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

Percentage Accurate: 99.5% → 99.8%

Time: 12.5s

Alternatives: 10

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: 99.8% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

Alternative 2: 74.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{if}\;x \leq -4 \cdot 10^{+143}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;x \leq -940 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))))
   (if (<= x -4e+143)
     t_0
     (if (<= x -1.9e+77)
       (* z (* (- y x) -6.0))
       (if (or (<= x -940.0) (not (<= x 1.45)))
         t_0
         (* y (+ 4.0 (* z -6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -4e+143) {
		tmp = t_0;
	} else if (x <= -1.9e+77) {
		tmp = z * ((y - x) * -6.0);
	} else if ((x <= -940.0) || !(x <= 1.45)) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x * ((-3.0d0) + (z * 6.0d0))
    if (x <= (-4d+143)) then
        tmp = t_0
    else if (x <= (-1.9d+77)) then
        tmp = z * ((y - x) * (-6.0d0))
    else if ((x <= (-940.0d0)) .or. (.not. (x <= 1.45d0))) then
        tmp = t_0
    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 t_0 = x * (-3.0 + (z * 6.0));
	double tmp;
	if (x <= -4e+143) {
		tmp = t_0;
	} else if (x <= -1.9e+77) {
		tmp = z * ((y - x) * -6.0);
	} else if ((x <= -940.0) || !(x <= 1.45)) {
		tmp = t_0;
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	tmp = 0
	if x <= -4e+143:
		tmp = t_0
	elif x <= -1.9e+77:
		tmp = z * ((y - x) * -6.0)
	elif (x <= -940.0) or not (x <= 1.45):
		tmp = t_0
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	tmp = 0.0
	if (x <= -4e+143)
		tmp = t_0;
	elseif (x <= -1.9e+77)
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	elseif ((x <= -940.0) || !(x <= 1.45))
		tmp = t_0;
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	tmp = 0.0;
	if (x <= -4e+143)
		tmp = t_0;
	elseif (x <= -1.9e+77)
		tmp = z * ((y - x) * -6.0);
	elseif ((x <= -940.0) || ~((x <= 1.45)))
		tmp = t_0;
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4e+143], t$95$0, If[LessEqual[x, -1.9e+77], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, -940.0], N[Not[LessEqual[x, 1.45]], $MachinePrecision]], t$95$0, N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.0000000000000001e143 or -1.9000000000000001e77 < x < -940 or 1.44999999999999996 < x

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. metadata-eval 99.8%

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

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 81.3%

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

      1. mul-1-neg 81.3%

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

      2. *-lft-identity 81.3%

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

      3. *-commutative 81.3%

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

      4. distribute-lft-neg-in 81.3%

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

      5. mul-1-neg 81.3%

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

      6. distribute-rgt-in 81.3%

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

      7. distribute-rgt-in 81.3%

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

      8. metadata-eval 81.3%

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

      9. associate-+r+ 81.3%

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

      10. metadata-eval 81.3%

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

      11. *-commutative 81.3%

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

      12. associate-*l* 81.3%

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

      13. metadata-eval 81.3%

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

   7. Simplified 81.3%

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

   if -4.0000000000000001e143 < x < -1.9000000000000001e77

   1. Initial program 100.0%

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

      1. +-commutative 100.0%

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

      2. associate-*l* 100.0%

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

      3. fma-define 100.0%

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

      4. sub-neg 100.0%

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

      5. distribute-rgt-in 100.0%

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

      6. metadata-eval 100.0%

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

      7. metadata-eval 100.0%

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

      8. distribute-lft-neg-out 100.0%

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

      9. distribute-rgt-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in z around inf 85.0%

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

      1. associate-+r+ 85.0%

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

      2. *-commutative 85.0%

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

      3. associate-*r/ 85.0%

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

      4. *-commutative 85.0%

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

      5. associate-/l* 85.0%

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

      6. distribute-lft-out 85.0%

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

   7. Simplified 85.0%

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

   8. Taylor expanded in z around inf 85.0%

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

      1. *-commutative 85.0%

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

   10. Simplified 85.0%

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

   if -940 < x < 1.44999999999999996

   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* 99.7%

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

      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 79.0%

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

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4 \cdot 10^{+143}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;x \leq -1.9 \cdot 10^{+77}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \mathbf{elif}\;x \leq -940 \lor \neg \left(x \leq 1.45\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 75.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7800 \lor \neg \left(x \leq 0.33\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -7800.0) (not (<= x 0.33)))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7800.0) || !(x <= 0.33)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-7800.0d0)) .or. (.not. (x <= 0.33d0))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -7800.0) || !(x <= 0.33)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -7800.0) or not (x <= 0.33):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -7800.0) || !(x <= 0.33))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -7800.0) || ~((x <= 0.33)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -7800.0], N[Not[LessEqual[x, 0.33]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -7800 or 0.330000000000000016 < x

