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

Percentage Accurate: 99.5% → 99.5%

Time: 17.3s

Alternatives: 14

Speedup: 1.2×

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

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in y around 0 99.7%

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

6. Final simplification 99.7%

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

Alternative 2: 74.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{if}\;z \leq -66000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4.7 \cdot 10^{-163}:\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq 235000:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* 6.0 (- x y)))))
   (if (<= z -66000.0)
     t_0
     (if (<= z -4.7e-163)
       (* x (+ -3.0 (* 6.0 z)))
       (if (<= z 235000.0) (* y (+ 4.0 (* -6.0 z))) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = z * (6.0 * (x - y));
	double tmp;
	if (z <= -66000.0) {
		tmp = t_0;
	} else if (z <= -4.7e-163) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 235000.0) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = z * (6.0d0 * (x - y))
    if (z <= (-66000.0d0)) then
        tmp = t_0
    else if (z <= (-4.7d-163)) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else if (z <= 235000.0d0) then
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (6.0 * (x - y));
	double tmp;
	if (z <= -66000.0) {
		tmp = t_0;
	} else if (z <= -4.7e-163) {
		tmp = x * (-3.0 + (6.0 * z));
	} else if (z <= 235000.0) {
		tmp = y * (4.0 + (-6.0 * z));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (6.0 * (x - y))
	tmp = 0
	if z <= -66000.0:
		tmp = t_0
	elif z <= -4.7e-163:
		tmp = x * (-3.0 + (6.0 * z))
	elif z <= 235000.0:
		tmp = y * (4.0 + (-6.0 * z))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(6.0 * Float64(x - y)))
	tmp = 0.0
	if (z <= -66000.0)
		tmp = t_0;
	elseif (z <= -4.7e-163)
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	elseif (z <= 235000.0)
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (6.0 * (x - y));
	tmp = 0.0;
	if (z <= -66000.0)
		tmp = t_0;
	elseif (z <= -4.7e-163)
		tmp = x * (-3.0 + (6.0 * z));
	elseif (z <= 235000.0)
		tmp = y * (4.0 + (-6.0 * z));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -66000.0], t$95$0, If[LessEqual[z, -4.7e-163], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 235000.0], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -66000 or 235000 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. fma-define 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in z around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. distribute-rgt-neg-in 99.4%

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

      3. metadata-eval 99.4%

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

      4. cancel-sign-sub-inv 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. distribute-lft-neg-in 99.4%

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

      7. metadata-eval 99.4%

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

   10. Simplified 99.4%

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

   if -66000 < z < -4.7e-163

   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 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. *-lft-identity 61.7%

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

      2. *-commutative 61.7%

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

      3. +-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. fma-define 61.7%

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

      6. associate-*r* 61.7%

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

      7. fma-define 61.7%

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

      8. distribute-lft-in 61.7%

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

      9. neg-mul-1 61.7%

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

      10. distribute-lft-neg-in 61.7%

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

      11. metadata-eval 61.7%

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

      12. metadata-eval 61.7%

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

      13. distribute-rgt-in 61.7%

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

      14. +-commutative 61.7%

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

      15. sub-neg 61.7%

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

      16. distribute-rgt-in 61.6%

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

      17. sub-neg 61.6%

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

      18. distribute-rgt-in 61.6%

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

      19. metadata-eval 61.6%

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

      20. distribute-lft-neg-in 61.6%

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

      21. associate-+r+ 61.7%

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

   7. Simplified 61.7%

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

   if -4.7e-163 < z < 235000

   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 inf 59.4%

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

Alternative 3: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.025:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-165}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.025)
   (* -6.0 (* y z))
   (if (<= z -1.65e-165)
     (* x -3.0)
     (if (<= z 0.65) (* y 4.0) (* z (* x 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.025) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.65e-165) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.025d0)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-1.65d-165)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.65d0) then
        tmp = y * 4.0d0
    else
        tmp = z * (x * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.025) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.65e-165) {
		tmp = x * -3.0;
	} else if (z <= 0.65) {
		tmp = y * 4.0;
	} else {
		tmp = z * (x * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.025:
		tmp = -6.0 * (y * z)
	elif z <= -1.65e-165:
		tmp = x * -3.0
	elif z <= 0.65:
		tmp = y * 4.0
	else:
		tmp = z * (x * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.025)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -1.65e-165)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.65)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(z * Float64(x * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.025)
		tmp = -6.0 * (y * z);
	elseif (z <= -1.65e-165)
		tmp = x * -3.0;
	elseif (z <= 0.65)
		tmp = y * 4.0;
	else
		tmp = z * (x * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.025], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.65e-165], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.65], N[(y * 4.0), $MachinePrecision], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.025000000000000001

