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

Percentage Accurate: 99.5% → 99.7%

Time: 9.0s

Alternatives: 11

Speedup: 1.2×

• 21.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

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

   3. fma-def 99.7%

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

   4. sub-neg 99.7%

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

   5. +-commutative 99.7%

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

   6. distribute-lft-in 99.7%

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

   7. neg-mul-1 99.7%

      \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   8. associate-*r* 99.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

   9. *-commutative 99.7%

      \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

   10. fma-def 99.8%

       \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

   11. metadata-eval 99.8%

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

   12. metadata-eval 99.8%

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

   13. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

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

Alternative 2: 50.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.4 \cdot 10^{+161}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+17}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-241}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -1.4e+161)
     t_0
     (if (<= z -3e+17)
       (* -6.0 (* y z))
       (if (<= z -1.5e-130)
         (* x -3.0)
         (if (<= z -6.6e-241)
           (* y 4.0)
           (if (<= z -1.3e-305)
             (* x -3.0)
             (if (<= z 0.55) (* y 4.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.4e+161) {
		tmp = t_0;
	} else if (z <= -3e+17) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.5e-130) {
		tmp = x * -3.0;
	} else if (z <= -6.6e-241) {
		tmp = y * 4.0;
	} else if (z <= -1.3e-305) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		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 * (x * z)
    if (z <= (-1.4d+161)) then
        tmp = t_0
    else if (z <= (-3d+17)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-1.5d-130)) then
        tmp = x * (-3.0d0)
    else if (z <= (-6.6d-241)) then
        tmp = y * 4.0d0
    else if (z <= (-1.3d-305)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.55d0) 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 * (x * z);
	double tmp;
	if (z <= -1.4e+161) {
		tmp = t_0;
	} else if (z <= -3e+17) {
		tmp = -6.0 * (y * z);
	} else if (z <= -1.5e-130) {
		tmp = x * -3.0;
	} else if (z <= -6.6e-241) {
		tmp = y * 4.0;
	} else if (z <= -1.3e-305) {
		tmp = x * -3.0;
	} else if (z <= 0.55) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -1.4e+161:
		tmp = t_0
	elif z <= -3e+17:
		tmp = -6.0 * (y * z)
	elif z <= -1.5e-130:
		tmp = x * -3.0
	elif z <= -6.6e-241:
		tmp = y * 4.0
	elif z <= -1.3e-305:
		tmp = x * -3.0
	elif z <= 0.55:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.4e+161)
		tmp = t_0;
	elseif (z <= -3e+17)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -1.5e-130)
		tmp = Float64(x * -3.0);
	elseif (z <= -6.6e-241)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.3e-305)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.55)
		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 * (x * z);
	tmp = 0.0;
	if (z <= -1.4e+161)
		tmp = t_0;
	elseif (z <= -3e+17)
		tmp = -6.0 * (y * z);
	elseif (z <= -1.5e-130)
		tmp = x * -3.0;
	elseif (z <= -6.6e-241)
		tmp = y * 4.0;
	elseif (z <= -1.3e-305)
		tmp = x * -3.0;
	elseif (z <= 0.55)
		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[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.4e+161], t$95$0, If[LessEqual[z, -3e+17], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.5e-130], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -6.6e-241], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.3e-305], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.4000000000000001e161 or 0.55000000000000004 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in x around inf 59.7%

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

      1. *-commutative 59.7%

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

      2. fma-neg 59.8%

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

      3. metadata-eval 59.8%

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

   5. Simplified 59.8%

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

   6. Taylor expanded in z around inf 59.7%

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

   if -1.4000000000000001e161 < z < -3e17

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in x around 0 67.8%

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

   4. Taylor expanded in z around inf 67.8%

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

      1. *-commutative 67.8%

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

   6. Simplified 67.8%

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

   if -3e17 < z < -1.49999999999999993e-130 or -6.5999999999999998e-241 < z < -1.3000000000000001e-305

