Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A

Percentage Accurate: 68.7% → 99.9%

Time: 8.7s

Alternatives: 14

Speedup: 1.2×

• 41.8% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

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 * x) + (y * y)) - (z * z)) / (y * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 68.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

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 * x) + (y * y)) - (z * z)) / (y * 2.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \left(\frac{z - x}{y} \cdot \left(x + z\right) - y\right) \cdot -0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* (- (* (/ (- z x) y) (+ x z)) y) -0.5))

C

double code(double x, double y, double z) {
	return ((((z - x) / y) * (x + z)) - y) * -0.5;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = ((((z - x) / y) * (x + z)) - y) * (-0.5d0)
end function

Java

public static double code(double x, double y, double z) {
	return ((((z - x) / y) * (x + z)) - y) * -0.5;
}

Python

def code(x, y, z):
	return ((((z - x) / y) * (x + z)) - y) * -0.5

Julia

function code(x, y, z)
	return Float64(Float64(Float64(Float64(Float64(z - x) / y) * Float64(x + z)) - y) * -0.5)
end

MATLAB

function tmp = code(x, y, z)
	tmp = ((((z - x) / y) * (x + z)) - y) * -0.5;
end

Wolfram

code[x_, y_, z_] := N[(N[(N[(N[(N[(z - x), $MachinePrecision] / y), $MachinePrecision] * N[(x + z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision] * -0.5), $MachinePrecision]

Derivation

1. Initial program 71.5%

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

   1. sub-neg 71.5%

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

   2. +-commutative 71.5%

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

   3. neg-sub0 71.5%

      \[\leadsto \frac{\color{blue}{\left(0 - z \cdot z\right)} + \left(x \cdot x + y \cdot y\right)}{y \cdot 2} \]

   4. associate-+l- 71.5%

      \[\leadsto \frac{\color{blue}{0 - \left(z \cdot z - \left(x \cdot x + y \cdot y\right)\right)}}{y \cdot 2} \]

   5. sub0-neg 71.5%

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

   6. neg-mul-1 71.5%

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

   7. *-commutative 71.5%

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

   8. times-frac 71.5%

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

   9. associate--r+ 71.5%

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

   10. div-sub 71.5%

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

   11. difference-of-squares 76.7%

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

   12. +-commutative 76.7%

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

   13. associate-*r/ 78.7%

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

   14. associate-/l* 99.9%

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

   15. *-inverses 99.9%

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

   16. /-rgt-identity 99.9%

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

   17. metadata-eval 99.9%

       \[\leadsto \left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot \color{blue}{-0.5} \]

3. Simplified 99.9%

   \[\leadsto \color{blue}{\left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot -0.5} \]

4. Final simplification 99.9%

   \[\leadsto \left(\frac{z - x}{y} \cdot \left(x + z\right) - y\right) \cdot -0.5 \]