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 91.9%

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

   6. Taylor expanded in z around inf 99.4%

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

   7. Taylor expanded in y around inf 58.0%

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

   if -0.025000000000000001 < z < -1.6499999999999999e-165

   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 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. *-lft-identity 61.7%

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

      2. *-commutative 61.7%

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

      3. +-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. fma-define 61.7%

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

      6. associate-*r* 61.7%

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

      7. fma-define 61.7%

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

      8. distribute-lft-in 61.7%

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

      9. neg-mul-1 61.7%

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

      10. distribute-lft-neg-in 61.7%

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

      11. metadata-eval 61.7%

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

      12. metadata-eval 61.7%

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

      13. distribute-rgt-in 61.7%

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

      14. +-commutative 61.7%

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

      15. sub-neg 61.7%

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

      16. distribute-rgt-in 61.6%

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

      17. sub-neg 61.6%

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

      18. distribute-rgt-in 61.6%

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

      19. metadata-eval 61.6%

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

      20. distribute-lft-neg-in 61.6%

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

      21. associate-+r+ 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in z around 0 59.9%

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

      1. *-commutative 59.9%

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

   10. Simplified 59.9%

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

   if -1.6499999999999999e-165 < z < 0.650000000000000022

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in x around 0 59.2%

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

      1. associate-*r* 59.1%

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

      2. *-commutative 59.1%

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

      3. associate-*r* 59.4%

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

      4. sub-neg 59.4%

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

      5. neg-mul-1 59.4%

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

      6. distribute-lft-in 59.4%

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

      7. metadata-eval 59.4%

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

      8. neg-mul-1 59.4%

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

      9. distribute-rgt-neg-in 59.4%

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

      10. distribute-lft-neg-in 59.4%

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

      11. metadata-eval 59.4%

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

      12. +-commutative 59.4%

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

      13. *-commutative 59.4%

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

      14. fma-define 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in z around 0 58.2%

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

       1. *-commutative 58.2%

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

   11. Simplified 58.2%

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

   if 0.650000000000000022 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 63.9%

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

      1. *-lft-identity 63.9%

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

      2. *-commutative 63.9%

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

      3. +-commutative 63.9%

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

      4. *-commutative 63.9%

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

      5. fma-define 63.8%

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

      6. associate-*r* 63.8%

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

      7. fma-define 63.9%

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

      8. distribute-lft-in 63.9%

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

      9. neg-mul-1 63.9%

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

      10. distribute-lft-neg-in 63.9%

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

      11. metadata-eval 63.9%

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

      12. metadata-eval 63.9%

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

      13. distribute-rgt-in 63.9%

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

      14. +-commutative 63.9%

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

      15. sub-neg 63.9%

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

      16. distribute-rgt-in 63.9%

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

      17. sub-neg 63.9%

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

      18. distribute-rgt-in 63.9%

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

      19. metadata-eval 63.9%

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

      20. distribute-lft-neg-in 63.9%

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

      21. associate-+r+ 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in z around inf 63.5%

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

      1. associate-*r* 63.5%

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

   10. Simplified 63.5%

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

4. Final simplification 59.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.025:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.65 \cdot 10^{-165}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -9.5:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{-163}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -9.5)
   (* -6.0 (* y z))
   (if (<= z -2.1e-163)
     (* x -3.0)
     (if (<= z 0.66) (* y 4.0) (* x (* 6.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5) {
		tmp = -6.0 * (y * z);
	} else if (z <= -2.1e-163) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-9.5d0)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-2.1d-163)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.66d0) then
        tmp = y * 4.0d0
    else
        tmp = x * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -9.5) {
		tmp = -6.0 * (y * z);
	} else if (z <= -2.1e-163) {
		tmp = x * -3.0;
	} else if (z <= 0.66) {
		tmp = y * 4.0;
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -9.5:
		tmp = -6.0 * (y * z)
	elif z <= -2.1e-163:
		tmp = x * -3.0
	elif z <= 0.66:
		tmp = y * 4.0
	else:
		tmp = x * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -9.5)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -2.1e-163)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.66)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -9.5)
		tmp = -6.0 * (y * z);
	elseif (z <= -2.1e-163)
		tmp = x * -3.0;
	elseif (z <= 0.66)
		tmp = y * 4.0;
	else
		tmp = x * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -9.5], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.1e-163], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.66], N[(y * 4.0), $MachinePrecision], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -9.5

