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

Percentage Accurate: 99.5% → 99.7%

Time: 9.9s

Alternatives: 12

Speedup: 1.2×

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, 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 2: 49.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-257}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-287}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+156} \lor \neg \left(z \leq 1.75 \cdot 10^{+239}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* x z))))
   (if (<= z -2.4e-16)
     t_0
     (if (<= z -6.3e-257)
       (* x -3.0)
       (if (<= z -2.6e-287)
         (* y 4.0)
         (if (<= z 5.1e-306)
           (* x -3.0)
           (if (<= z 4.5e-104)
             (* y 4.0)
             (if (<= z 0.5)
               (* x -3.0)
               (if (or (<= z 4.8e+156) (not (<= z 1.75e+239)))
                 (* -6.0 (* y z))
                 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.4e-16) {
		tmp = t_0;
	} else if (z <= -6.3e-257) {
		tmp = x * -3.0;
	} else if (z <= -2.6e-287) {
		tmp = y * 4.0;
	} else if (z <= 5.1e-306) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-104) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 4.8e+156) || !(z <= 1.75e+239)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (x * z)
    if (z <= (-2.4d-16)) then
        tmp = t_0
    else if (z <= (-6.3d-257)) then
        tmp = x * (-3.0d0)
    else if (z <= (-2.6d-287)) then
        tmp = y * 4.0d0
    else if (z <= 5.1d-306) then
        tmp = x * (-3.0d0)
    else if (z <= 4.5d-104) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 4.8d+156) .or. (.not. (z <= 1.75d+239))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.4e-16) {
		tmp = t_0;
	} else if (z <= -6.3e-257) {
		tmp = x * -3.0;
	} else if (z <= -2.6e-287) {
		tmp = y * 4.0;
	} else if (z <= 5.1e-306) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-104) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 4.8e+156) || !(z <= 1.75e+239)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (x * z)
	tmp = 0
	if z <= -2.4e-16:
		tmp = t_0
	elif z <= -6.3e-257:
		tmp = x * -3.0
	elif z <= -2.6e-287:
		tmp = y * 4.0
	elif z <= 5.1e-306:
		tmp = x * -3.0
	elif z <= 4.5e-104:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif (z <= 4.8e+156) or not (z <= 1.75e+239):
		tmp = -6.0 * (y * z)
	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 <= -2.4e-16)
		tmp = t_0;
	elseif (z <= -6.3e-257)
		tmp = Float64(x * -3.0);
	elseif (z <= -2.6e-287)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.1e-306)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.5e-104)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif ((z <= 4.8e+156) || !(z <= 1.75e+239))
		tmp = Float64(-6.0 * Float64(y * z));
	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 <= -2.4e-16)
		tmp = t_0;
	elseif (z <= -6.3e-257)
		tmp = x * -3.0;
	elseif (z <= -2.6e-287)
		tmp = y * 4.0;
	elseif (z <= 5.1e-306)
		tmp = x * -3.0;
	elseif (z <= 4.5e-104)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif ((z <= 4.8e+156) || ~((z <= 1.75e+239)))
		tmp = -6.0 * (y * z);
	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, -2.4e-16], t$95$0, If[LessEqual[z, -6.3e-257], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -2.6e-287], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.1e-306], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.5e-104], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 4.8e+156], N[Not[LessEqual[z, 1.75e+239]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.40000000000000005e-16 or 4.8000000000000002e156 < z < 1.7500000000000001e239

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 95.6%

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

   3. Taylor expanded in x around inf 67.2%

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

   4. Taylor expanded in z around inf 67.2%

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

   if -2.40000000000000005e-16 < z < -6.29999999999999993e-257 or -2.6e-287 < z < 5.09999999999999972e-306 or 4.4999999999999997e-104 < z < 0.5

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 99.2%

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

   3. Taylor expanded in z around 0 99.3%

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

      1. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around inf 60.7%

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

   if -6.29999999999999993e-257 < z < -2.6e-287 or 5.09999999999999972e-306 < z < 4.4999999999999997e-104

   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-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 62.4%

