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

Percentage Accurate: 99.5% → 99.8%

Time: 17.6s

Alternatives: 16

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -4.5e+213)
   (* z (* x 6.0))
   (if (<= z -1.08e-26)
     (* y (* z -6.0))
     (if (<= z -2.4e-181)
       (* y 4.0)
       (if (<= z 0.65) (* x -3.0) (* -6.0 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+213) {
		tmp = z * (x * 6.0);
	} else if (z <= -1.08e-26) {
		tmp = y * (z * -6.0);
	} else if (z <= -2.4e-181) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-4.5d+213)) then
        tmp = z * (x * 6.0d0)
    else if (z <= (-1.08d-26)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-2.4d-181)) then
        tmp = y * 4.0d0
    else if (z <= 0.65d0) then
        tmp = x * (-3.0d0)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -4.5e+213) {
		tmp = z * (x * 6.0);
	} else if (z <= -1.08e-26) {
		tmp = y * (z * -6.0);
	} else if (z <= -2.4e-181) {
		tmp = y * 4.0;
	} else if (z <= 0.65) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -4.5e+213:
		tmp = z * (x * 6.0)
	elif z <= -1.08e-26:
		tmp = y * (z * -6.0)
	elif z <= -2.4e-181:
		tmp = y * 4.0
	elif z <= 0.65:
		tmp = x * -3.0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -4.5e+213)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= -1.08e-26)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -2.4e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.65)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -4.5e+213)
		tmp = z * (x * 6.0);
	elseif (z <= -1.08e-26)
		tmp = y * (z * -6.0);
	elseif (z <= -2.4e-181)
		tmp = y * 4.0;
	elseif (z <= 0.65)
		tmp = x * -3.0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -4.5e+213], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-26], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.4e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(x * -3.0), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -4.5000000000000002e213

   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 inf 100.0%

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

      1. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 67.2%

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

   9. Taylor expanded in z around inf 67.2%

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

       1. associate-*r* 67.3%

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

       2. *-commutative 67.3%

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

       3. *-commutative 67.3%

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

       4. *-commutative 67.3%

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

   11. Simplified 67.3%

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

   if -4.5000000000000002e213 < z < -1.07999999999999996e-26

   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 y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. *-commutative 55.0%

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

   8. Simplified 55.0%

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

   9. Taylor expanded in z around inf 53.7%

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

       1. *-commutative 53.7%

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

       2. associate-*r* 53.8%

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

       3. *-commutative 53.8%

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

   11. Simplified 53.8%

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

   if -1.07999999999999996e-26 < z < -2.4000000000000001e-181

   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 95.8%

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

   6. Taylor expanded in z around 0 95.8%

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

   7. Taylor expanded in y around inf 77.1%

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

   if -2.4000000000000001e-181 < z < 0.650000000000000022

   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. +-commutative 99.3%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 56.0%

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

      1. *-lft-identity 56.0%

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

      2. *-commutative 56.0%

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

      3. +-commutative 56.0%

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

      4. *-commutative 56.0%

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

      5. fma-undefine 56.0%

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

      6. associate-*r* 56.0%

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

      7. fma-undefine 56.0%

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

      8. *-commutative 56.0%

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

      9. +-commutative 56.0%

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

      10. distribute-rgt-in 56.0%

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

      11. distribute-lft-in 56.0%

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

      12. metadata-eval 56.0%

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

      13. associate-+r+ 56.0%

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

      14. metadata-eval 56.0%

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

      15. associate-*r* 56.0%

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

      16. metadata-eval 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in z around 0 56.0%

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

      1. *-commutative 56.0%

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

   10. Simplified 56.0%

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

   if 0.650000000000000022 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in 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 y around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. *-commutative 69.1%