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 91.9%

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

   6. Taylor expanded in z around inf 99.4%

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

   7. Taylor expanded in y around inf 58.0%

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

   if -9.5 < z < -2.09999999999999998e-163

   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 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. *-lft-identity 61.7%

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

      2. *-commutative 61.7%

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

      3. +-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. fma-define 61.7%

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

      6. associate-*r* 61.7%

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

      7. fma-define 61.7%

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

      8. distribute-lft-in 61.7%

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

      9. neg-mul-1 61.7%

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

      10. distribute-lft-neg-in 61.7%

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

      11. metadata-eval 61.7%

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

      12. metadata-eval 61.7%

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

      13. distribute-rgt-in 61.7%

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

      14. +-commutative 61.7%

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

      15. sub-neg 61.7%

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

      16. distribute-rgt-in 61.6%

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

      17. sub-neg 61.6%

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

      18. distribute-rgt-in 61.6%

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

      19. metadata-eval 61.6%

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

      20. distribute-lft-neg-in 61.6%

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

      21. associate-+r+ 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in z around 0 59.9%

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

      1. *-commutative 59.9%

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

   10. Simplified 59.9%

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

   if -2.09999999999999998e-163 < z < 0.660000000000000031

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in x around 0 59.2%

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

      1. associate-*r* 59.1%

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

      2. *-commutative 59.1%

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

      3. associate-*r* 59.4%

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

      4. sub-neg 59.4%

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

      5. neg-mul-1 59.4%

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

      6. distribute-lft-in 59.4%

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

      7. metadata-eval 59.4%

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

      8. neg-mul-1 59.4%

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

      9. distribute-rgt-neg-in 59.4%

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

      10. distribute-lft-neg-in 59.4%

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

      11. metadata-eval 59.4%

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

      12. +-commutative 59.4%

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

      13. *-commutative 59.4%

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

      14. fma-define 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in z around 0 58.2%

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

       1. *-commutative 58.2%

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

   11. Simplified 58.2%

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

   if 0.660000000000000031 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 63.9%

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

      1. *-lft-identity 63.9%

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

      2. *-commutative 63.9%

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

      3. +-commutative 63.9%

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

      4. *-commutative 63.9%

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

      5. fma-define 63.8%

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

      6. associate-*r* 63.8%

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

      7. fma-define 63.9%

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

      8. distribute-lft-in 63.9%

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

      9. neg-mul-1 63.9%

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

      10. distribute-lft-neg-in 63.9%

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

      11. metadata-eval 63.9%

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

      12. metadata-eval 63.9%

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

      13. distribute-rgt-in 63.9%

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

      14. +-commutative 63.9%

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

      15. sub-neg 63.9%

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

      16. distribute-rgt-in 63.9%

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

      17. sub-neg 63.9%

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

      18. distribute-rgt-in 63.9%

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

      19. metadata-eval 63.9%

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

      20. distribute-lft-neg-in 63.9%

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

      21. associate-+r+ 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in z around inf 63.5%

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

Alternative 5: 50.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -6.8:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-163}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -6.8)
   (* -6.0 (* y z))
   (if (<= z -2.7e-163)
     (* x -3.0)
     (if (<= z 0.52) (* y 4.0) (* 6.0 (* x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8) {
		tmp = -6.0 * (y * z);
	} else if (z <= -2.7e-163) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-6.8d0)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-2.7d-163)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.52d0) then
        tmp = y * 4.0d0
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -6.8) {
		tmp = -6.0 * (y * z);
	} else if (z <= -2.7e-163) {
		tmp = x * -3.0;
	} else if (z <= 0.52) {
		tmp = y * 4.0;
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -6.8:
		tmp = -6.0 * (y * z)
	elif z <= -2.7e-163:
		tmp = x * -3.0
	elif z <= 0.52:
		tmp = y * 4.0
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -6.8)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -2.7e-163)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.52)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -6.8)
		tmp = -6.0 * (y * z);
	elseif (z <= -2.7e-163)
		tmp = x * -3.0;
	elseif (z <= 0.52)
		tmp = y * 4.0;
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -6.8], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.7e-163], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(y * 4.0), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -6.79999999999999982