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. +-commutative 69.7%

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

      3. sub-neg 69.7%

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

      4. distribute-rgt-in 69.7%

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

      5. metadata-eval 69.7%

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

      6. metadata-eval 69.7%

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

      7. neg-mul-1 69.7%

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

      8. associate-*r* 69.7%

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

      9. *-commutative 69.7%

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

      10. distribute-lft-in 69.7%

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

      11. +-commutative 69.7%

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

      12. distribute-lft-in 69.7%

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

      13. associate-+r+ 69.8%

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

      14. metadata-eval 69.8%

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

      15. metadata-eval 69.8%

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

      16. metadata-eval 69.8%

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

      17. distribute-lft-in 69.8%

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

      18. mul-1-neg 69.8%

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

      19. +-commutative 69.8%

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

      20. fma-def 69.8%

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

   4. Simplified 69.8%

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

   5. Taylor expanded in z around 0 65.9%

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

      1. *-commutative 65.9%

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

   7. Simplified 65.9%

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

   if -1.49999999999999993e-130 < z < -6.5999999999999998e-241 or -1.3000000000000001e-305 < z < 0.55000000000000004

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      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-def 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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 59.4%

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

   5. Taylor expanded in z around 0 59.0%

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

      1. *-commutative 59.0%

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

   7. Simplified 59.0%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.4 \cdot 10^{+161}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{+17}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -6.6 \cdot 10^{-241}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0095:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-239}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0095)
     t_0
     (if (<= z -5.5e-130)
       (* x -3.0)
       (if (<= z -1.4e-239)
         (* y 4.0)
         (if (<= z -5.8e-307) (* x -3.0) (if (<= z 0.56) (* y 4.0) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0095) {
		tmp = t_0;
	} else if (z <= -5.5e-130) {
		tmp = x * -3.0;
	} else if (z <= -1.4e-239) {
		tmp = y * 4.0;
	} else if (z <= -5.8e-307) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		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 - x) * z)
    if (z <= (-0.0095d0)) then
        tmp = t_0
    else if (z <= (-5.5d-130)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.4d-239)) then
        tmp = y * 4.0d0
    else if (z <= (-5.8d-307)) then
        tmp = x * (-3.0d0)
    else if (z <= 0.56d0) 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 - x) * z);
	double tmp;
	if (z <= -0.0095) {
		tmp = t_0;
	} else if (z <= -5.5e-130) {
		tmp = x * -3.0;
	} else if (z <= -1.4e-239) {
		tmp = y * 4.0;
	} else if (z <= -5.8e-307) {
		tmp = x * -3.0;
	} else if (z <= 0.56) {
		tmp = y * 4.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.0095:
		tmp = t_0
	elif z <= -5.5e-130:
		tmp = x * -3.0
	elif z <= -1.4e-239:
		tmp = y * 4.0
	elif z <= -5.8e-307:
		tmp = x * -3.0
	elif z <= 0.56:
		tmp = y * 4.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.0095)
		tmp = t_0;
	elseif (z <= -5.5e-130)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.4e-239)
		tmp = Float64(y * 4.0);
	elseif (z <= -5.8e-307)
		tmp = Float64(x * -3.0);
	elseif (z <= 0.56)
		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 - x) * z);
	tmp = 0.0;
	if (z <= -0.0095)
		tmp = t_0;
	elseif (z <= -5.5e-130)
		tmp = x * -3.0;
	elseif (z <= -1.4e-239)
		tmp = y * 4.0;
	elseif (z <= -5.8e-307)
		tmp = x * -3.0;
	elseif (z <= 0.56)
		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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0095], t$95$0, If[LessEqual[z, -5.5e-130], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.4e-239], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5.8e-307], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.00949999999999999976 or 0.56000000000000005 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   if -0.00949999999999999976 < z < -5.50000000000000007e-130 or -1.40000000000000006e-239 < z < -5.8000000000000001e-307

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. +-commutative 69.2%

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

      3. sub-neg 69.2%

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

      4. distribute-rgt-in 69.2%

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

      5. metadata-eval 69.2%

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

      6. metadata-eval 69.2%

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

      7. neg-mul-1 69.2%

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

      8. associate-*r* 69.2%

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

      9. *-commutative 69.2%

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

      10. distribute-lft-in 69.2%

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

      11. +-commutative 69.2%

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

      12. distribute-lft-in 69.2%

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

      13. associate-+r+ 69.2%

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

      14. metadata-eval 69.2%

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

      15. metadata-eval 69.2%

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

      16. metadata-eval 69.2%

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

      17. distribute-lft-in 69.2%

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

      18. mul-1-neg 69.2%

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

      19. +-commutative 69.2%

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

      20. fma-def 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in z around 0 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if -5.50000000000000007e-130 < z < -1.40000000000000006e-239 or -5.8000000000000001e-307 < z < 0.56000000000000005