Alternative 2: 53.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{-209}:\\ \;\;\;\;\frac{-0.5}{\frac{\frac{y}{z}}{z}}\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-156}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \cdot x \leq 10^{-73}:\\ \;\;\;\;\frac{-0.5 \cdot \left(z \cdot z\right)}{y}\\ \mathbf{elif}\;x \cdot x \leq 10^{+72}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* x x) 2e-209)
   (/ -0.5 (/ (/ y z) z))
   (if (<= (* x x) 5e-156)
     (* y 0.5)
     (if (<= (* x x) 1e-73)
       (/ (* -0.5 (* z z)) y)
       (if (<= (* x x) 1e+72) (* y 0.5) (* 0.5 (/ x (/ y x))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 2e-209) {
		tmp = -0.5 / ((y / z) / z);
	} else if ((x * x) <= 5e-156) {
		tmp = y * 0.5;
	} else if ((x * x) <= 1e-73) {
		tmp = (-0.5 * (z * z)) / y;
	} else if ((x * x) <= 1e+72) {
		tmp = y * 0.5;
	} else {
		tmp = 0.5 * (x / (y / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x * x) <= 2d-209) then
        tmp = (-0.5d0) / ((y / z) / z)
    else if ((x * x) <= 5d-156) then
        tmp = y * 0.5d0
    else if ((x * x) <= 1d-73) then
        tmp = ((-0.5d0) * (z * z)) / y
    else if ((x * x) <= 1d+72) then
        tmp = y * 0.5d0
    else
        tmp = 0.5d0 * (x / (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 2e-209) {
		tmp = -0.5 / ((y / z) / z);
	} else if ((x * x) <= 5e-156) {
		tmp = y * 0.5;
	} else if ((x * x) <= 1e-73) {
		tmp = (-0.5 * (z * z)) / y;
	} else if ((x * x) <= 1e+72) {
		tmp = y * 0.5;
	} else {
		tmp = 0.5 * (x / (y / x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x * x) <= 2e-209:
		tmp = -0.5 / ((y / z) / z)
	elif (x * x) <= 5e-156:
		tmp = y * 0.5
	elif (x * x) <= 1e-73:
		tmp = (-0.5 * (z * z)) / y
	elif (x * x) <= 1e+72:
		tmp = y * 0.5
	else:
		tmp = 0.5 * (x / (y / x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x * x) <= 2e-209)
		tmp = Float64(-0.5 / Float64(Float64(y / z) / z));
	elseif (Float64(x * x) <= 5e-156)
		tmp = Float64(y * 0.5);
	elseif (Float64(x * x) <= 1e-73)
		tmp = Float64(Float64(-0.5 * Float64(z * z)) / y);
	elseif (Float64(x * x) <= 1e+72)
		tmp = Float64(y * 0.5);
	else
		tmp = Float64(0.5 * Float64(x / Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x * x) <= 2e-209)
		tmp = -0.5 / ((y / z) / z);
	elseif ((x * x) <= 5e-156)
		tmp = y * 0.5;
	elseif ((x * x) <= 1e-73)
		tmp = (-0.5 * (z * z)) / y;
	elseif ((x * x) <= 1e+72)
		tmp = y * 0.5;
	else
		tmp = 0.5 * (x / (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x * x), $MachinePrecision], 2e-209], N[(-0.5 / N[(N[(y / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 5e-156], N[(y * 0.5), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 1e-73], N[(N[(-0.5 * N[(z * z), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision], If[LessEqual[N[(x * x), $MachinePrecision], 1e+72], N[(y * 0.5), $MachinePrecision], N[(0.5 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if (*.f64 x x) < 2.0000000000000001e-209

   1. Initial program 72.3%

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

   2. Taylor expanded in z around inf 56.5%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. unpow2 56.5%

         \[\leadsto -0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

      2. associate-*r/ 56.5%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   4. Simplified 56.5%

      \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]
   5. Step-by-step derivation

      1. clear-num 56.5%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{-0.5 \cdot \left(z \cdot z\right)}}} \]

      2. inv-pow 56.5%

         \[\leadsto \color{blue}{{\left(\frac{y}{-0.5 \cdot \left(z \cdot z\right)}\right)}^{-1}} \]

      3. *-un-lft-identity 56.5%

         \[\leadsto {\left(\frac{\color{blue}{1 \cdot y}}{-0.5 \cdot \left(z \cdot z\right)}\right)}^{-1} \]

      4. times-frac 56.5%

         \[\leadsto {\color{blue}{\left(\frac{1}{-0.5} \cdot \frac{y}{z \cdot z}\right)}}^{-1} \]

      5. metadata-eval 56.5%

         \[\leadsto {\left(\color{blue}{-2} \cdot \frac{y}{z \cdot z}\right)}^{-1} \]

   6. Applied egg-rr 56.5%

      \[\leadsto \color{blue}{{\left(-2 \cdot \frac{y}{z \cdot z}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 56.5%

         \[\leadsto \color{blue}{\frac{1}{-2 \cdot \frac{y}{z \cdot z}}} \]

      2. associate-/r* 56.5%

         \[\leadsto \color{blue}{\frac{\frac{1}{-2}}{\frac{y}{z \cdot z}}} \]

      3. metadata-eval 56.5%

         \[\leadsto \frac{\color{blue}{-0.5}}{\frac{y}{z \cdot z}} \]