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

   5. Taylor expanded in z around 0 62.4%

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

      1. *-commutative 62.4%

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

   7. Simplified 62.4%

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

   if 0.5 < z < 4.8000000000000002e156 or 1.7500000000000001e239 < z

   1. Initial program 99.6%

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

      1. +-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-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 99.8%

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

      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 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 73.3%

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

   5. Taylor expanded in z around inf 67.9%

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

      1. *-commutative 67.9%

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

   7. Simplified 67.9%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.3 \cdot 10^{-257}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-287}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.1 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-104}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.8 \cdot 10^{+156} \lor \neg \left(z \leq 1.75 \cdot 10^{+239}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 3: 49.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(1 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+156} \lor \neg \left(z \leq 1.75 \cdot 10^{+239}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2.4e-16)
   (* x (+ 1.0 (* 6.0 z)))
   (if (<= z -7e-260)
     (* x -3.0)
     (if (<= z -3.5e-282)
       (* y 4.0)
       (if (<= z 3.6e-306)
         (* x -3.0)
         (if (<= z 1.3e-107)
           (* y 4.0)
           (if (<= z 0.5)
             (* x -3.0)
             (if (or (<= z 9e+156) (not (<= z 1.75e+239)))
               (* -6.0 (* y z))
               (* 6.0 (* x z))))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e-16) {
		tmp = x * (1.0 + (6.0 * z));
	} else if (z <= -7e-260) {
		tmp = x * -3.0;
	} else if (z <= -3.5e-282) {
		tmp = y * 4.0;
	} else if (z <= 3.6e-306) {
		tmp = x * -3.0;
	} else if (z <= 1.3e-107) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 9e+156) || !(z <= 1.75e+239)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2.4d-16)) then
        tmp = x * (1.0d0 + (6.0d0 * z))
    else if (z <= (-7d-260)) then
        tmp = x * (-3.0d0)
    else if (z <= (-3.5d-282)) then
        tmp = y * 4.0d0
    else if (z <= 3.6d-306) then
        tmp = x * (-3.0d0)
    else if (z <= 1.3d-107) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 9d+156) .or. (.not. (z <= 1.75d+239))) then
        tmp = (-6.0d0) * (y * z)
    else
        tmp = 6.0d0 * (x * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2.4e-16) {
		tmp = x * (1.0 + (6.0 * z));
	} else if (z <= -7e-260) {
		tmp = x * -3.0;
	} else if (z <= -3.5e-282) {
		tmp = y * 4.0;
	} else if (z <= 3.6e-306) {
		tmp = x * -3.0;
	} else if (z <= 1.3e-107) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 9e+156) || !(z <= 1.75e+239)) {
		tmp = -6.0 * (y * z);
	} else {
		tmp = 6.0 * (x * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2.4e-16:
		tmp = x * (1.0 + (6.0 * z))
	elif z <= -7e-260:
		tmp = x * -3.0
	elif z <= -3.5e-282:
		tmp = y * 4.0
	elif z <= 3.6e-306:
		tmp = x * -3.0
	elif z <= 1.3e-107:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif (z <= 9e+156) or not (z <= 1.75e+239):
		tmp = -6.0 * (y * z)
	else:
		tmp = 6.0 * (x * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2.4e-16)
		tmp = Float64(x * Float64(1.0 + Float64(6.0 * z)));
	elseif (z <= -7e-260)
		tmp = Float64(x * -3.0);
	elseif (z <= -3.5e-282)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.6e-306)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.3e-107)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif ((z <= 9e+156) || !(z <= 1.75e+239))
		tmp = Float64(-6.0 * Float64(y * z));
	else
		tmp = Float64(6.0 * Float64(x * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2.4e-16)
		tmp = x * (1.0 + (6.0 * z));
	elseif (z <= -7e-260)
		tmp = x * -3.0;
	elseif (z <= -3.5e-282)
		tmp = y * 4.0;
	elseif (z <= 3.6e-306)
		tmp = x * -3.0;
	elseif (z <= 1.3e-107)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif ((z <= 9e+156) || ~((z <= 1.75e+239)))
		tmp = -6.0 * (y * z);
	else
		tmp = 6.0 * (x * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2.4e-16], N[(x * N[(1.0 + N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7e-260], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -3.5e-282], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.6e-306], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.3e-107], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 9e+156], N[Not[LessEqual[z, 1.75e+239]], $MachinePrecision]], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.40000000000000005e-16