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      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-def 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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 59.4%

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

   5. Taylor expanded in z around 0 59.0%

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

      1. *-commutative 59.0%

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

   7. Simplified 59.0%

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

4. Final simplification 80.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0095:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-239}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 4: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -0.0055:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-131}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-240}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 170000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -0.0055)
     t_0
     (if (<= z -3.45e-131)
       (* x -3.0)
       (if (<= z -1.05e-240)
         (* y 4.0)
         (if (<= z -4.2e-305)
           (* x -3.0)
           (if (<= z 170000.0) (* y (+ 4.0 (* z -6.0))) t_0)))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0055) {
		tmp = t_0;
	} else if (z <= -3.45e-131) {
		tmp = x * -3.0;
	} else if (z <= -1.05e-240) {
		tmp = y * 4.0;
	} else if (z <= -4.2e-305) {
		tmp = x * -3.0;
	} else if (z <= 170000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * ((y - x) * z)
    if (z <= (-0.0055d0)) then
        tmp = t_0
    else if (z <= (-3.45d-131)) then
        tmp = x * (-3.0d0)
    else if (z <= (-1.05d-240)) then
        tmp = y * 4.0d0
    else if (z <= (-4.2d-305)) then
        tmp = x * (-3.0d0)
    else if (z <= 170000.0d0) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * ((y - x) * z);
	double tmp;
	if (z <= -0.0055) {
		tmp = t_0;
	} else if (z <= -3.45e-131) {
		tmp = x * -3.0;
	} else if (z <= -1.05e-240) {
		tmp = y * 4.0;
	} else if (z <= -4.2e-305) {
		tmp = x * -3.0;
	} else if (z <= 170000.0) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * ((y - x) * z)
	tmp = 0
	if z <= -0.0055:
		tmp = t_0
	elif z <= -3.45e-131:
		tmp = x * -3.0
	elif z <= -1.05e-240:
		tmp = y * 4.0
	elif z <= -4.2e-305:
		tmp = x * -3.0
	elif z <= 170000.0:
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -0.0055)
		tmp = t_0;
	elseif (z <= -3.45e-131)
		tmp = Float64(x * -3.0);
	elseif (z <= -1.05e-240)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.2e-305)
		tmp = Float64(x * -3.0);
	elseif (z <= 170000.0)
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -0.0055)
		tmp = t_0;
	elseif (z <= -3.45e-131)
		tmp = x * -3.0;
	elseif (z <= -1.05e-240)
		tmp = y * 4.0;
	elseif (z <= -4.2e-305)
		tmp = x * -3.0;
	elseif (z <= 170000.0)
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -0.0055], t$95$0, If[LessEqual[z, -3.45e-131], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -1.05e-240], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.2e-305], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 170000.0], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -0.0054999999999999997 or 1.7e5 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   if -0.0054999999999999997 < z < -3.45000000000000008e-131 or -1.04999999999999997e-240 < z < -4.2e-305

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 69.2%

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

      1. *-commutative 69.2%

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

      2. +-commutative 69.2%

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

      3. sub-neg 69.2%

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

      4. distribute-rgt-in 69.2%

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

      5. metadata-eval 69.2%

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

      6. metadata-eval 69.2%

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

      7. neg-mul-1 69.2%

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

      8. associate-*r* 69.2%

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

      9. *-commutative 69.2%

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

      10. distribute-lft-in 69.2%

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

      11. +-commutative 69.2%

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

      12. distribute-lft-in 69.2%

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

      13. associate-+r+ 69.2%

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

      14. metadata-eval 69.2%

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

      15. metadata-eval 69.2%

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

      16. metadata-eval 69.2%

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

      17. distribute-lft-in 69.2%

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

      18. mul-1-neg 69.2%

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

      19. +-commutative 69.2%

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

      20. fma-def 69.2%

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

   4. Simplified 69.2%

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

   5. Taylor expanded in z around 0 67.0%

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

      1. *-commutative 67.0%

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

   7. Simplified 67.0%

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

   if -3.45000000000000008e-131 < z < -1.04999999999999997e-240

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-*l* 99.9%

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

      3. fma-def 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-lft-in 99.9%

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

      7. neg-mul-1 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.9%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 64.7%