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

   8. Simplified 69.1%

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

   9. Taylor expanded in z around inf 66.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+213}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.4 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 51.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+215}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.8e+215)
   (* 6.0 (* x z))
   (if (<= z -1.08e-26)
     (* y (* z -6.0))
     (if (<= z -1.82e-181)
       (* y 4.0)
       (if (<= z 0.58) (* x -3.0) (* -6.0 (* y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+215) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.82e-181) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.8d+215)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-1.08d-26)) then
        tmp = y * (z * (-6.0d0))
    else if (z <= (-1.82d-181)) then
        tmp = y * 4.0d0
    else if (z <= 0.58d0) then
        tmp = x * (-3.0d0)
    else
        tmp = (-6.0d0) * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.8e+215) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = y * (z * -6.0);
	} else if (z <= -1.82e-181) {
		tmp = y * 4.0;
	} else if (z <= 0.58) {
		tmp = x * -3.0;
	} else {
		tmp = -6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.8e+215:
		tmp = 6.0 * (x * z)
	elif z <= -1.08e-26:
		tmp = y * (z * -6.0)
	elif z <= -1.82e-181:
		tmp = y * 4.0
	elif z <= 0.58:
		tmp = x * -3.0
	else:
		tmp = -6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.8e+215)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -1.08e-26)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (z <= -1.82e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.58)
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(-6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.8e+215)
		tmp = 6.0 * (x * z);
	elseif (z <= -1.08e-26)
		tmp = y * (z * -6.0);
	elseif (z <= -1.82e-181)
		tmp = y * 4.0;
	elseif (z <= 0.58)
		tmp = x * -3.0;
	else
		tmp = -6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.8e+215], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-26], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.82e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.58], N[(x * -3.0), $MachinePrecision], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -1.79999999999999987e215

   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 inf 100.0%

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

      1. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 67.2%

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

   9. Taylor expanded in z around inf 67.2%

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

   if -1.79999999999999987e215 < z < -1.07999999999999996e-26

   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 y around inf 55.0%

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

      1. +-commutative 55.0%

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

      2. *-commutative 55.0%

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

   8. Simplified 55.0%

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

   9. Taylor expanded in z around inf 53.7%

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

       1. *-commutative 53.7%

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

       2. associate-*r* 53.8%

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

       3. *-commutative 53.8%

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

   11. Simplified 53.8%

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

   if -1.07999999999999996e-26 < z < -1.8199999999999999e-181

   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 95.8%

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

   6. Taylor expanded in z around 0 95.8%

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

   7. Taylor expanded in y around inf 77.1%

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

   if -1.8199999999999999e-181 < z < 0.57999999999999996

   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. +-commutative 99.3%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 56.0%

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

      1. *-lft-identity 56.0%

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

      2. *-commutative 56.0%

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

      3. +-commutative 56.0%

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

      4. *-commutative 56.0%

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

      5. fma-undefine 56.0%

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

      6. associate-*r* 56.0%

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

      7. fma-undefine 56.0%

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

      8. *-commutative 56.0%

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

      9. +-commutative 56.0%

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

      10. distribute-rgt-in 56.0%

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

      11. distribute-lft-in 56.0%

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

      12. metadata-eval 56.0%

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

      13. associate-+r+ 56.0%

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

      14. metadata-eval 56.0%

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

      15. associate-*r* 56.0%

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

      16. metadata-eval 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in z around 0 56.0%

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

      1. *-commutative 56.0%

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

   10. Simplified 56.0%

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

   if 0.57999999999999996 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. 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 y around inf 69.1%