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 93.7%

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

   3. Taylor expanded in x around inf 62.9%

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

   if -2.40000000000000005e-16 < z < -6.9999999999999999e-260 or -3.50000000000000006e-282 < z < 3.59999999999999991e-306 or 1.3e-107 < z < 0.5

   1. Initial program 99.2%

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

   2. Taylor expanded in y around 0 99.2%

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

   3. Taylor expanded in z around 0 99.3%

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

      1. *-commutative 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around inf 60.7%

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

   if -6.9999999999999999e-260 < z < -3.50000000000000006e-282 or 3.59999999999999991e-306 < z < 1.3e-107

   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-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 62.4%

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

   5. Taylor expanded in z around 0 62.4%

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

      1. *-commutative 62.4%

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

   7. Simplified 62.4%

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

   if 0.5 < z < 9.00000000000000061e156 or 1.7500000000000001e239 < z

   1. Initial program 99.6%

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

      1. +-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-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 99.8%

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

      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 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 73.3%

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

   5. Taylor expanded in z around inf 67.9%

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

      1. *-commutative 67.9%

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

   7. Simplified 67.9%

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

   if 9.00000000000000061e156 < z < 1.7500000000000001e239

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 99.8%

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

   3. Taylor expanded in x around inf 77.0%

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

   4. Taylor expanded in z around inf 77.0%

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

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.4 \cdot 10^{-16}:\\ \;\;\;\;x \cdot \left(1 + 6 \cdot z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-260}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -3.5 \cdot 10^{-282}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.6 \cdot 10^{-306}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+156} \lor \neg \left(z \leq 1.75 \cdot 10^{+239}\right):\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 49.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{+24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-258}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-274}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-105}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -4.8e+24)
     t_0
     (if (<= z -9.6e-258)
       (* x -3.0)
       (if (<= z -5.6e-274)
         (* y 4.0)
         (if (<= z 5.5e-307)
           (* x -3.0)
           (if (<= z 1.75e-105)
             (* y 4.0)
             (if (<= z 0.62) (* x -3.0) t_0))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -4.8e+24) {
		tmp = t_0;
	} else if (z <= -9.6e-258) {
		tmp = x * -3.0;
	} else if (z <= -5.6e-274) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-307) {
		tmp = x * -3.0;
	} else if (z <= 1.75e-105) {
		tmp = y * 4.0;
	} else if (z <= 0.62) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-4.8d+24)) then
        tmp = t_0
    else if (z <= (-9.6d-258)) then
        tmp = x * (-3.0d0)
    else if (z <= (-5.6d-274)) then
        tmp = y * 4.0d0
    else if (z <= 5.5d-307) then
        tmp = x * (-3.0d0)
    else if (z <= 1.75d-105) then
        tmp = y * 4.0d0
    else if (z <= 0.62d0) then
        tmp = x * (-3.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -4.8e+24) {
		tmp = t_0;
	} else if (z <= -9.6e-258) {
		tmp = x * -3.0;
	} else if (z <= -5.6e-274) {
		tmp = y * 4.0;
	} else if (z <= 5.5e-307) {
		tmp = x * -3.0;
	} else if (z <= 1.75e-105) {
		tmp = y * 4.0;
	} else if (z <= 0.62) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -4.8e+24:
		tmp = t_0
	elif z <= -9.6e-258:
		tmp = x * -3.0
	elif z <= -5.6e-274:
		tmp = y * 4.0
	elif z <= 5.5e-307:
		tmp = x * -3.0
	elif z <= 1.75e-105:
		tmp = y * 4.0
	elif z <= 0.62:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -4.8e+24)
		tmp = t_0;
	elseif (z <= -9.6e-258)
		tmp = Float64(x * -3.0);
	elseif (z <= -5.6e-274)
		tmp = Float64(y * 4.0);
	elseif (z <= 5.5e-307)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.75e-105)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.62)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -4.8e+24)
		tmp = t_0;
	elseif (z <= -9.6e-258)
		tmp = x * -3.0;
	elseif (z <= -5.6e-274)
		tmp = y * 4.0;
	elseif (z <= 5.5e-307)
		tmp = x * -3.0;
	elseif (z <= 1.75e-105)
		tmp = y * 4.0;
	elseif (z <= 0.62)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e+24], t$95$0, If[LessEqual[z, -9.6e-258], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, -5.6e-274], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 5.5e-307], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.75e-105], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.62], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -4.8000000000000001e24 or 0.619999999999999996 < z