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

   5. Taylor expanded in z around 0 64.7%

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

      1. *-commutative 64.7%

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

   7. Simplified 64.7%

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

   if -4.2e-305 < z < 1.7e5

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      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-def 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. +-commutative 99.8%

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

      6. distribute-lft-in 99.8%

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

      7. neg-mul-1 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 57.5%

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

4. Final simplification 80.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.0055:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -3.45 \cdot 10^{-131}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-240}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-305}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 170000:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]

Alternative 5: 50.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3 \cdot 10^{+17}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-131}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-241}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -3e+17)
     t_0
     (if (<= z -2.8e-131)
       (* x -3.0)
       (if (<= z -7.2e-241)
         (* y 4.0)
         (if (<= z -1.25e-306)
           (* x -3.0)
           (if (<= z 7.2e+15) (* 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 <= -3e+17) {
		tmp = t_0;
	} else if (z <= -2.8e-131) {
		tmp = x * -3.0;
	} else if (z <= -7.2e-241) {
		tmp = y * 4.0;
	} else if (z <= -1.25e-306) {
		tmp = x * -3.0;
	} else if (z <= 7.2e+15) {
		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 <= (-3d+17)) then
        tmp = t_0
    else if (z <= (-2.8d-131)) then
        tmp = x * (-3.0d0)
    else if (z <= (-7.2d-241)) then
        tmp = y * 4.0d0
    else if (z <= (-1.25d-306)) then
        tmp = x * (-3.0d0)
    else if (z <= 7.2d+15) 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 <= -3e+17) {
		tmp = t_0;
	} else if (z <= -2.8e-131) {
		tmp = x * -3.0;
	} else if (z <= -7.2e-241) {
		tmp = y * 4.0;
	} else if (z <= -1.25e-306) {
		tmp = x * -3.0;
	} else if (z <= 7.2e+15) {
		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 <= -3e+17:
		tmp = t_0
	elif z <= -2.8e-131:
		tmp = x * -3.0
	elif z <= -7.2e-241:
		tmp = y * 4.0
	elif z <= -1.25e-306:
		tmp = x * -3.0
	elif z <= 7.2e+15:
		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 <= -3e+17)
		tmp = t_0;
	elseif (z <= -2.8e-131)
		tmp = Float64(x * -3.0);
	elseif (z <= -7.2e-241)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.25e-306)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.2e+15)
		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 <= -3e+17)
		tmp = t_0;
	elseif (z <= -2.8e-131)
		tmp = x * -3.0;
	elseif (z <= -7.2e-241)
		tmp = y * 4.0;
	elseif (z <= -1.25e-306)
		tmp = x * -3.0;
	elseif (z <= 7.2e+15)
		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, -3e+17], t$95$0, If[LessEqual[z, -2.8e-131], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -7.2e-241], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.25e-306], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.2e+15], N[(y * 4.0), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3e17 or 7.2e15 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in x around 0 49.6%