      4. associate-/r* 57.7%

         \[\leadsto \frac{-0.5}{\color{blue}{\frac{\frac{y}{z}}{z}}} \]

   8. Simplified 57.7%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{\frac{y}{z}}{z}}} \]

   if 2.0000000000000001e-209 < (*.f64 x x) < 5.00000000000000007e-156 or 9.99999999999999997e-74 < (*.f64 x x) < 9.99999999999999944e71

   1. Initial program 61.3%

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

   2. Taylor expanded in y around inf 66.9%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
   3. Step-by-step derivation

      1. *-commutative 66.9%

         \[\leadsto \color{blue}{y \cdot 0.5} \]

   4. Simplified 66.9%

      \[\leadsto \color{blue}{y \cdot 0.5} \]

   if 5.00000000000000007e-156 < (*.f64 x x) < 9.99999999999999997e-74

   1. Initial program 95.0%

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

   2. Taylor expanded in z around inf 71.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. unpow2 71.0%

         \[\leadsto -0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

      2. associate-*r/ 71.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   4. Simplified 71.0%

      \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   if 9.99999999999999944e71 < (*.f64 x x)

   1. Initial program 70.4%

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

   2. Taylor expanded in x around inf 62.3%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 62.3%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 62.3%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   5. Taylor expanded in x around 0 62.3%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   6. Step-by-step derivation

      1. unpow2 62.3%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x}}{y} \]

      2. *-commutative 62.3%

         \[\leadsto \color{blue}{\frac{x \cdot x}{y} \cdot 0.5} \]

      3. associate-/l* 67.3%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}}} \cdot 0.5 \]

   7. Simplified 67.3%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}} \cdot 0.5} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 2 \cdot 10^{-209}:\\ \;\;\;\;\frac{-0.5}{\frac{\frac{y}{z}}{z}}\\ \mathbf{elif}\;x \cdot x \leq 5 \cdot 10^{-156}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \cdot x \leq 10^{-73}:\\ \;\;\;\;\frac{-0.5 \cdot \left(z \cdot z\right)}{y}\\ \mathbf{elif}\;x \cdot x \leq 10^{+72}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \end{array} \]

Alternative 3: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \mathbf{if}\;x \leq -2.4 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-37}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \frac{z \cdot -0.5}{y}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (* x (/ 0.5 y)))))
   (if (<= x -2.4e+79)
     t_0
     (if (<= x -3.55e-37)
       (* y 0.5)
       (if (<= x 3.5e-105)
         (* z (/ (* z -0.5) y))
         (if (<= x 4.1e+30) (* y 0.5) t_0))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (x * (0.5 / y));
	double tmp;
	if (x <= -2.4e+79) {
		tmp = t_0;
	} else if (x <= -3.55e-37) {
		tmp = y * 0.5;
	} else if (x <= 3.5e-105) {
		tmp = z * ((z * -0.5) / y);
	} else if (x <= 4.1e+30) {
		tmp = y * 0.5;
	} 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 * (x * (0.5d0 / y))
    if (x <= (-2.4d+79)) then
        tmp = t_0
    else if (x <= (-3.55d-37)) then
        tmp = y * 0.5d0
    else if (x <= 3.5d-105) then
        tmp = z * ((z * (-0.5d0)) / y)
    else if (x <= 4.1d+30) then
        tmp = y * 0.5d0
    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 * (x * (0.5 / y));
	double tmp;
	if (x <= -2.4e+79) {
		tmp = t_0;
	} else if (x <= -3.55e-37) {
		tmp = y * 0.5;
	} else if (x <= 3.5e-105) {
		tmp = z * ((z * -0.5) / y);
	} else if (x <= 4.1e+30) {
		tmp = y * 0.5;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (x * (0.5 / y))
	tmp = 0
	if x <= -2.4e+79:
		tmp = t_0
	elif x <= -3.55e-37:
		tmp = y * 0.5
	elif x <= 3.5e-105:
		tmp = z * ((z * -0.5) / y)
	elif x <= 4.1e+30:
		tmp = y * 0.5
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(x * Float64(0.5 / y)))
	tmp = 0.0
	if (x <= -2.4e+79)
		tmp = t_0;
	elseif (x <= -3.55e-37)
		tmp = Float64(y * 0.5);
	elseif (x <= 3.5e-105)
		tmp = Float64(z * Float64(Float64(z * -0.5) / y));
	elseif (x <= 4.1e+30)
		tmp = Float64(y * 0.5);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (x * (0.5 / y));
	tmp = 0.0;
	if (x <= -2.4e+79)
		tmp = t_0;
	elseif (x <= -3.55e-37)
		tmp = y * 0.5;
	elseif (x <= 3.5e-105)
		tmp = z * ((z * -0.5) / y);
	elseif (x <= 4.1e+30)
		tmp = y * 0.5;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.4e+79], t$95$0, If[LessEqual[x, -3.55e-37], N[(y * 0.5), $MachinePrecision], If[LessEqual[x, 3.5e-105], N[(z * N[(N[(z * -0.5), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+30], N[(y * 0.5), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.39999999999999986e79 or 4.10000000000000005e30 < x