   1. Initial program 99.8%

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

      1. +-commutative 99.8%

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

      2. associate-*l* 99.7%

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

      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 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

      13. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 52.7%

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

   5. Taylor expanded in z around inf 50.4%

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

      1. *-commutative 50.4%

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

   7. Simplified 50.4%

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

   if -4.8000000000000001e24 < z < -9.6000000000000007e-258 or -5.5999999999999995e-274 < z < 5.50000000000000039e-307 or 1.75e-105 < z < 0.619999999999999996

   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 y around 0 99.2%

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

   3. Taylor expanded in z around 0 94.3%

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

      1. *-commutative 94.3%

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

   5. Simplified 94.3%

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

   6. Taylor expanded in x around inf 57.2%

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

   if -9.6000000000000007e-258 < z < -5.5999999999999995e-274 or 5.50000000000000039e-307 < z < 1.75e-105

   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-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 62.4%

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

   5. Taylor expanded in z around 0 62.4%

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

      1. *-commutative 62.4%

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

   7. Simplified 62.4%

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

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{+24}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -9.6 \cdot 10^{-258}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{-274}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 5.5 \cdot 10^{-307}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-105}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.62:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]

Alternative 5: 75.1% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -46:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+155} \lor \neg \left(z \leq 1.25 \cdot 10^{+242}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (+ x (* z (* x 6.0)))))
   (if (<= z -46.0)
     t_0
     (if (<= z 8.5e-7)
       (+ (* x -3.0) (* y 4.0))
       (if (or (<= z 9e+155) (not (<= z 1.25e+242)))
         (* y (+ 4.0 (* z -6.0)))
         t_0)))))

C

double code(double x, double y, double z) {
	double t_0 = x + (z * (x * 6.0));
	double tmp;
	if (z <= -46.0) {
		tmp = t_0;
	} else if (z <= 8.5e-7) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if ((z <= 9e+155) || !(z <= 1.25e+242)) {
		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 = x + (z * (x * 6.0d0))
    if (z <= (-46.0d0)) then
        tmp = t_0
    else if (z <= 8.5d-7) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else if ((z <= 9d+155) .or. (.not. (z <= 1.25d+242))) 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 = x + (z * (x * 6.0));
	double tmp;
	if (z <= -46.0) {
		tmp = t_0;
	} else if (z <= 8.5e-7) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if ((z <= 9e+155) || !(z <= 1.25e+242)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x + (z * (x * 6.0))
	tmp = 0
	if z <= -46.0:
		tmp = t_0
	elif z <= 8.5e-7:
		tmp = (x * -3.0) + (y * 4.0)
	elif (z <= 9e+155) or not (z <= 1.25e+242):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x + Float64(z * Float64(x * 6.0)))
	tmp = 0.0
	if (z <= -46.0)
		tmp = t_0;
	elseif (z <= 8.5e-7)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	elseif ((z <= 9e+155) || !(z <= 1.25e+242))
		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 = x + (z * (x * 6.0));
	tmp = 0.0;
	if (z <= -46.0)
		tmp = t_0;
	elseif (z <= 8.5e-7)
		tmp = (x * -3.0) + (y * 4.0);
	elseif ((z <= 9e+155) || ~((z <= 1.25e+242)))
		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[(x + N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -46.0], t$95$0, If[LessEqual[z, 8.5e-7], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 9e+155], N[Not[LessEqual[z, 1.25e+242]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if z < -46 or 8.99999999999999947e155 < z < 1.2500000000000001e242