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

      1. +-commutative 69.1%

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

      2. *-commutative 69.1%

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

   8. Simplified 69.1%

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

   9. Taylor expanded in z around inf 66.9%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.8 \cdot 10^{+215}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.82 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+216}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -3e+216)
     (* 6.0 (* x z))
     (if (<= z -1.08e-26)
       t_0
       (if (<= z -1.9e-181) (* y 4.0) (if (<= z 0.68) (* x -3.0) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -3e+216) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -1.9e-181) {
		tmp = y * 4.0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-3d+216)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-1.08d-26)) then
        tmp = t_0
    else if (z <= (-1.9d-181)) then
        tmp = y * 4.0d0
    else if (z <= 0.68d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -3e+216) {
		tmp = 6.0 * (x * z);
	} else if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -1.9e-181) {
		tmp = y * 4.0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -3e+216:
		tmp = 6.0 * (x * z)
	elif z <= -1.08e-26:
		tmp = t_0
	elif z <= -1.9e-181:
		tmp = y * 4.0
	elif z <= 0.68:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3e+216)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -1.9e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.68)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3e+216)
		tmp = 6.0 * (x * z);
	elseif (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -1.9e-181)
		tmp = y * 4.0;
	elseif (z <= 0.68)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3e+216], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.08e-26], t$95$0, If[LessEqual[z, -1.9e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.9999999999999998e216

   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 inf 100.0%

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

      1. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around 0 67.2%

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

   9. Taylor expanded in z around inf 67.2%

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

   if -2.9999999999999998e216 < z < -1.07999999999999996e-26 or 0.680000000000000049 < 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 99.7%

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

   6. Taylor expanded in y around inf 62.8%

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

      1. +-commutative 62.8%

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

      2. *-commutative 62.8%

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

   8. Simplified 62.8%

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

   9. Taylor expanded in z around inf 61.0%

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

   if -1.07999999999999996e-26 < z < -1.8999999999999999e-181

   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 95.8%

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

   6. Taylor expanded in z around 0 95.8%

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

   7. Taylor expanded in y around inf 77.1%

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

   if -1.8999999999999999e-181 < z < 0.680000000000000049

   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. +-commutative 99.3%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 56.0%

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

      1. *-lft-identity 56.0%

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

      2. *-commutative 56.0%

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

      3. +-commutative 56.0%

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

      4. *-commutative 56.0%

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

      5. fma-undefine 56.0%

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

      6. associate-*r* 56.0%

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

      7. fma-undefine 56.0%

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

      8. *-commutative 56.0%

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

      9. +-commutative 56.0%

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

      10. distribute-rgt-in 56.0%

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

      11. distribute-lft-in 56.0%

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

      12. metadata-eval 56.0%

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

      13. associate-+r+ 56.0%

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

      14. metadata-eval 56.0%

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

      15. associate-*r* 56.0%

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

      16. metadata-eval 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in z around 0 56.0%

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

      1. *-commutative 56.0%

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

   10. Simplified 56.0%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+216}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 59.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.6 \cdot 10^{+215}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq -1.1 \cdot 10^{+96}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 1.5 \cdot 10^{+97}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -6.6e+215)
   (* x -3.0)
   (if (<= x -1.1e+96)
     (* 6.0 (* x z))
     (if (<= x 1.5e+97) (* 6.0 (* y (- 0.6666666666666666 z))) (* x -3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -6.6e+215) {
		tmp = x * -3.0;
	} else if (x <= -1.1e+96) {
		tmp = 6.0 * (x * z);
	} else if (x <= 1.5e+97) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} 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 (x <= (-6.6d+215)) then
        tmp = x * (-3.0d0)
    else if (x <= (-1.1d+96)) then
        tmp = 6.0d0 * (x * z)
    else if (x <= 1.5d+97) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    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 (x <= -6.6e+215) {
		tmp = x * -3.0;
	} else if (x <= -1.1e+96) {
		tmp = 6.0 * (x * z);
	} else if (x <= 1.5e+97) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -6.6e+215:
		tmp = x * -3.0
	elif x <= -1.1e+96:
		tmp = 6.0 * (x * z)
	elif x <= 1.5e+97:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -6.6e+215)
		tmp = Float64(x * -3.0);
	elseif (x <= -1.1e+96)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (x <= 1.5e+97)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -6.6e+215)
		tmp = x * -3.0;
	elseif (x <= -1.1e+96)
		tmp = 6.0 * (x * z);
	elseif (x <= 1.5e+97)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -6.6e+215], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, -1.1e+96], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.5e+97], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.5999999999999997e215 or 1.4999999999999999e97 < x