   1. Initial program 70.5%

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

   2. Taylor expanded in x around inf 63.1%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 63.1%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 63.1%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 68.2%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{2}} \]

      2. div-inv 68.2%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 68.2%

         \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 68.2%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.5\right)} \]

   7. Taylor expanded in x around 0 63.1%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 63.1%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.5} \]

      2. unpow2 63.1%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y} \cdot 0.5 \]

      3. associate-*r/ 68.2%

         \[\leadsto \color{blue}{\left(x \cdot \frac{x}{y}\right)} \cdot 0.5 \]

      4. associate-*r* 68.2%

         \[\leadsto \color{blue}{x \cdot \left(\frac{x}{y} \cdot 0.5\right)} \]

      5. associate-*l/ 68.2%

         \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.5}{y}} \]

      6. *-lft-identity 68.2%

         \[\leadsto x \cdot \frac{x \cdot 0.5}{\color{blue}{1 \cdot y}} \]

      7. times-frac 68.1%

         \[\leadsto x \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{0.5}{y}\right)} \]

      8. /-rgt-identity 68.1%

         \[\leadsto x \cdot \left(\color{blue}{x} \cdot \frac{0.5}{y}\right) \]

   9. Simplified 68.1%

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \frac{0.5}{y}\right)} \]

   if -2.39999999999999986e79 < x < -3.54999999999999989e-37 or 3.5e-105 < x < 4.10000000000000005e30

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 58.1%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
   3. Step-by-step derivation

      1. *-commutative 58.1%

         \[\leadsto \color{blue}{y \cdot 0.5} \]

   4. Simplified 58.1%

      \[\leadsto \color{blue}{y \cdot 0.5} \]

   if -3.54999999999999989e-37 < x < 3.5e-105

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. unpow2 59.0%

         \[\leadsto -0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

      2. associate-*r/ 59.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   4. Simplified 59.0%

      \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   5. Taylor expanded in z around 0 59.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{{z}^{2}}{y}} \]
   6. Step-by-step derivation

      1. unpow2 59.0%

         \[\leadsto -0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

      2. metadata-eval 59.0%

         \[\leadsto \color{blue}{\frac{-0.5}{1}} \cdot \frac{z \cdot z}{y} \]

      3. times-frac 59.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{1 \cdot y}} \]

      4. *-commutative 59.0%

         \[\leadsto \frac{\color{blue}{\left(z \cdot z\right) \cdot -0.5}}{1 \cdot y} \]

      5. associate-*l* 59.0%

         \[\leadsto \frac{\color{blue}{z \cdot \left(z \cdot -0.5\right)}}{1 \cdot y} \]

      6. *-commutative 59.0%

         \[\leadsto \frac{z \cdot \color{blue}{\left(-0.5 \cdot z\right)}}{1 \cdot y} \]

      7. times-frac 60.0%

         \[\leadsto \color{blue}{\frac{z}{1} \cdot \frac{-0.5 \cdot z}{y}} \]

      8. /-rgt-identity 60.0%

         \[\leadsto \color{blue}{z} \cdot \frac{-0.5 \cdot z}{y} \]