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

   4. Taylor expanded in z around inf 49.6%

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

      1. *-commutative 49.6%

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

   6. Simplified 49.6%

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

   if -3e17 < z < -2.8e-131 or -7.1999999999999998e-241 < z < -1.25e-306

   1. Initial program 99.3%

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

   2. Taylor expanded in x around inf 69.7%

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

      1. *-commutative 69.7%

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

      2. +-commutative 69.7%

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

      3. sub-neg 69.7%

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

      4. distribute-rgt-in 69.7%

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

      5. metadata-eval 69.7%

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

      6. metadata-eval 69.7%

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

      7. neg-mul-1 69.7%

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

      8. associate-*r* 69.7%

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

      9. *-commutative 69.7%

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

      10. distribute-lft-in 69.7%

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

      11. +-commutative 69.7%

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

      12. distribute-lft-in 69.7%

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

      13. associate-+r+ 69.8%

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

      14. metadata-eval 69.8%

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

      15. metadata-eval 69.8%

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

      16. metadata-eval 69.8%

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

      17. distribute-lft-in 69.8%

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

      18. mul-1-neg 69.8%

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

      19. +-commutative 69.8%

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

      20. fma-def 69.8%

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

   4. Simplified 69.8%

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

   5. Taylor expanded in z around 0 65.9%

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

      1. *-commutative 65.9%

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

   7. Simplified 65.9%

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

   if -2.8e-131 < z < -7.1999999999999998e-241 or -1.25e-306 < z < 7.2e15

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      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-def 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. +-commutative 99.8%

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

      6. distribute-lft-in 99.9%

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

      7. neg-mul-1 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.9%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.9%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.9%

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

      12. metadata-eval 99.9%

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

      13. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 58.7%

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

   5. Taylor expanded in z around 0 58.4%

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

      1. *-commutative 58.4%

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

   7. Simplified 58.4%

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

4. Final simplification 55.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3 \cdot 10^{+17}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{-131}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{-241}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.25 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{+15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 6: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((y - x) * 4.0) + (x + (-6.0 * ((y - x) * 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 = ((y - x) * 4.0d0) + (x + ((-6.0d0) * ((y - x) * z)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around 0 99.8%

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

3. Final simplification 99.8%

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

Alternative 7: 76.3% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -50000000000000 \lor \neg \left(x \leq 1.15 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -50000000000000.0) (not (<= x 1.15e-24)))
   (* x (- (* z 6.0) 3.0))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -50000000000000.0) || !(x <= 1.15e-24)) {
		tmp = x * ((z * 6.0) - 3.0);
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-50000000000000.0d0)) .or. (.not. (x <= 1.15d-24))) then
        tmp = x * ((z * 6.0d0) - 3.0d0)
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -50000000000000.0) || !(x <= 1.15e-24)) {
		tmp = x * ((z * 6.0) - 3.0);
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -50000000000000.0) or not (x <= 1.15e-24):
		tmp = x * ((z * 6.0) - 3.0)
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -50000000000000.0) || !(x <= 1.15e-24))
		tmp = Float64(x * Float64(Float64(z * 6.0) - 3.0));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -50000000000000.0) || ~((x <= 1.15e-24)))
		tmp = x * ((z * 6.0) - 3.0);
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -50000000000000.0], N[Not[LessEqual[x, 1.15e-24]], $MachinePrecision]], N[(x * N[(N[(z * 6.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5e13 or 1.1500000000000001e-24 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in z around 0 99.8%

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

   3. Taylor expanded in x around inf 85.1%

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

   if -5e13 < x < 1.1500000000000001e-24

   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* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.7%

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

      7. neg-mul-1 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 82.3%

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

4. Final simplification 83.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -50000000000000 \lor \neg \left(x \leq 1.15 \cdot 10^{-24}\right):\\ \;\;\;\;x \cdot \left(z \cdot 6 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]

Alternative 8: 97.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.6)))
   (* -6.0 (* (- y x) z))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.6)) {
		tmp = -6.0 * ((y - x) * z);
	} 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 <= (-0.58d0)) .or. (.not. (z <= 0.6d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    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 <= -0.58) || !(z <= 0.6)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.6):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.6))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	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 <= -0.58) || ~((z <= 0.6)))
		tmp = -6.0 * ((y - x) * z);
	else
		tmp = (x * -3.0) + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.6]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.599999999999999978 < z

   1. Initial program 99.7%

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

   2. Taylor expanded in z around 0 99.7%

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

   3. Taylor expanded in z around inf 99.7%

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

   if -0.57999999999999996 < z < 0.599999999999999978

   1. Initial program 99.4%

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

   2. Taylor expanded in z around 0 98.5%

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

   3. Taylor expanded in x around 0 98.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]

Alternative 9: 99.7% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. associate-*l* 99.7%