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.9%

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

      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 78.2%

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

      1. mul-1-neg 78.2%

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

      2. *-lft-identity 78.2%

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

      3. *-commutative 78.2%

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

      4. distribute-lft-neg-in 78.2%

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

      5. mul-1-neg 78.2%

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

      6. distribute-rgt-in 78.2%

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

      7. distribute-rgt-in 78.2%

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

      8. metadata-eval 78.2%

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

      9. associate-+r+ 78.2%

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

      10. metadata-eval 78.2%

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

      11. *-commutative 78.2%

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

      12. associate-*l* 78.2%

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

      13. metadata-eval 78.2%

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

   7. Simplified 78.2%

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

   if -7800 < x < 0.330000000000000016

   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* 99.7%

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

      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 79.0%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7800 \lor \neg \left(x \leq 0.33\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 58.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-59} \lor \neg \left(x \leq 0.65\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.35e-59) (not (<= x 0.65)))
   (* x (+ -3.0 (* z 6.0)))
   (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.35e-59) || !(x <= 0.65)) {
		tmp = x * (-3.0 + (z * 6.0));
	} 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 <= (-1.35d-59)) .or. (.not. (x <= 0.65d0))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    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 <= -1.35e-59) || !(x <= 0.65)) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.35e-59) or not (x <= 0.65):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.35e-59) || !(x <= 0.65))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.35e-59) || ~((x <= 0.65)))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.35e-59], N[Not[LessEqual[x, 0.65]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3499999999999999e-59 or 0.650000000000000022 < x

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. sub-neg 99.8%

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

      5. distribute-rgt-in 99.9%

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

      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 75.6%

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

      1. mul-1-neg 75.6%

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

      2. *-lft-identity 75.6%

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

      3. *-commutative 75.6%

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

      4. distribute-lft-neg-in 75.6%

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

      5. mul-1-neg 75.6%

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

      6. distribute-rgt-in 75.6%

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

      7. distribute-rgt-in 75.6%

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

      8. metadata-eval 75.6%

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

      9. associate-+r+ 75.6%

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

      10. metadata-eval 75.6%

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

      11. *-commutative 75.6%

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

      12. associate-*l* 75.6%

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

      13. metadata-eval 75.6%

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

   7. Simplified 75.6%

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

   if -1.3499999999999999e-59 < x < 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. +-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-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 inf 99.7%

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

   6. Taylor expanded in z around 0 53.4%

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

      1. +-commutative 53.4%

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

      2. distribute-lft1-in 53.4%

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

      3. fma-define 53.4%

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

      4. metadata-eval 53.4%

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

   8. Simplified 53.4%

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

   9. Taylor expanded in y around inf 45.6%

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

4. Final simplification 63.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-59} \lor \neg \left(x \leq 0.65\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.65)
   (+ x (* z (+ (* y -6.0) (* x 6.0))))
   (if (<= z 0.5) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + (z * ((y * -6.0) + (x * 6.0)));
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.65d0)) then
        tmp = x + (z * ((y * (-6.0d0)) + (x * 6.0d0)))
    else if (z <= 0.5d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.65) {
		tmp = x + (z * ((y * -6.0) + (x * 6.0)));
	} else if (z <= 0.5) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.65:
		tmp = x + (z * ((y * -6.0) + (x * 6.0)))
	elif z <= 0.5:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.65)
		tmp = Float64(x + Float64(z * Float64(Float64(y * -6.0) + Float64(x * 6.0))));
	elseif (z <= 0.5)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.65)
		tmp = x + (z * ((y * -6.0) + (x * 6.0)));
	elseif (z <= 0.5)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.65], N[(x + N[(z * N[(N[(y * -6.0), $MachinePrecision] + N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.5], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.650000000000000022

   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. Taylor expanded in z around inf 98.7%