      9. *-commutative 60.0%

         \[\leadsto z \cdot \frac{\color{blue}{z \cdot -0.5}}{y} \]

   7. Simplified 60.0%

      \[\leadsto \color{blue}{z \cdot \frac{z \cdot -0.5}{y}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.4 \cdot 10^{+79}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \mathbf{elif}\;x \leq -3.55 \cdot 10^{-37}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 3.5 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \frac{z \cdot -0.5}{y}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \]

Alternative 4: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.5\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-38}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \frac{z \cdot -0.5}{y}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+28}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3.4e+79)
   (* (/ x y) (* x 0.5))
   (if (<= x -3e-38)
     (* y 0.5)
     (if (<= x 6.5e-105)
       (* z (/ (* z -0.5) y))
       (if (<= x 1.1e+28) (* y 0.5) (* x (* x (/ 0.5 y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e+79) {
		tmp = (x / y) * (x * 0.5);
	} else if (x <= -3e-38) {
		tmp = y * 0.5;
	} else if (x <= 6.5e-105) {
		tmp = z * ((z * -0.5) / y);
	} else if (x <= 1.1e+28) {
		tmp = y * 0.5;
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-3.4d+79)) then
        tmp = (x / y) * (x * 0.5d0)
    else if (x <= (-3d-38)) then
        tmp = y * 0.5d0
    else if (x <= 6.5d-105) then
        tmp = z * ((z * (-0.5d0)) / y)
    else if (x <= 1.1d+28) then
        tmp = y * 0.5d0
    else
        tmp = x * (x * (0.5d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -3.4e+79) {
		tmp = (x / y) * (x * 0.5);
	} else if (x <= -3e-38) {
		tmp = y * 0.5;
	} else if (x <= 6.5e-105) {
		tmp = z * ((z * -0.5) / y);
	} else if (x <= 1.1e+28) {
		tmp = y * 0.5;
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3.4e+79:
		tmp = (x / y) * (x * 0.5)
	elif x <= -3e-38:
		tmp = y * 0.5
	elif x <= 6.5e-105:
		tmp = z * ((z * -0.5) / y)
	elif x <= 1.1e+28:
		tmp = y * 0.5
	else:
		tmp = x * (x * (0.5 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3.4e+79)
		tmp = Float64(Float64(x / y) * Float64(x * 0.5));
	elseif (x <= -3e-38)
		tmp = Float64(y * 0.5);
	elseif (x <= 6.5e-105)
		tmp = Float64(z * Float64(Float64(z * -0.5) / y));
	elseif (x <= 1.1e+28)
		tmp = Float64(y * 0.5);
	else
		tmp = Float64(x * Float64(x * Float64(0.5 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -3.4e+79)
		tmp = (x / y) * (x * 0.5);
	elseif (x <= -3e-38)
		tmp = y * 0.5;
	elseif (x <= 6.5e-105)
		tmp = z * ((z * -0.5) / y);
	elseif (x <= 1.1e+28)
		tmp = y * 0.5;
	else
		tmp = x * (x * (0.5 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3.4e+79], N[(N[(x / y), $MachinePrecision] * N[(x * 0.5), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -3e-38], N[(y * 0.5), $MachinePrecision], If[LessEqual[x, 6.5e-105], N[(z * N[(N[(z * -0.5), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+28], N[(y * 0.5), $MachinePrecision], N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.40000000000000032e79

   1. Initial program 73.3%

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

   2. Taylor expanded in x around inf 69.0%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 69.0%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 69.0%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 74.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{2}} \]

      2. div-inv 74.4%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 74.4%

         \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 74.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.5\right)} \]

   if -3.40000000000000032e79 < x < -2.99999999999999989e-38 or 6.50000000000000006e-105 < x < 1.09999999999999993e28

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 58.1%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
   3. Step-by-step derivation

      1. *-commutative 58.1%

         \[\leadsto \color{blue}{y \cdot 0.5} \]