   1. Initial program 99.9%

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

   2. Taylor expanded in z around inf 96.9%

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

   3. Taylor expanded in y around 0 68.1%

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

      1. associate-*r* 68.1%

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

      2. *-commutative 68.1%

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

      3. associate-*l* 68.2%

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

   5. Simplified 68.2%

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

   if -46 < z < 8.50000000000000014e-7

   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 0 99.5%

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

      1. fma-def 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.6%

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

   if 8.50000000000000014e-7 < z < 8.99999999999999947e155 or 1.2500000000000001e242 < z

   1. Initial program 99.6%

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

      1. +-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-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 99.8%

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

      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 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 73.3%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -46:\\ \;\;\;\;x + z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{-7}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+155} \lor \neg \left(z \leq 1.25 \cdot 10^{+242}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 6: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(\left(-z \cdot -6\right) - 3\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-7}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+157} \lor \neg \left(z \leq 3.15 \cdot 10^{+242}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.55e-6)
   (* x (- (- (* z -6.0)) 3.0))
   (if (<= z 6e-7)
     (+ (* x -3.0) (* y 4.0))
     (if (or (<= z 6e+157) (not (<= z 3.15e+242)))
       (* y (+ 4.0 (* z -6.0)))
       (+ x (* z (* x 6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e-6) {
		tmp = x * (-(z * -6.0) - 3.0);
	} else if (z <= 6e-7) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if ((z <= 6e+157) || !(z <= 3.15e+242)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x + (z * (x * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.55d-6)) then
        tmp = x * (-(z * (-6.0d0)) - 3.0d0)
    else if (z <= 6d-7) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else if ((z <= 6d+157) .or. (.not. (z <= 3.15d+242))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x + (z * (x * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.55e-6) {
		tmp = x * (-(z * -6.0) - 3.0);
	} else if (z <= 6e-7) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if ((z <= 6e+157) || !(z <= 3.15e+242)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x + (z * (x * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.55e-6:
		tmp = x * (-(z * -6.0) - 3.0)
	elif z <= 6e-7:
		tmp = (x * -3.0) + (y * 4.0)
	elif (z <= 6e+157) or not (z <= 3.15e+242):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x + (z * (x * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.55e-6)
		tmp = Float64(x * Float64(Float64(-Float64(z * -6.0)) - 3.0));
	elseif (z <= 6e-7)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	elseif ((z <= 6e+157) || !(z <= 3.15e+242))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x + Float64(z * Float64(x * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.55e-6)
		tmp = x * (-(z * -6.0) - 3.0);
	elseif (z <= 6e-7)
		tmp = (x * -3.0) + (y * 4.0);
	elseif ((z <= 6e+157) || ~((z <= 3.15e+242)))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x + (z * (x * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.55e-6], N[(x * N[((-N[(z * -6.0), $MachinePrecision]) - 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e-7], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 6e+157], N[Not[LessEqual[z, 3.15e+242]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.55e-6

   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* 99.7%

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

      3. fma-def 99.6%

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

      4. sub-neg 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-lft-in 99.6%

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

      7. neg-mul-1 99.6%

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

      8. associate-*r* 99.6%

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

      9. *-commutative 99.6%

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

      10. fma-def 99.6%

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

      11. metadata-eval 99.6%

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

      12. metadata-eval 99.6%

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

      13. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around -inf 68.2%

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

   if -1.55e-6 < z < 5.9999999999999997e-7

   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 0 99.5%

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

      1. fma-def 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.6%

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

   if 5.9999999999999997e-7 < z < 6.00000000000000021e157 or 3.1499999999999999e242 < z

   1. Initial program 99.6%

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

      1. +-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-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 99.8%

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

      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 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 73.3%