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 87.6%

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

      1. *-lft-identity 87.6%

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

      2. *-commutative 87.6%

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

      3. +-commutative 87.6%

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

      4. *-commutative 87.6%

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

      5. fma-undefine 87.6%

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

      6. associate-*r* 87.6%

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

      7. fma-undefine 87.6%

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

      8. *-commutative 87.6%

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

      9. +-commutative 87.6%

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

      10. distribute-rgt-in 87.6%

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

      11. distribute-lft-in 87.6%

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

      12. metadata-eval 87.6%

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

      13. associate-+r+ 87.6%

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

      14. metadata-eval 87.6%

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

      15. associate-*r* 87.6%

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

      16. metadata-eval 87.6%

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

   7. Simplified 87.6%

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

   8. Taylor expanded in z around 0 57.5%

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

      1. *-commutative 57.5%

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

   10. Simplified 57.5%

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

   if -6.5999999999999997e215 < x < -1.0999999999999999e96

   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 inf 63.4%

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

      1. neg-mul-1 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in y around 0 58.5%

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

   9. Taylor expanded in z around inf 58.8%

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

   if -1.0999999999999999e96 < x < 1.4999999999999999e97

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 72.2%

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

   6. Taylor expanded in x around 0 72.4%

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

Alternative 6: 51.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -1.08e-26)
     t_0
     (if (<= z -3e-181) (* y 4.0) (if (<= z 0.68) (* x -3.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -3e-181) {
		tmp = y * 4.0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-1.08d-26)) then
        tmp = t_0
    else if (z <= (-3d-181)) then
        tmp = y * 4.0d0
    else if (z <= 0.68d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -1.08e-26) {
		tmp = t_0;
	} else if (z <= -3e-181) {
		tmp = y * 4.0;
	} else if (z <= 0.68) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -1.08e-26:
		tmp = t_0
	elif z <= -3e-181:
		tmp = y * 4.0
	elif z <= 0.68:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -3e-181)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.68)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -1.08e-26)
		tmp = t_0;
	elseif (z <= -3e-181)
		tmp = y * 4.0;
	elseif (z <= 0.68)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.08e-26], t$95$0, If[LessEqual[z, -3e-181], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.68], N[(x * -3.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.07999999999999996e-26 or 0.680000000000000049 < 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 y around inf 59.6%

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

      1. +-commutative 59.6%

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

      2. *-commutative 59.6%

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

   8. Simplified 59.6%

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

   9. Taylor expanded in z around inf 58.0%

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

   if -1.07999999999999996e-26 < z < -2.99999999999999974e-181

   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 95.8%

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

   6. Taylor expanded in z around 0 95.8%

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

   7. Taylor expanded in y around inf 77.1%

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

   if -2.99999999999999974e-181 < z < 0.680000000000000049

   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. +-commutative 99.3%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 56.0%

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

      1. *-lft-identity 56.0%

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

      2. *-commutative 56.0%

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

      3. +-commutative 56.0%

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

      4. *-commutative 56.0%

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

      5. fma-undefine 56.0%

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

      6. associate-*r* 56.0%

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

      7. fma-undefine 56.0%

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

      8. *-commutative 56.0%

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

      9. +-commutative 56.0%

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

      10. distribute-rgt-in 56.0%

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

      11. distribute-lft-in 56.0%

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

      12. metadata-eval 56.0%

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

      13. associate-+r+ 56.0%

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

      14. metadata-eval 56.0%

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

      15. associate-*r* 56.0%

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

      16. metadata-eval 56.0%

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

   7. Simplified 56.0%

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

   8. Taylor expanded in z around 0 56.0%

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

      1. *-commutative 56.0%

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

   10. Simplified 56.0%

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

4. Final simplification 59.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.08 \cdot 10^{-26}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-181}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* (- y x) (* z -6.0))
   (if (<= z 0.68) (+ x (* (- y x) 4.0)) (+ x (* z (* 6.0 (- x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.68) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (z * (6.0 * (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.6d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.68d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x + (z * (6.0d0 * (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.68) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x + (z * (6.0 * (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.68:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x + (z * (6.0 * (x - y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.68)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x + Float64(z * Float64(6.0 * Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.6)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.68)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x + (z * (6.0 * (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.68], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   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 inf 95.7%