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 91.9%

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

   6. Taylor expanded in z around inf 99.4%

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

   7. Taylor expanded in y around inf 58.0%

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

   if -6.79999999999999982 < z < -2.70000000000000015e-163

   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 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. *-lft-identity 61.7%

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

      2. *-commutative 61.7%

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

      3. +-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. fma-define 61.7%

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

      6. associate-*r* 61.7%

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

      7. fma-define 61.7%

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

      8. distribute-lft-in 61.7%

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

      9. neg-mul-1 61.7%

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

      10. distribute-lft-neg-in 61.7%

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

      11. metadata-eval 61.7%

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

      12. metadata-eval 61.7%

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

      13. distribute-rgt-in 61.7%

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

      14. +-commutative 61.7%

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

      15. sub-neg 61.7%

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

      16. distribute-rgt-in 61.6%

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

      17. sub-neg 61.6%

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

      18. distribute-rgt-in 61.6%

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

      19. metadata-eval 61.6%

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

      20. distribute-lft-neg-in 61.6%

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

      21. associate-+r+ 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in z around 0 59.9%

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

      1. *-commutative 59.9%

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

   10. Simplified 59.9%

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

   if -2.70000000000000015e-163 < z < 0.52000000000000002

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in x around 0 59.2%

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

      1. associate-*r* 59.1%

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

      2. *-commutative 59.1%

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

      3. associate-*r* 59.4%

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

      4. sub-neg 59.4%

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

      5. neg-mul-1 59.4%

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

      6. distribute-lft-in 59.4%

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

      7. metadata-eval 59.4%

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

      8. neg-mul-1 59.4%

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

      9. distribute-rgt-neg-in 59.4%

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

      10. distribute-lft-neg-in 59.4%

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

      11. metadata-eval 59.4%

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

      12. +-commutative 59.4%

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

      13. *-commutative 59.4%

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

      14. fma-define 59.4%

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

   8. Simplified 59.4%

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

   9. Taylor expanded in z around 0 58.2%

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

       1. *-commutative 58.2%

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

   11. Simplified 58.2%

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

   if 0.52000000000000002 < z

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 63.9%

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

      1. *-lft-identity 63.9%

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

      2. *-commutative 63.9%

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

      3. +-commutative 63.9%

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

      4. *-commutative 63.9%

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

      5. fma-define 63.8%

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

      6. associate-*r* 63.8%

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

      7. fma-define 63.9%

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

      8. distribute-lft-in 63.9%

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

      9. neg-mul-1 63.9%

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

      10. distribute-lft-neg-in 63.9%

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

      11. metadata-eval 63.9%

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

      12. metadata-eval 63.9%

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

      13. distribute-rgt-in 63.9%

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

      14. +-commutative 63.9%

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

      15. sub-neg 63.9%

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

      16. distribute-rgt-in 63.9%

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

      17. sub-neg 63.9%

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

      18. distribute-rgt-in 63.9%

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

      19. metadata-eval 63.9%

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

      20. distribute-lft-neg-in 63.9%

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

      21. associate-+r+ 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in z around inf 63.5%

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

Alternative 6: 50.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -0.116:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8.2 \cdot 10^{-165}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 64000000000:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -0.116)
     t_0
     (if (<= z -8.2e-165)
       (* x -3.0)
       (if (<= z 64000000000.0) (* y 4.0) t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.116) {
		tmp = t_0;
	} else if (z <= -8.2e-165) {
		tmp = x * -3.0;
	} else if (z <= 64000000000.0) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-0.116d0)) then
        tmp = t_0
    else if (z <= (-8.2d-165)) then
        tmp = x * (-3.0d0)
    else if (z <= 64000000000.0d0) then
        tmp = y * 4.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -0.116) {
		tmp = t_0;
	} else if (z <= -8.2e-165) {
		tmp = x * -3.0;
	} else if (z <= 64000000000.0) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -0.116:
		tmp = t_0
	elif z <= -8.2e-165:
		tmp = x * -3.0
	elif z <= 64000000000.0:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -0.116)
		tmp = t_0;
	elseif (z <= -8.2e-165)
		tmp = Float64(x * -3.0);
	elseif (z <= 64000000000.0)
		tmp = Float64(y * 4.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -0.116)
		tmp = t_0;
	elseif (z <= -8.2e-165)
		tmp = x * -3.0;
	elseif (z <= 64000000000.0)
		tmp = y * 4.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.116], t$95$0, If[LessEqual[z, -8.2e-165], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 64000000000.0], N[(y * 4.0), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.116000000000000006 or 6.4e10 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in x around 0 95.6%