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

   if 6.00000000000000021e157 < z < 3.1499999999999999e242

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 99.8%

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

   3. Taylor expanded in y around 0 77.0%

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

      1. associate-*r* 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*l* 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.55 \cdot 10^{-6}:\\ \;\;\;\;x \cdot \left(\left(-z \cdot -6\right) - 3\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{-7}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+157} \lor \neg \left(z \leq 3.15 \cdot 10^{+242}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 7: 75.4% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 + \left(0.6666666666666666 - z\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-6}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+155} \lor \neg \left(z \leq 1.8 \cdot 10^{+242}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.2e-5)
   (* x (+ 1.0 (* (- 0.6666666666666666 z) -6.0)))
   (if (<= z 2.1e-6)
     (+ (* x -3.0) (* y 4.0))
     (if (or (<= z 4.6e+155) (not (<= z 1.8e+242)))
       (* y (+ 4.0 (* z -6.0)))
       (+ x (* z (* x 6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e-5) {
		tmp = x * (1.0 + ((0.6666666666666666 - z) * -6.0));
	} else if (z <= 2.1e-6) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if ((z <= 4.6e+155) || !(z <= 1.8e+242)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x + (z * (x * 6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.2d-5)) then
        tmp = x * (1.0d0 + ((0.6666666666666666d0 - z) * (-6.0d0)))
    else if (z <= 2.1d-6) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else if ((z <= 4.6d+155) .or. (.not. (z <= 1.8d+242))) then
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    else
        tmp = x + (z * (x * 6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.2e-5) {
		tmp = x * (1.0 + ((0.6666666666666666 - z) * -6.0));
	} else if (z <= 2.1e-6) {
		tmp = (x * -3.0) + (y * 4.0);
	} else if ((z <= 4.6e+155) || !(z <= 1.8e+242)) {
		tmp = y * (4.0 + (z * -6.0));
	} else {
		tmp = x + (z * (x * 6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.2e-5:
		tmp = x * (1.0 + ((0.6666666666666666 - z) * -6.0))
	elif z <= 2.1e-6:
		tmp = (x * -3.0) + (y * 4.0)
	elif (z <= 4.6e+155) or not (z <= 1.8e+242):
		tmp = y * (4.0 + (z * -6.0))
	else:
		tmp = x + (z * (x * 6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.2e-5)
		tmp = Float64(x * Float64(1.0 + Float64(Float64(0.6666666666666666 - z) * -6.0)));
	elseif (z <= 2.1e-6)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	elseif ((z <= 4.6e+155) || !(z <= 1.8e+242))
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	else
		tmp = Float64(x + Float64(z * Float64(x * 6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.2e-5)
		tmp = x * (1.0 + ((0.6666666666666666 - z) * -6.0));
	elseif (z <= 2.1e-6)
		tmp = (x * -3.0) + (y * 4.0);
	elseif ((z <= 4.6e+155) || ~((z <= 1.8e+242)))
		tmp = y * (4.0 + (z * -6.0));
	else
		tmp = x + (z * (x * 6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.2e-5], N[(x * N[(1.0 + N[(N[(0.6666666666666666 - z), $MachinePrecision] * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 2.1e-6], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, 4.6e+155], N[Not[LessEqual[z, 1.8e+242]], $MachinePrecision]], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.19999999999999968e-5

   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. associate-*r* 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. +-commutative 99.7%

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

      4. metadata-eval 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-*r* 99.7%

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

      7. fma-def 99.7%

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

      8. metadata-eval 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in x around inf 68.2%

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

   if -5.19999999999999968e-5 < z < 2.0999999999999998e-6

   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 0 99.5%

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

      1. fma-def 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.6%

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

   if 2.0999999999999998e-6 < z < 4.59999999999999996e155 or 1.79999999999999997e242 < z

   1. Initial program 99.6%

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

      1. +-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-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 99.8%

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

      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 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 73.3%

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

   if 4.59999999999999996e155 < z < 1.79999999999999997e242

   1. Initial program 99.8%

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

   2. Taylor expanded in z around inf 99.8%

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

   3. Taylor expanded in y around 0 77.0%

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

      1. associate-*r* 77.0%

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

      2. *-commutative 77.0%

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

      3. associate-*l* 77.1%

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

   5. Simplified 77.1%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{-5}:\\ \;\;\;\;x \cdot \left(1 + \left(0.6666666666666666 - z\right) \cdot -6\right)\\ \mathbf{elif}\;z \leq 2.1 \cdot 10^{-6}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{elif}\;z \leq 4.6 \cdot 10^{+155} \lor \neg \left(z \leq 1.8 \cdot 10^{+242}\right):\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \left(x \cdot 6\right)\\ \end{array} \]