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

      1. neg-mul-1 95.7%

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

   7. Simplified 95.7%

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

      1. add-sqr-sqrt 48.4%

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

      2. fma-define 48.4%

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

      3. distribute-rgt-neg-out 48.4%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 0.3%

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

      6. sqr-neg 0.3%

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

      7. sqrt-unprod 0.3%

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

      8. add-sqr-sqrt 0.3%

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

      9. fma-neg 0.3%

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

      10. add-sqr-sqrt 0.6%

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

      11. associate-*l* 0.6%

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

      12. add-sqr-sqrt 0.6%

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

      13. sqrt-unprod 0.6%

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

      14. sqr-neg 0.6%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 95.8%

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

      17. *-commutative 95.8%

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

   9. Applied egg-rr 95.8%

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

   10. Taylor expanded in z around inf 95.8%

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

       1. *-commutative 95.8%

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

       2. associate-*r* 95.8%

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

       3. *-commutative 95.8%

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

       4. associate-*r* 95.8%

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

   12. Simplified 95.8%

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

   if -0.599999999999999978 < z < 0.680000000000000049

   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 z around 0 98.8%

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

   if 0.680000000000000049 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.6%

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

      1. neg-mul-1 96.6%

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

   7. Simplified 96.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.68:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x - -6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.58)
   (* (- y x) (* z -6.0))
   (if (<= z 0.54) (+ x (* (- y x) 4.0)) (- x (* -6.0 (* z (- x y)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.54) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x - (-6.0 * (z * (x - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.58d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.54d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = x - ((-6.0d0) * (z * (x - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.58) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.54) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = x - (-6.0 * (z * (x - y)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.58:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.54:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = x - (-6.0 * (z * (x - y)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.58)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.54)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(x - Float64(-6.0 * Float64(z * Float64(x - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.58)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.54)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = x - (-6.0 * (z * (x - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.58], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.54], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(x - N[(-6.0 * N[(z * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.57999999999999996