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

   6. Taylor expanded in z around inf 99.6%

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

   7. Taylor expanded in y around inf 51.0%

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

   if -0.116000000000000006 < z < -8.2000000000000004e-165

   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 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 61.7%

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

      1. *-lft-identity 61.7%

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

      2. *-commutative 61.7%

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

      3. +-commutative 61.7%

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

      4. *-commutative 61.7%

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

      5. fma-define 61.7%

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

      6. associate-*r* 61.7%

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

      7. fma-define 61.7%

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

      8. distribute-lft-in 61.7%

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

      9. neg-mul-1 61.7%

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

      10. distribute-lft-neg-in 61.7%

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

      11. metadata-eval 61.7%

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

      12. metadata-eval 61.7%

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

      13. distribute-rgt-in 61.7%

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

      14. +-commutative 61.7%

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

      15. sub-neg 61.7%

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

      16. distribute-rgt-in 61.6%

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

      17. sub-neg 61.6%

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

      18. distribute-rgt-in 61.6%

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

      19. metadata-eval 61.6%

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

      20. distribute-lft-neg-in 61.6%

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

      21. associate-+r+ 61.7%

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

   7. Simplified 61.7%

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

   8. Taylor expanded in z around 0 59.9%

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

      1. *-commutative 59.9%

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

   10. Simplified 59.9%

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

   if -8.2000000000000004e-165 < z < 6.4e10

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in x around 0 58.5%

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

      1. associate-*r* 58.4%

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

      2. *-commutative 58.4%

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

      3. associate-*r* 58.7%

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

      4. sub-neg 58.7%

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

      5. neg-mul-1 58.7%

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

      6. distribute-lft-in 58.7%

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

      7. metadata-eval 58.7%

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

      8. neg-mul-1 58.7%

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

      9. distribute-rgt-neg-in 58.7%

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

      10. distribute-lft-neg-in 58.7%

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

      11. metadata-eval 58.7%

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

      12. +-commutative 58.7%

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

      13. *-commutative 58.7%

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

      14. fma-define 58.7%

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

   8. Simplified 58.7%

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

   9. Taylor expanded in z around 0 57.5%

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

       1. *-commutative 57.5%

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

   11. Simplified 57.5%

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

Alternative 7: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.56\right):\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.56)))
   (* z (* 6.0 (- x y)))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.56)) {
		tmp = z * (6.0 * (x - y));
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.6d0)) .or. (.not. (z <= 0.56d0))) then
        tmp = z * (6.0d0 * (x - y))
    else
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.56)) {
		tmp = z * (6.0 * (x - y));
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.56):
		tmp = z * (6.0 * (x - y))
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.56))
		tmp = Float64(z * Float64(6.0 * Float64(x - y)));
	else
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.56)))
		tmp = z * (6.0 * (x - y));
	else
		tmp = (x * -3.0) + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.56]], $MachinePrecision]], N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.56000000000000005 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. fma-define 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in z around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. distribute-rgt-neg-in 99.4%

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

      3. metadata-eval 99.4%

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

      4. cancel-sign-sub-inv 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. distribute-lft-neg-in 99.4%

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

      7. metadata-eval 99.4%

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

   10. Simplified 99.4%

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

   if -0.599999999999999978 < z < 0.56000000000000005

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.7%

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

   6. Taylor expanded in z around 0 98.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.56\right):\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.8% accurate, 0.8× speedup

Math

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

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.56) (not (<= z 0.56)))
   (* z (* 6.0 (- x y)))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.56) || !(z <= 0.56)) {
		tmp = z * (6.0 * (x - y));
	} 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 <= (-0.56d0)) .or. (.not. (z <= 0.56d0))) then
        tmp = z * (6.0d0 * (x - y))
    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 <= -0.56) || !(z <= 0.56)) {
		tmp = z * (6.0 * (x - y));
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.56) or not (z <= 0.56):
		tmp = z * (6.0 * (x - y))
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.56) || !(z <= 0.56))
		tmp = Float64(z * Float64(6.0 * Float64(x - y)));
	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 <= -0.56) || ~((z <= 0.56)))
		tmp = z * (6.0 * (x - y));
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.56], N[Not[LessEqual[z, 0.56]], $MachinePrecision]], N[(z * N[(6.0 * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.56000000000000005 or 0.56000000000000005 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 99.8%

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

      1. +-commutative 99.8%

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

      2. fma-define 99.8%

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

      3. fma-define 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in z around inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. distribute-rgt-neg-in 99.4%