Alternative 8: 59.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{if}\;y \leq -3.15 \cdot 10^{-93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-179}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (+ 4.0 (* z -6.0)))))
   (if (<= y -3.15e-93)
     t_0
     (if (<= y -1.4e-179)
       (* x -3.0)
       (if (<= y -1.36e-179)
         (* y (* z -6.0))
         (if (<= y 2.45e-119) (* x (* 6.0 z)) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -3.15e-93) {
		tmp = t_0;
	} else if (y <= -1.4e-179) {
		tmp = x * -3.0;
	} else if (y <= -1.36e-179) {
		tmp = y * (z * -6.0);
	} else if (y <= 2.45e-119) {
		tmp = x * (6.0 * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (4.0d0 + (z * (-6.0d0)))
    if (y <= (-3.15d-93)) then
        tmp = t_0
    else if (y <= (-1.4d-179)) then
        tmp = x * (-3.0d0)
    else if (y <= (-1.36d-179)) then
        tmp = y * (z * (-6.0d0))
    else if (y <= 2.45d-119) then
        tmp = x * (6.0d0 * z)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (4.0 + (z * -6.0));
	double tmp;
	if (y <= -3.15e-93) {
		tmp = t_0;
	} else if (y <= -1.4e-179) {
		tmp = x * -3.0;
	} else if (y <= -1.36e-179) {
		tmp = y * (z * -6.0);
	} else if (y <= 2.45e-119) {
		tmp = x * (6.0 * z);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (4.0 + (z * -6.0))
	tmp = 0
	if y <= -3.15e-93:
		tmp = t_0
	elif y <= -1.4e-179:
		tmp = x * -3.0
	elif y <= -1.36e-179:
		tmp = y * (z * -6.0)
	elif y <= 2.45e-119:
		tmp = x * (6.0 * z)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(4.0 + Float64(z * -6.0)))
	tmp = 0.0
	if (y <= -3.15e-93)
		tmp = t_0;
	elseif (y <= -1.4e-179)
		tmp = Float64(x * -3.0);
	elseif (y <= -1.36e-179)
		tmp = Float64(y * Float64(z * -6.0));
	elseif (y <= 2.45e-119)
		tmp = Float64(x * Float64(6.0 * z));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (4.0 + (z * -6.0));
	tmp = 0.0;
	if (y <= -3.15e-93)
		tmp = t_0;
	elseif (y <= -1.4e-179)
		tmp = x * -3.0;
	elseif (y <= -1.36e-179)
		tmp = y * (z * -6.0);
	elseif (y <= 2.45e-119)
		tmp = x * (6.0 * z);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.15e-93], t$95$0, If[LessEqual[y, -1.4e-179], N[(x * -3.0), $MachinePrecision], If[LessEqual[y, -1.36e-179], N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.45e-119], N[(x * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.15000000000000014e-93 or 2.45e-119 < y

   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-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 67.6%

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

   if -3.15000000000000014e-93 < y < -1.4e-179

   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 y around 0 99.3%

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

   3. Taylor expanded in z around 0 75.8%

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

      1. *-commutative 75.8%

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

   5. Simplified 75.8%

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

   6. Taylor expanded in x around inf 51.6%

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

   if -1.4e-179 < y < -1.35999999999999993e-179

   1. Initial program 98.4%

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

      1. +-commutative 98.4%

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

      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-def 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. +-commutative 100.0%

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

      6. distribute-lft-in 100.0%

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

      7. neg-mul-1 100.0%

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

      8. associate-*r* 100.0%

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

      9. *-commutative 100.0%

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

      10. fma-def 98.4%

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

      11. metadata-eval 98.4%

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

      12. metadata-eval 98.4%

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

      13. metadata-eval 98.4%

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

   3. Simplified 98.4%

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

   4. Taylor expanded in y around inf 100.0%

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

   5. Taylor expanded in z around inf 100.0%

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

   if -1.35999999999999993e-179 < y < 2.45e-119

   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 inf 55.8%

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

   3. Taylor expanded in x around inf 49.3%

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

   4. Taylor expanded in z around inf 50.4%

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

      1. associate-*r* 50.4%

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

      2. *-commutative 50.4%

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

      3. *-commutative 50.4%

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

      4. *-commutative 50.4%

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

   6. Simplified 50.4%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{-93}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \mathbf{elif}\;y \leq -1.4 \cdot 10^{-179}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;y \leq -1.36 \cdot 10^{-179}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;y \leq 2.45 \cdot 10^{-119}:\\ \;\;\;\;x \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]