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in z around inf 95.7%

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

      1. neg-mul-1 95.7%

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

   7. Simplified 95.7%

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

      1. add-sqr-sqrt 48.4%

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

      2. fma-define 48.4%

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

      3. distribute-rgt-neg-out 48.4%

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

      4. add-sqr-sqrt 0.0%

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

      5. sqrt-unprod 0.3%

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

      6. sqr-neg 0.3%

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

      7. sqrt-unprod 0.3%

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

      8. add-sqr-sqrt 0.3%

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

      9. fma-neg 0.3%

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

      10. add-sqr-sqrt 0.6%

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

      11. associate-*l* 0.6%

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

      12. add-sqr-sqrt 0.6%

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

      13. sqrt-unprod 0.6%

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

      14. sqr-neg 0.6%

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

      15. sqrt-unprod 0.0%

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

      16. add-sqr-sqrt 95.8%

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

      17. *-commutative 95.8%

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

   9. Applied egg-rr 95.8%

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

   10. Taylor expanded in z around inf 95.8%

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

       1. *-commutative 95.8%

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

       2. associate-*r* 95.8%

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

       3. *-commutative 95.8%

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

       4. associate-*r* 95.8%

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

   12. Simplified 95.8%

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

   if -0.57999999999999996 < z < 0.54000000000000004

   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 z around 0 98.8%

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

   if 0.54000000000000004 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in z around inf 96.6%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x - -6 \cdot \left(z \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 97.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.62 \lor \neg \left(z \leq 0.68\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.62) (not (<= z 0.68)))
   (* (- y x) (* z -6.0))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.62) || !(z <= 0.68)) {
		tmp = (y - x) * (z * -6.0);
	} 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 <= (-0.62d0)) .or. (.not. (z <= 0.68d0))) then
        tmp = (y - x) * (z * (-6.0d0))
    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 <= -0.62) || !(z <= 0.68)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.62) or not (z <= 0.68):
		tmp = (y - x) * (z * -6.0)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.62) || !(z <= 0.68))
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	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 <= -0.62) || ~((z <= 0.68)))
		tmp = (y - x) * (z * -6.0);
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.62], N[Not[LessEqual[z, 0.68]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.619999999999999996 or 0.680000000000000049 < 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 inf 96.1%

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

      1. neg-mul-1 96.1%

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

   7. Simplified 96.1%

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

      1. add-sqr-sqrt 49.6%

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

      2. fma-define 49.6%

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

      3. distribute-rgt-neg-out 49.6%

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

      4. add-sqr-sqrt 25.4%

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

      5. sqrt-unprod 19.1%

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

      6. sqr-neg 19.1%

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

      7. sqrt-unprod 0.2%

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

      8. add-sqr-sqrt 0.3%

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

      9. fma-neg 0.3%

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

      10. add-sqr-sqrt 0.6%

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

      11. associate-*l* 0.6%

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

      12. add-sqr-sqrt 0.3%

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

      13. sqrt-unprod 38.5%

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

      14. sqr-neg 38.5%

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

      15. sqrt-unprod 48.1%

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

      16. add-sqr-sqrt 96.1%

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

      17. *-commutative 96.1%

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

   9. Applied egg-rr 96.1%

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

   10. Taylor expanded in z around inf 96.2%

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

       1. *-commutative 96.2%

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

       2. associate-*r* 96.2%

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

       3. *-commutative 96.2%

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

       4. associate-*r* 96.2%

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

   12. Simplified 96.2%

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

   if -0.619999999999999996 < z < 0.680000000000000049

   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 z around 0 98.8%

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

4. Final simplification 97.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.62 \lor \neg \left(z \leq 0.68\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -39000000000 \lor \neg \left(x \leq 1.28 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -39000000000.0) (not (<= x 1.28e+41)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -39000000000.0) || !(x <= 1.28e+41)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-39000000000.0d0)) .or. (.not. (x <= 1.28d+41))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -39000000000.0) || !(x <= 1.28e+41)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -39000000000.0) or not (x <= 1.28e+41):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -39000000000.0) || !(x <= 1.28e+41))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -39000000000.0) || ~((x <= 1.28e+41)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -39000000000.0], N[Not[LessEqual[x, 1.28e+41]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.9e10 or 1.27999999999999992e41 < x

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 80.6%

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

      1. *-lft-identity 80.6%

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

      2. *-commutative 80.6%

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

      3. +-commutative 80.6%

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

      4. *-commutative 80.6%

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

      5. fma-undefine 80.7%

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

      6. associate-*r* 80.7%

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

      7. fma-undefine 80.6%

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

      8. *-commutative 80.6%

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

      9. +-commutative 80.6%

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

      10. distribute-rgt-in 80.6%

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

      11. distribute-lft-in 80.6%

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

      12. metadata-eval 80.6%

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

      13. associate-+r+ 80.6%

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

      14. metadata-eval 80.6%

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

      15. associate-*r* 80.6%

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

      16. metadata-eval 80.6%

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

   7. Simplified 80.6%

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

   if -3.9e10 < x < 1.27999999999999992e41

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around inf 75.5%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -39000000000 \lor \neg \left(x \leq 1.28 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 76.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -11500000000 \lor \neg \left(x \leq 3.3 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -11500000000.0) (not (<= x 3.3e+41)))
   (* x (+ -3.0 (* z 6.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -11500000000.0) || !(x <= 3.3e+41)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-11500000000.0d0)) .or. (.not. (x <= 3.3d+41))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -11500000000.0) || !(x <= 3.3e+41)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -11500000000.0) or not (x <= 3.3e+41):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -11500000000.0) || !(x <= 3.3e+41))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -11500000000.0) || ~((x <= 3.3e+41)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -11500000000.0], N[Not[LessEqual[x, 3.3e+41]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e10 or 3.3e41 < x