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

      3. metadata-eval 99.4%

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

      4. cancel-sign-sub-inv 99.4%

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

      5. distribute-lft-out-- 99.4%

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

      6. distribute-lft-neg-in 99.4%

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

      7. metadata-eval 99.4%

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

   10. Simplified 99.4%

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

   if -0.56000000000000005 < z < 0.56000000000000005

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in z around 0 98.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56 \lor \neg \left(z \leq 0.56\right):\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+17} \lor \neg \left(x \leq 2.75 \cdot 10^{-73}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6.5e+17) (not (<= x 2.75e-73)))
   (* x (+ -3.0 (* 6.0 z)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e+17) || !(x <= 2.75e-73)) {
		tmp = x * (-3.0 + (6.0 * z));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-6.5d+17)) .or. (.not. (x <= 2.75d-73))) then
        tmp = x * ((-3.0d0) + (6.0d0 * z))
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6.5e+17) || !(x <= 2.75e-73)) {
		tmp = x * (-3.0 + (6.0 * z));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6.5e+17) or not (x <= 2.75e-73):
		tmp = x * (-3.0 + (6.0 * z))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6.5e+17) || !(x <= 2.75e-73))
		tmp = Float64(x * Float64(-3.0 + Float64(6.0 * z)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6.5e+17) || ~((x <= 2.75e-73)))
		tmp = x * (-3.0 + (6.0 * z));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6.5e+17], N[Not[LessEqual[x, 2.75e-73]], $MachinePrecision]], N[(x * N[(-3.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.5e17 or 2.75000000000000003e-73 < x

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.8%

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

      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 74.4%

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

      1. *-lft-identity 74.4%

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

      2. *-commutative 74.4%

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

      3. +-commutative 74.4%

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

      4. *-commutative 74.4%

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

      5. fma-define 74.3%

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

      6. associate-*r* 74.3%

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

      7. fma-define 74.4%

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

      8. distribute-lft-in 74.4%

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

      9. neg-mul-1 74.4%

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

      10. distribute-lft-neg-in 74.4%

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

      11. metadata-eval 74.4%

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

      12. metadata-eval 74.4%

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

      13. distribute-rgt-in 74.4%

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

      14. +-commutative 74.4%

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

      15. sub-neg 74.4%

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

      16. distribute-rgt-in 74.4%

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

      17. sub-neg 74.4%

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

      18. distribute-rgt-in 74.4%

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

      19. metadata-eval 74.4%

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

      20. distribute-lft-neg-in 74.4%

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

      21. associate-+r+ 74.4%

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

   7. Simplified 74.4%

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

   if -6.5e17 < x < 2.75000000000000003e-73

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 99.6%

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

   6. Taylor expanded in x around 0 81.4%

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

4. Final simplification 77.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+17} \lor \neg \left(x \leq 2.75 \cdot 10^{-73}\right):\\ \;\;\;\;x \cdot \left(-3 + 6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;z \cdot \left(-6 \cdot y + x \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* z (+ (* -6.0 y) (* x 6.0)))
   (if (<= z 0.65) (+ (* x -3.0) (* y 4.0)) (* z (* 6.0 (- x y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = z * ((-6.0 * y) + (x * 6.0));
	} else if (z <= 0.65) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = 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 = z * (((-6.0d0) * y) + (x * 6.0d0))
    else if (z <= 0.65d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = 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 = z * ((-6.0 * y) + (x * 6.0));
	} else if (z <= 0.65) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * (6.0 * (x - y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = z * ((-6.0 * y) + (x * 6.0))
	elif z <= 0.65:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = z * (6.0 * (x - y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(z * Float64(Float64(-6.0 * y) + Float64(x * 6.0)));
	elseif (z <= 0.65)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = 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 = z * ((-6.0 * y) + (x * 6.0));
	elseif (z <= 0.65)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = z * (6.0 * (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(z * N[(N[(-6.0 * y), $MachinePrecision] + N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(6.0 * N[(x - y), $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 x around 0 91.9%

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

   6. Taylor expanded in z around inf 99.4%

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

   if -0.599999999999999978 < z < 0.650000000000000022

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around 0 99.7%

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

   6. Taylor expanded in z around 0 98.5%

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

   if 0.650000000000000022 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 99.9%