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

      1. *-commutative 98.7%

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

      2. *-commutative 98.7%

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

      3. fma-undefine 98.6%

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

      4. neg-mul-1 98.6%

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

      5. distribute-rgt-neg-in 98.6%

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

      6. fma-undefine 98.7%

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

      7. *-commutative 98.7%

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

      8. *-commutative 98.7%

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

      9. +-commutative 98.7%

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

      10. *-commutative 98.7%

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

      11. *-commutative 98.7%

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

      12. distribute-neg-in 98.7%

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

      13. *-commutative 98.7%

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

      14. distribute-lft-neg-in 98.7%

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

      15. metadata-eval 98.7%

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

      16. distribute-rgt-neg-in 98.7%

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

      17. metadata-eval 98.7%

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

   8. Simplified 98.7%

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

   if -0.650000000000000022 < z < 0.5

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 97.4%

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

   if 0.5 < 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* 99.8%

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

      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 z around inf 99.9%

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

      1. associate-+r+ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 98.3%

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

      4. *-commutative 98.3%

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

      5. associate-/l* 99.9%

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

      6. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.65:\\ \;\;\;\;x + z \cdot \left(y \cdot -6 + x \cdot 6\right)\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* (- y x) (* z -6.0))
   (if (<= z 0.66) (+ x (* (- y x) 4.0)) (* z (* (- y x) -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-0.55d0)) then
        tmp = (y - x) * (z * (-6.0d0))
    else if (z <= 0.66d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((y - x) * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = (y - x) * (z * -6.0);
	} else if (z <= 0.66) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * ((y - x) * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = (y - x) * (z * -6.0)
	elif z <= 0.66:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * ((y - x) * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	elseif (z <= 0.66)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(Float64(y - x) * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = (y - x) * (z * -6.0);
	elseif (z <= 0.66)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * ((y - x) * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.66], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(N[(y - x), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   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* 99.7%

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

      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 z around inf 99.7%

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

      1. associate-+r+ 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*r/ 99.7%

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

      4. *-commutative 99.7%

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

      5. associate-/l* 99.7%

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

      6. distribute-lft-out 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in z around inf 98.6%

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

      1. associate-*r* 98.6%

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

      2. *-commutative 98.6%

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

   10. Simplified 98.6%

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

   if -0.55000000000000004 < z < 0.660000000000000031

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in z around 0 97.4%

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

   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* 99.8%

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

      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 z around inf 99.9%

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

      1. associate-+r+ 99.9%

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

      2. *-commutative 99.9%

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

      3. associate-*r/ 98.3%

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

      4. *-commutative 98.3%

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

      5. associate-/l* 99.9%

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

      6. distribute-lft-out 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in z around inf 99.9%

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

      1. *-commutative 99.9%

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

   10. Simplified 99.9%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq 0.66:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(\left(y - x\right) \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 38.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-27} \lor \neg \left(x \leq 1.15 \cdot 10^{+36}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.8e-27) (not (<= x 1.15e+36))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-27) || !(x <= 1.15e+36)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-2.8d-27)) .or. (.not. (x <= 1.15d+36))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.8e-27) || !(x <= 1.15e+36)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.8e-27) or not (x <= 1.15e+36):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.8e-27) || !(x <= 1.15e+36))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.8e-27) || ~((x <= 1.15e+36)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.8e-27], N[Not[LessEqual[x, 1.15e+36]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.8e-27 or 1.14999999999999998e36 < x

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate-*l* 99.9%

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

      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 99.9%

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

      6. metadata-eval 99.9%

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

      7. metadata-eval 99.9%

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

      8. distribute-lft-neg-out 99.9%

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

      9. distribute-rgt-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around inf 70.0%

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

   6. Taylor expanded in z around 0 33.5%

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

      1. +-commutative 33.5%

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

      2. distribute-lft1-in 40.4%

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

      3. fma-define 40.4%

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

      4. metadata-eval 40.4%

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

   8. Simplified 40.4%

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

   9. Taylor expanded in y around 0 38.9%

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

   if -2.8e-27 < x < 1.14999999999999998e36

   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-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 inf 99.7%

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

   6. Taylor expanded in z around 0 53.6%

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

      1. +-commutative 53.6%

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

      2. distribute-lft1-in 53.6%

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

      3. fma-define 53.6%

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

      4. metadata-eval 53.6%

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

   8. Simplified 53.6%

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

   9. Taylor expanded in y around inf 44.8%

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

4. Final simplification 41.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.8 \cdot 10^{-27} \lor \neg \left(x \leq 1.15 \cdot 10^{+36}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.5% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. 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. Final simplification 99.6%

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

Alternative 9: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 + ((0.6666666666666666d0 - z) * ((y - x) * 6.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. metadata-eval 99.6%

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

3. Simplified 99.6%

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

5. Final simplification 99.6%

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

Alternative 10: 26.7% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.6%

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

   1. +-commutative 99.6%

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

   2. associate-*l* 99.8%

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

   3. fma-define 99.8%

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

   4. sub-neg 99.8%

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

   5. distribute-rgt-in 99.8%

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

   6. metadata-eval 99.8%

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

   7. metadata-eval 99.8%

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

   8. distribute-lft-neg-out 99.8%

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

   9. distribute-rgt-neg-in 99.8%

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

   10. metadata-eval 99.8%

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

3. Simplified 99.8%

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

5. Taylor expanded in y around inf 83.9%

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

6. Taylor expanded in z around 0 42.9%

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

   1. +-commutative 42.9%

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

   2. distribute-lft1-in 46.6%

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

   3. fma-define 46.6%

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

   4. metadata-eval 46.6%

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

8. Simplified 46.6%

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

9. Taylor expanded in y around 0 25.8%

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

10. Final simplification 25.8%

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

Reproduce

herbie shell --seed 2024111 
(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))))