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 80.6%

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

      1. *-lft-identity 80.6%

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

      2. *-commutative 80.6%

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

      3. +-commutative 80.6%

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

      4. *-commutative 80.6%

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

      5. fma-undefine 80.7%

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

      6. associate-*r* 80.7%

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

      7. fma-undefine 80.6%

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

      8. *-commutative 80.6%

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

      9. +-commutative 80.6%

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

      10. distribute-rgt-in 80.6%

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

      11. distribute-lft-in 80.6%

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

      12. metadata-eval 80.6%

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

      13. associate-+r+ 80.6%

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

      14. metadata-eval 80.6%

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

      15. associate-*r* 80.6%

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

      16. metadata-eval 80.6%

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

   7. Simplified 80.6%

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

   if -1.15e10 < x < 3.3e41

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 75.2%

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

   6. Taylor expanded in x around 0 75.4%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -11500000000 \lor \neg \left(x \leq 3.3 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

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

Alternative 13: 38.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-73} \lor \neg \left(x \leq 2.4 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.4e-73) (not (<= x 2.4e+41))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e-73) || !(x <= 2.4e+41)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-1.4d-73)) .or. (.not. (x <= 2.4d+41))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.4e-73) || !(x <= 2.4e+41)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.4e-73) or not (x <= 2.4e+41):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.4e-73) || !(x <= 2.4e+41))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.4e-73) || ~((x <= 2.4e+41)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.4e-73], N[Not[LessEqual[x, 2.4e+41]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.40000000000000006e-73 or 2.4000000000000002e41 < x

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 77.0%

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

      1. *-lft-identity 77.0%

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

      2. *-commutative 77.0%

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

      3. +-commutative 77.0%

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

      4. *-commutative 77.0%

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

      5. fma-undefine 77.0%

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

      6. associate-*r* 77.0%

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

      7. fma-undefine 77.0%

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

      8. *-commutative 77.0%

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

      9. +-commutative 77.0%

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

      10. distribute-rgt-in 77.0%

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

      11. distribute-lft-in 77.0%

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

      12. metadata-eval 77.0%

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

      13. associate-+r+ 77.0%

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

      14. metadata-eval 77.0%

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

      15. associate-*r* 77.0%

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

      16. metadata-eval 77.0%

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

   7. Simplified 77.0%

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

   8. Taylor expanded in z around 0 46.0%

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

      1. *-commutative 46.0%

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

   10. Simplified 46.0%

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

   if -1.40000000000000006e-73 < x < 2.4000000000000002e41

   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 96.5%

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

   6. Taylor expanded in z around 0 53.5%

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

   7. Taylor expanded in y around inf 35.0%

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

4. Final simplification 39.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.4 \cdot 10^{-73} \lor \neg \left(x \leq 2.4 \cdot 10^{+41}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 * (x - y)) * (z - 0.6666666666666666d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 15: 26.4% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ y \cdot 4 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y 4.0))

C

double code(double x, double y, double z) {
	return y * 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 = y * 4.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(y * 4.0), $MachinePrecision]

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around inf 88.1%

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

6. Taylor expanded in z around 0 59.1%

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

7. Taylor expanded in y around inf 24.8%

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

8. Final simplification 24.8%

   \[\leadsto y \cdot 4 \]
9. Add Preprocessing

Alternative 16: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Taylor expanded in y around inf 53.8%

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

6. Taylor expanded in x around inf 2.5%

   \[\leadsto \color{blue}{x} \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024130 
(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))))