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

      1. +-commutative 99.9%

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

      2. fma-define 99.9%

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

      3. fma-define 99.8%

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

   7. Applied egg-rr 99.8%

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

   8. Taylor expanded in z around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-rgt-neg-in 99.5%

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

      3. metadata-eval 99.5%

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

      4. cancel-sign-sub-inv 99.5%

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

      5. distribute-lft-out-- 99.5%

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

      6. distribute-lft-neg-in 99.5%

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

      7. metadata-eval 99.5%

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

   10. Simplified 99.5%

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

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;z \cdot \left(-6 \cdot y + x \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(6 \cdot \left(x - y\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 59.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+83}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -4.6e+21)
   (* z (* x 6.0))
   (if (<= x 4e+83) (* 6.0 (* y (- 0.6666666666666666 z))) (* x (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+21) {
		tmp = z * (x * 6.0);
	} else if (x <= 4e+83) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-4.6d+21)) then
        tmp = z * (x * 6.0d0)
    else if (x <= 4d+83) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else
        tmp = x * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -4.6e+21) {
		tmp = z * (x * 6.0);
	} else if (x <= 4e+83) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else {
		tmp = x * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -4.6e+21:
		tmp = z * (x * 6.0)
	elif x <= 4e+83:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	else:
		tmp = x * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -4.6e+21)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (x <= 4e+83)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	else
		tmp = Float64(x * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -4.6e+21)
		tmp = z * (x * 6.0);
	elseif (x <= 4e+83)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	else
		tmp = x * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -4.6e+21], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4e+83], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.6e21

   1. Initial program 99.9%

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

      1. +-commutative 99.9%

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

      2. associate-*l* 99.9%

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

      3. fma-define 99.9%

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

      4. sub-neg 99.9%

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

      5. distribute-rgt-in 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 81.8%

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

      1. *-lft-identity 81.8%

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

      2. *-commutative 81.8%

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

      3. +-commutative 81.8%

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

      4. *-commutative 81.8%

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

      5. fma-define 81.8%

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

      6. associate-*r* 81.8%

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

      7. fma-define 81.8%

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

      8. distribute-lft-in 81.8%

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

      9. neg-mul-1 81.8%

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

      10. distribute-lft-neg-in 81.8%

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

      11. metadata-eval 81.8%

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

      12. metadata-eval 81.8%

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

      13. distribute-rgt-in 81.8%

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

      14. +-commutative 81.8%

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

      15. sub-neg 81.8%

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

      16. distribute-rgt-in 81.8%

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

      17. sub-neg 81.8%

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

      18. distribute-rgt-in 81.8%

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

      19. metadata-eval 81.8%

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

      20. distribute-lft-neg-in 81.8%

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

      21. associate-+r+ 81.8%

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

   7. Simplified 81.8%

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

   8. Taylor expanded in z around inf 54.0%

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

      1. associate-*r* 54.1%

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

   10. Simplified 54.1%

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

   if -4.6e21 < x < 4.00000000000000012e83

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.6%

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

   6. Taylor expanded in x around 0 73.4%

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

   if 4.00000000000000012e83 < x

   1. Initial program 99.7%

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

      1. +-commutative 99.7%

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

      2. associate-*l* 99.8%

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

      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 76.3%

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

      1. *-lft-identity 76.3%

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

      2. *-commutative 76.3%

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

      3. +-commutative 76.3%

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

      4. *-commutative 76.3%

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

      5. fma-define 76.3%

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

      6. associate-*r* 76.3%

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

      7. fma-define 76.3%

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

      8. distribute-lft-in 76.3%

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

      9. neg-mul-1 76.3%

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

      10. distribute-lft-neg-in 76.3%

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

      11. metadata-eval 76.3%

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

      12. metadata-eval 76.3%

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

      13. distribute-rgt-in 76.3%

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

      14. +-commutative 76.3%

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

      15. sub-neg 76.3%

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

      16. distribute-rgt-in 76.3%

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

      17. sub-neg 76.3%

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

      18. distribute-rgt-in 76.3%

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

      19. metadata-eval 76.3%

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

      20. distribute-lft-neg-in 76.3%

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

      21. associate-+r+ 76.3%

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

   7. Simplified 76.3%

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

   8. Taylor expanded in z around inf 55.9%

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

4. Final simplification 65.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{+21}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+83}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 34.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{-109} \lor \neg \left(x \leq 3.7 \cdot 10^{+219}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.04e-109) (not (<= x 3.7e+219))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.04e-109) || !(x <= 3.7e+219)) {
		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 <= (-1.04d-109)) .or. (.not. (x <= 3.7d+219))) 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 <= -1.04e-109) || !(x <= 3.7e+219)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.04e-109) or not (x <= 3.7e+219):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.04e-109) || !(x <= 3.7e+219))
		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 <= -1.04e-109) || ~((x <= 3.7e+219)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.04e-109], N[Not[LessEqual[x, 3.7e+219]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.03999999999999996e-109 or 3.7e219 < x