   4. Simplified 58.1%

      \[\leadsto \color{blue}{y \cdot 0.5} \]

   if -2.99999999999999989e-38 < x < 6.50000000000000006e-105

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. unpow2 59.0%

         \[\leadsto -0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

      2. associate-*r/ 59.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   4. Simplified 59.0%

      \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   5. Taylor expanded in z around 0 59.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{{z}^{2}}{y}} \]
   6. Step-by-step derivation

      1. unpow2 59.0%

         \[\leadsto -0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

      2. metadata-eval 59.0%

         \[\leadsto \color{blue}{\frac{-0.5}{1}} \cdot \frac{z \cdot z}{y} \]

      3. times-frac 59.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{1 \cdot y}} \]

      4. *-commutative 59.0%

         \[\leadsto \frac{\color{blue}{\left(z \cdot z\right) \cdot -0.5}}{1 \cdot y} \]

      5. associate-*l* 59.0%

         \[\leadsto \frac{\color{blue}{z \cdot \left(z \cdot -0.5\right)}}{1 \cdot y} \]

      6. *-commutative 59.0%

         \[\leadsto \frac{z \cdot \color{blue}{\left(-0.5 \cdot z\right)}}{1 \cdot y} \]

      7. times-frac 60.0%

         \[\leadsto \color{blue}{\frac{z}{1} \cdot \frac{-0.5 \cdot z}{y}} \]

      8. /-rgt-identity 60.0%

         \[\leadsto \color{blue}{z} \cdot \frac{-0.5 \cdot z}{y} \]

      9. *-commutative 60.0%

         \[\leadsto z \cdot \frac{\color{blue}{z \cdot -0.5}}{y} \]

   7. Simplified 60.0%

      \[\leadsto \color{blue}{z \cdot \frac{z \cdot -0.5}{y}} \]

   if 1.09999999999999993e28 < x

   1. Initial program 68.3%

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

   2. Taylor expanded in x around inf 58.6%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 58.6%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 58.6%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 63.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{2}} \]

      2. div-inv 63.4%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 63.4%

         \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 63.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.5\right)} \]

   7. Taylor expanded in x around 0 58.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 58.6%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.5} \]

      2. unpow2 58.6%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y} \cdot 0.5 \]

      3. associate-*r/ 63.4%

         \[\leadsto \color{blue}{\left(x \cdot \frac{x}{y}\right)} \cdot 0.5 \]

      4. associate-*r* 63.4%

         \[\leadsto \color{blue}{x \cdot \left(\frac{x}{y} \cdot 0.5\right)} \]

      5. associate-*l/ 63.4%

         \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.5}{y}} \]

      6. *-lft-identity 63.4%

         \[\leadsto x \cdot \frac{x \cdot 0.5}{\color{blue}{1 \cdot y}} \]

      7. times-frac 63.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{0.5}{y}\right)} \]

      8. /-rgt-identity 63.4%

         \[\leadsto x \cdot \left(\color{blue}{x} \cdot \frac{0.5}{y}\right) \]

   9. Simplified 63.4%

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \frac{0.5}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+79}:\\ \;\;\;\;\frac{x}{y} \cdot \left(x \cdot 0.5\right)\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-38}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \frac{z \cdot -0.5}{y}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+28}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \]