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

   2. metadata-eval 99.7%

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

3. Simplified 99.7%

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

4. Final simplification 99.7%

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

Alternative 10: 38.2% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{-70}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.3e-70) (* x -3.0) (if (<= x 2.1e-27) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.3e-70) {
		tmp = x * -3.0;
	} else if (x <= 2.1e-27) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-5.3d-70)) then
        tmp = x * (-3.0d0)
    else if (x <= 2.1d-27) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.3e-70) {
		tmp = x * -3.0;
	} else if (x <= 2.1e-27) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.3e-70:
		tmp = x * -3.0
	elif x <= 2.1e-27:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.3e-70)
		tmp = Float64(x * -3.0);
	elseif (x <= 2.1e-27)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.3e-70)
		tmp = x * -3.0;
	elseif (x <= 2.1e-27)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.3e-70], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 2.1e-27], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -5.29999999999999983e-70 or 2.10000000000000015e-27 < x

   1. Initial program 99.5%

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

   2. Taylor expanded in x around inf 80.2%

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

      1. *-commutative 80.2%

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

      2. +-commutative 80.2%

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

      3. sub-neg 80.2%

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

      4. distribute-rgt-in 80.2%

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

      5. metadata-eval 80.2%

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

      6. metadata-eval 80.2%

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

      7. neg-mul-1 80.2%

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

      8. associate-*r* 80.2%

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

      9. *-commutative 80.2%

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

      10. distribute-lft-in 80.2%

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

      11. +-commutative 80.2%

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

      12. distribute-lft-in 80.2%

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

      13. associate-+r+ 80.2%

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

      14. metadata-eval 80.2%

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

      15. metadata-eval 80.2%

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

      16. metadata-eval 80.2%

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

      17. distribute-lft-in 80.2%

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

      18. mul-1-neg 80.2%

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

      19. +-commutative 80.2%

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

      20. fma-def 80.3%

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

   4. Simplified 80.3%

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

   5. Taylor expanded in z around 0 43.1%

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

      1. *-commutative 43.1%

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

   7. Simplified 43.1%

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

   if -5.29999999999999983e-70 < x < 2.10000000000000015e-27

   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* 99.7%

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

      3. fma-def 99.7%

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

      4. sub-neg 99.7%

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

      5. +-commutative 99.7%

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

      6. distribute-lft-in 99.7%

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

      7. neg-mul-1 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(-1 \cdot z\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      8. associate-*r* 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\left(6 \cdot -1\right) \cdot z} + 6 \cdot \frac{2}{3}, x\right) \]

      9. *-commutative 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{z \cdot \left(6 \cdot -1\right)} + 6 \cdot \frac{2}{3}, x\right) \]

      10. fma-def 99.8%

          \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\mathsf{fma}\left(z, 6 \cdot -1, 6 \cdot \frac{2}{3}\right)}, x\right) \]

      11. metadata-eval 99.8%

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

      12. metadata-eval 99.8%

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

      13. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 84.3%

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

   5. Taylor expanded in z around 0 47.2%

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

      1. *-commutative 47.2%

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

   7. Simplified 47.2%

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

4. Final simplification 44.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.3 \cdot 10^{-70}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-27}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 11: 26.6% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in x around inf 53.6%

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

   1. *-commutative 53.6%

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

   2. +-commutative 53.6%

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

   3. sub-neg 53.6%

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

   4. distribute-rgt-in 53.6%

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

   5. metadata-eval 53.6%

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

   6. metadata-eval 53.6%

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

   7. neg-mul-1 53.6%

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

   8. associate-*r* 53.6%

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

   9. *-commutative 53.6%

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

   10. distribute-lft-in 53.6%

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

   11. +-commutative 53.6%

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

   12. distribute-lft-in 53.6%

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

   13. associate-+r+ 53.6%

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

   14. metadata-eval 53.6%

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

   15. metadata-eval 53.6%

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

   16. metadata-eval 53.6%

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

   17. distribute-lft-in 53.6%

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

   18. mul-1-neg 53.6%

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

   19. +-commutative 53.6%

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

   20. fma-def 53.7%

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

4. Simplified 53.7%

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

5. Taylor expanded in z around 0 28.2%

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

   1. *-commutative 28.2%

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

7. Simplified 28.2%

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

8. Final simplification 28.2%

   \[\leadsto x \cdot -3 \]

Reproduce

herbie shell --seed 2023214 
(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))))