$1, If[LessEqual[z, -7.8e-291], t$95$0, If[LessEqual[z, 2.2e-239], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.5e-171], t$95$0, If[LessEqual[z, 1.75e+15], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.00279999999999999997 or 1.75e15 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 98.5%

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

   if -0.00279999999999999997 < z < -7.80000000000000031e-291 or 2.19999999999999983e-239 < z < 8.50000000000000032e-171

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around inf 58.7%

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

      1. associate-*r* 58.7%

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

   7. Simplified 58.7%

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

   8. Taylor expanded in z around 0 57.1%

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

      1. *-commutative 57.1%

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

   10. Simplified 57.1%

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

   if -7.80000000000000031e-291 < z < 2.19999999999999983e-239

   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 69.8%

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

      1. sub-neg 69.8%

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

      2. distribute-rgt-in 69.8%

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

      3. metadata-eval 69.8%

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

      4. metadata-eval 69.8%

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

      5. distribute-lft-neg-in 69.8%

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

      6. associate-+r+ 69.8%

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

      7. metadata-eval 69.8%

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

      8. metadata-eval 69.8%

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

      9. distribute-rgt-neg-in 69.8%

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

      10. metadata-eval 69.8%

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

   7. Simplified 69.8%

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

   8. Taylor expanded in z around 0 69.8%

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

      1. *-commutative 69.8%

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

   10. Simplified 69.8%

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

   if 8.50000000000000032e-171 < z < 1.75e15

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in x around inf 64.5%

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

      1. sub-neg 64.5%

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

      2. distribute-rgt-in 64.6%

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

      3. metadata-eval 64.6%

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

      4. metadata-eval 64.6%

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

      5. distribute-lft-neg-in 64.6%

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

      6. associate-+r+ 64.6%

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

      7. metadata-eval 64.6%

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

      8. metadata-eval 64.6%

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

      9. distribute-rgt-neg-in 64.6%

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

      10. metadata-eval 64.6%

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

   7. Simplified 64.6%

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

4. Final simplification 77.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0028:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -7.8 \cdot 10^{-291}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 2.2 \cdot 10^{-239}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-171}:\\ \;\;\;\;x + y \cdot 4\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{+15}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 72.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+111} \lor \neg \left(y \leq -2.7 \cdot 10^{-33} \lor \neg \left(y \leq -2.95 \cdot 10^{-95}\right) \land y \leq 4.2 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.9e+111)
         (not
          (or (<= y -2.7e-33) (and (not (<= y -2.95e-95)) (<= y 4.2e+45)))))
   (* y (+ 4.0 (* -6.0 z)))
   (* x (+ -3.0 (* z 6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.9e+111) || !((y <= -2.7e-33) || (!(y <= -2.95e-95) && (y <= 4.2e+45)))) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-3.9d+111)) .or. (.not. (y <= (-2.7d-33)) .or. (.not. (y <= (-2.95d-95))) .and. (y <= 4.2d+45))) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.9e+111) || !((y <= -2.7e-33) || (!(y <= -2.95e-95) && (y <= 4.2e+45)))) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = x * (-3.0 + (z * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.9e+111) or not ((y <= -2.7e-33) or (not (y <= -2.95e-95) and (y <= 4.2e+45))):
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = x * (-3.0 + (z * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.9e+111) || !((y <= -2.7e-33) || (!(y <= -2.95e-95) && (y <= 4.2e+45))))
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -3.9e+111) || ~(((y <= -2.7e-33) || (~((y <= -2.95e-95)) && (y <= 4.2e+45)))))
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = x * (-3.0 + (z * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.9e+111], N[Not[Or[LessEqual[y, -2.7e-33], And[N[Not[LessEqual[y, -2.95e-95]], $MachinePrecision], LessEqual[y, 4.2e+45]]]], $MachinePrecision]], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.89999999999999979e111 or -2.7000000000000001e-33 < y < -2.9499999999999999e-95 or 4.1999999999999999e45 < y

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 88.4%

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

   if -3.89999999999999979e111 < y < -2.7000000000000001e-33 or -2.9499999999999999e-95 < y < 4.1999999999999999e45

   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 73.1%

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

      1. sub-neg 73.1%

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

      2. distribute-rgt-in 73.1%

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

      3. metadata-eval 73.1%

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

      4. metadata-eval 73.1%

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

      5. distribute-lft-neg-in 73.1%

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

      6. associate-+r+ 73.1%

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

      7. metadata-eval 73.1%

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

      8. metadata-eval 73.1%

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

      9. distribute-rgt-neg-in 73.1%

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

      10. metadata-eval 73.1%

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

   7. Simplified 73.1%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+111} \lor \neg \left(y \leq -2.7 \cdot 10^{-33} \lor \neg \left(y \leq -2.95 \cdot 10^{-95}\right) \land y \leq 4.2 \cdot 10^{+45}\right):\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.7% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.52) (not (<= z 0.5)))
   (* -6.0 (* z (- y x)))
   (+ x (* (- y x) 4.0))))

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.52d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = (-6.0d0) * (z * (y - x))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

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

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.52) or not (z <= 0.5):
		tmp = -6.0 * (z * (y - x))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.52], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.52000000000000002 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 99.2%

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

   if -0.52000000000000002 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 97.1%