Alternative 9: 97.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.6) (not (<= z 0.52)))
   (* z (+ (* x 6.0) (* y -6.0)))
   (+ (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.52)) {
		tmp = z * ((x * 6.0) + (y * -6.0));
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.6d0)) .or. (.not. (z <= 0.52d0))) then
        tmp = z * ((x * 6.0d0) + (y * (-6.0d0)))
    else
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.6) || !(z <= 0.52)) {
		tmp = z * ((x * 6.0) + (y * -6.0));
	} else {
		tmp = (x * -3.0) + (y * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.6) or not (z <= 0.52):
		tmp = z * ((x * 6.0) + (y * -6.0))
	else:
		tmp = (x * -3.0) + (y * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.6) || !(z <= 0.52))
		tmp = Float64(z * Float64(Float64(x * 6.0) + Float64(y * -6.0)));
	else
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.6) || ~((z <= 0.52)))
		tmp = z * ((x * 6.0) + (y * -6.0));
	else
		tmp = (x * -3.0) + (y * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.6], N[Not[LessEqual[z, 0.52]], $MachinePrecision]], N[(z * N[(N[(x * 6.0), $MachinePrecision] + N[(y * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.599999999999999978 or 0.52000000000000002 < z

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 95.4%

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

      1. fma-def 98.8%

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

      2. *-commutative 98.8%

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

      3. associate-*r* 98.8%

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

   4. Simplified 98.8%

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

   5. Taylor expanded in z around inf 95.5%

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

   if -0.599999999999999978 < z < 0.52000000000000002

   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 0 99.5%

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

      1. fma-def 99.6%

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

      2. *-commutative 99.6%

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

      3. associate-*r* 99.8%

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

   4. Simplified 99.8%

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

   5. Taylor expanded in z around 0 99.6%

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

4. Final simplification 97.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6 \lor \neg \left(z \leq 0.52\right):\\ \;\;\;\;z \cdot \left(x \cdot 6 + y \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \end{array} \]

Alternative 10: 37.8% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-88}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.1e-88) (* y 4.0) (if (<= y 8.8e+63) (* x -3.0) (* y 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.1e-88) {
		tmp = y * 4.0;
	} else if (y <= 8.8e+63) {
		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 (y <= (-3.1d-88)) then
        tmp = y * 4.0d0
    else if (y <= 8.8d+63) 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 (y <= -3.1e-88) {
		tmp = y * 4.0;
	} else if (y <= 8.8e+63) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.1e-88:
		tmp = y * 4.0
	elif y <= 8.8e+63:
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.1e-88)
		tmp = Float64(y * 4.0);
	elseif (y <= 8.8e+63)
		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 (y <= -3.1e-88)
		tmp = y * 4.0;
	elseif (y <= 8.8e+63)
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.1e-88], N[(y * 4.0), $MachinePrecision], If[LessEqual[y, 8.8e+63], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.0999999999999998e-88 or 8.7999999999999995e63 < y

   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-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 75.2%

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

   5. Taylor expanded in z around 0 42.1%

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

      1. *-commutative 42.1%

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

   7. Simplified 42.1%

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

   if -3.0999999999999998e-88 < y < 8.7999999999999995e63

   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 y around 0 99.4%

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

   3. Taylor expanded in z around 0 65.0%

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

      1. *-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in x around inf 42.1%

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

4. Final simplification 42.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.1 \cdot 10^{-88}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+63}:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]

Alternative 11: 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 99.5%

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

2. Taylor expanded in y around 0 97.5%

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

3. Taylor expanded in z around 0 77.8%

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

   1. *-commutative 77.8%

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

5. Simplified 77.8%

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

6. Taylor expanded in x around inf 30.0%

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

7. Final simplification 30.0%

   \[\leadsto x \cdot -3 \]

Alternative 12: 2.6% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

2. Taylor expanded in z around inf 44.3%

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

3. Taylor expanded in z around 0 2.7%

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

4. Final simplification 2.7%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023238 
(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))))