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.8%

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

      3. fma-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 74.8%

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

      1. *-lft-identity 74.8%

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

      2. *-commutative 74.8%

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

      3. +-commutative 74.8%

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

      4. *-commutative 74.8%

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

      5. fma-define 74.8%

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

      6. associate-*r* 74.8%

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

      7. fma-define 74.8%

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

      8. distribute-lft-in 74.8%

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

      9. neg-mul-1 74.8%

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

      10. distribute-lft-neg-in 74.8%

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

      11. metadata-eval 74.8%

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

      12. metadata-eval 74.8%

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

      13. distribute-rgt-in 74.8%

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

      14. +-commutative 74.8%

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

      15. sub-neg 74.8%

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

      16. distribute-rgt-in 74.8%

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

      17. sub-neg 74.8%

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

      18. distribute-rgt-in 74.8%

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

      19. metadata-eval 74.8%

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

      20. distribute-lft-neg-in 74.8%

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

      21. associate-+r+ 74.8%

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

   7. Simplified 74.8%

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

   8. Taylor expanded in z around 0 32.7%

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

      1. *-commutative 32.7%

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

   10. Simplified 32.7%

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

   if -1.03999999999999996e-109 < x < 3.7e219

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 99.6%

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

   6. Taylor expanded in x around 0 68.9%

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

      1. associate-*r* 68.8%

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

      2. *-commutative 68.8%

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

      3. associate-*r* 68.4%

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

      4. sub-neg 68.4%

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

      5. neg-mul-1 68.4%

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

      6. distribute-lft-in 68.4%

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

      7. metadata-eval 68.4%

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

      8. neg-mul-1 68.4%

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

      9. distribute-rgt-neg-in 68.4%

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

      10. distribute-lft-neg-in 68.4%

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

      11. metadata-eval 68.4%

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

      12. +-commutative 68.4%

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

      13. *-commutative 68.4%

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

      14. fma-define 68.3%

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

   8. Simplified 68.3%

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

   9. Taylor expanded in z around 0 37.5%

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

       1. *-commutative 37.5%

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

   11. Simplified 37.5%

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

4. Final simplification 35.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{-109} \lor \neg \left(x \leq 3.7 \cdot 10^{+219}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((0.6666666666666666 - z) * (6.0 * (y - 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 + ((0.6666666666666666d0 - z) * (6.0d0 * (y - x)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Final simplification 99.7%

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

Alternative 14: 26.4% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.7%

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

   1. +-commutative 99.7%

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

   2. associate-*l* 99.4%

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

   3. fma-define 99.4%

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

   4. sub-neg 99.4%

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

   5. distribute-rgt-in 99.4%

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

   6. metadata-eval 99.4%

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

   7. metadata-eval 99.4%

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

   8. distribute-lft-neg-out 99.4%

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

   9. distribute-rgt-neg-in 99.4%

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

   10. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in y around 0 50.7%

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

   1. *-lft-identity 50.7%

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

   2. *-commutative 50.7%

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

   3. +-commutative 50.7%

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

   4. *-commutative 50.7%

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

   5. fma-define 50.6%

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

   6. associate-*r* 50.6%

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

   7. fma-define 50.7%

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

   8. distribute-lft-in 50.7%

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

   9. neg-mul-1 50.7%

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

   10. distribute-lft-neg-in 50.7%

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

   11. metadata-eval 50.7%

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

   12. metadata-eval 50.7%

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

   13. distribute-rgt-in 50.7%

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

   14. +-commutative 50.7%

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

   15. sub-neg 50.7%

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

   16. distribute-rgt-in 50.6%

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

   17. sub-neg 50.6%

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

   18. distribute-rgt-in 50.6%

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

   19. metadata-eval 50.6%

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

   20. distribute-lft-neg-in 50.6%

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

   21. associate-+r+ 50.6%

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

7. Simplified 50.6%

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

8. Taylor expanded in z around 0 21.7%

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

   1. *-commutative 21.7%

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

10. Simplified 21.7%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Reproduce

herbie shell --seed 2024160 
(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))))