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

4. Final simplification 98.1%

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

Alternative 10: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.55\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.55)))
   (* -6.0 (* z (- y x)))
   (+ (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.55)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.6d0)) .or. (.not. (z <= 0.55d0))) then
        tmp = (-6.0d0) * (z * (y - x))
    else
        tmp = (y * 4.0d0) + (x * (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.55)) {
		tmp = -6.0 * (z * (y - x));
	} else {
		tmp = (y * 4.0) + (x * -3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.55):
		tmp = -6.0 * (z * (y - x))
	else:
		tmp = (y * 4.0) + (x * -3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.55))
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	else
		tmp = Float64(Float64(y * 4.0) + Float64(x * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.55)))
		tmp = -6.0 * (z * (y - x));
	else
		tmp = (y * 4.0) + (x * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.55]], $MachinePrecision]], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y * 4.0), $MachinePrecision] + N[(x * -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.55000000000000004 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 99.2%

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

   if -0.599999999999999978 < z < 0.55000000000000004

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in x around 0 99.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + \left(4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]
   7. Step-by-step derivation

      1. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(-6, y \cdot z, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right)} \]

      2. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(-6, \color{blue}{z \cdot y}, 4 \cdot y + x \cdot \left(6 \cdot z - 3\right)\right) \]

      3. +-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{x \cdot \left(6 \cdot z - 3\right) + 4 \cdot y}\right) \]

      4. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \left(\color{blue}{z \cdot 6} - 3\right) + 4 \cdot y\right) \]

      5. fma-neg 99.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \color{blue}{\mathsf{fma}\left(z, 6, -3\right)} + 4 \cdot y\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, x \cdot \mathsf{fma}\left(z, 6, \color{blue}{-3}\right) + 4 \cdot y\right) \]

      7. fma-def 99.9%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \color{blue}{\mathsf{fma}\left(x, \mathsf{fma}\left(z, 6, -3\right), 4 \cdot y\right)}\right) \]

      8. fma-udef 99.9%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{z \cdot 6 + -3}, 4 \cdot y\right)\right) \]

      9. *-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{6 \cdot z} + -3, 4 \cdot y\right)\right) \]

      10. fma-udef 99.9%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \color{blue}{\mathsf{fma}\left(6, z, -3\right)}, 4 \cdot y\right)\right) \]

      11. *-commutative 99.9%

          \[\leadsto \mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), \color{blue}{y \cdot 4}\right)\right) \]

   8. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(-6, z \cdot y, \mathsf{fma}\left(x, \mathsf{fma}\left(6, z, -3\right), y \cdot 4\right)\right)} \]

   9. Taylor expanded in z around 0 97.1%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.55\right):\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4 + x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.3% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -900 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -900.0) (not (<= z 0.5))) (* -6.0 (* z y)) (* x -3.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -900.0) || !(z <= 0.5)) {
		tmp = -6.0 * (z * y);
	} else {
		tmp = x * -3.0;
	}
	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 <= (-900.0d0)) .or. (.not. (z <= 0.5d0))) then
        tmp = (-6.0d0) * (z * y)
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -900.0) || !(z <= 0.5)) {
		tmp = -6.0 * (z * y);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -900.0) or not (z <= 0.5):
		tmp = -6.0 * (z * y)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -900.0) || !(z <= 0.5))
		tmp = Float64(-6.0 * Float64(z * y));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -900.0) || ~((z <= 0.5)))
		tmp = -6.0 * (z * y);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -900.0], N[Not[LessEqual[z, 0.5]], $MachinePrecision]], N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -900 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around 0 99.8%

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

   6. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.6%

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

      2. *-commutative 99.6%

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

   8. Simplified 99.6%

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

   9. Taylor expanded in y around inf 54.9%

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

   if -900 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around inf 50.2%

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

      1. sub-neg 50.2%

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

      2. distribute-rgt-in 50.2%

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

      3. metadata-eval 50.2%

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

      4. metadata-eval 50.2%

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

      5. distribute-lft-neg-in 50.2%

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

      6. associate-+r+ 50.2%

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

      7. metadata-eval 50.2%

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

      8. metadata-eval 50.2%

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

      9. distribute-rgt-neg-in 50.2%

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

      10. metadata-eval 50.2%

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

   7. Simplified 50.2%

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

   8. Taylor expanded in z around 0 48.2%

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

      1. *-commutative 48.2%

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

   10. Simplified 48.2%

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

4. Final simplification 51.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -900 \lor \neg \left(z \leq 0.5\right):\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 13: 26.3% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. 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 50.8%

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

   1. sub-neg 50.8%

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

   2. distribute-rgt-in 50.9%

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

   3. metadata-eval 50.9%

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

   4. metadata-eval 50.9%

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

   5. distribute-lft-neg-in 50.9%

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

   6. associate-+r+ 50.9%

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

   7. metadata-eval 50.9%

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

   8. metadata-eval 50.9%

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

   9. distribute-rgt-neg-in 50.9%

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

   10. metadata-eval 50.9%

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

7. Simplified 50.9%

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

8. Taylor expanded in z around 0 27.3%

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

   1. *-commutative 27.3%

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

10. Simplified 27.3%

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

11. Final simplification 27.3%

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

Alternative 14: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in y around inf 52.2%

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

   1. associate-*r* 52.2%

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

7. Simplified 52.2%

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

8. Taylor expanded in x around inf 2.9%

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

9. Final simplification 2.9%

   \[\leadsto x \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024024 
(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))))