Alternative 5: 53.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+79}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-39}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \frac{z \cdot -0.5}{y}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+30}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -2.2e+79)
   (* 0.5 (/ x (/ y x)))
   (if (<= x -8.8e-39)
     (* y 0.5)
     (if (<= x 5.7e-105)
       (* z (/ (* z -0.5) y))
       (if (<= x 1.8e+30) (* y 0.5) (* x (* x (/ 0.5 y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.2e+79) {
		tmp = 0.5 * (x / (y / x));
	} else if (x <= -8.8e-39) {
		tmp = y * 0.5;
	} else if (x <= 5.7e-105) {
		tmp = z * ((z * -0.5) / y);
	} else if (x <= 1.8e+30) {
		tmp = y * 0.5;
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-2.2d+79)) then
        tmp = 0.5d0 * (x / (y / x))
    else if (x <= (-8.8d-39)) then
        tmp = y * 0.5d0
    else if (x <= 5.7d-105) then
        tmp = z * ((z * (-0.5d0)) / y)
    else if (x <= 1.8d+30) then
        tmp = y * 0.5d0
    else
        tmp = x * (x * (0.5d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -2.2e+79) {
		tmp = 0.5 * (x / (y / x));
	} else if (x <= -8.8e-39) {
		tmp = y * 0.5;
	} else if (x <= 5.7e-105) {
		tmp = z * ((z * -0.5) / y);
	} else if (x <= 1.8e+30) {
		tmp = y * 0.5;
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -2.2e+79:
		tmp = 0.5 * (x / (y / x))
	elif x <= -8.8e-39:
		tmp = y * 0.5
	elif x <= 5.7e-105:
		tmp = z * ((z * -0.5) / y)
	elif x <= 1.8e+30:
		tmp = y * 0.5
	else:
		tmp = x * (x * (0.5 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -2.2e+79)
		tmp = Float64(0.5 * Float64(x / Float64(y / x)));
	elseif (x <= -8.8e-39)
		tmp = Float64(y * 0.5);
	elseif (x <= 5.7e-105)
		tmp = Float64(z * Float64(Float64(z * -0.5) / y));
	elseif (x <= 1.8e+30)
		tmp = Float64(y * 0.5);
	else
		tmp = Float64(x * Float64(x * Float64(0.5 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -2.2e+79)
		tmp = 0.5 * (x / (y / x));
	elseif (x <= -8.8e-39)
		tmp = y * 0.5;
	elseif (x <= 5.7e-105)
		tmp = z * ((z * -0.5) / y);
	elseif (x <= 1.8e+30)
		tmp = y * 0.5;
	else
		tmp = x * (x * (0.5 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -2.2e+79], N[(0.5 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -8.8e-39], N[(y * 0.5), $MachinePrecision], If[LessEqual[x, 5.7e-105], N[(z * N[(N[(z * -0.5), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.8e+30], N[(y * 0.5), $MachinePrecision], N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.1999999999999999e79

   1. Initial program 73.3%

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

   2. Taylor expanded in x around inf 69.0%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 69.0%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 69.0%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   5. Taylor expanded in x around 0 69.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   6. Step-by-step derivation

      1. unpow2 69.0%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x}}{y} \]

      2. *-commutative 69.0%

         \[\leadsto \color{blue}{\frac{x \cdot x}{y} \cdot 0.5} \]

      3. associate-/l* 74.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}}} \cdot 0.5 \]

   7. Simplified 74.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}} \cdot 0.5} \]

   if -2.1999999999999999e79 < x < -8.80000000000000003e-39 or 5.69999999999999963e-105 < x < 1.8000000000000001e30

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 58.1%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
   3. Step-by-step derivation

      1. *-commutative 58.1%

         \[\leadsto \color{blue}{y \cdot 0.5} \]

   4. Simplified 58.1%

      \[\leadsto \color{blue}{y \cdot 0.5} \]

   if -8.80000000000000003e-39 < x < 5.69999999999999963e-105

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. unpow2 59.0%

         \[\leadsto -0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

      2. associate-*r/ 59.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   4. Simplified 59.0%

      \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   5. Taylor expanded in z around 0 59.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{{z}^{2}}{y}} \]
   6. Step-by-step derivation

      1. unpow2 59.0%

         \[\leadsto -0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

      2. metadata-eval 59.0%

         \[\leadsto \color{blue}{\frac{-0.5}{1}} \cdot \frac{z \cdot z}{y} \]

      3. times-frac 59.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{1 \cdot y}} \]

      4. *-commutative 59.0%

         \[\leadsto \frac{\color{blue}{\left(z \cdot z\right) \cdot -0.5}}{1 \cdot y} \]

      5. associate-*l* 59.0%

         \[\leadsto \frac{\color{blue}{z \cdot \left(z \cdot -0.5\right)}}{1 \cdot y} \]

      6. *-commutative 59.0%

         \[\leadsto \frac{z \cdot \color{blue}{\left(-0.5 \cdot z\right)}}{1 \cdot y} \]

      7. times-frac 60.0%

         \[\leadsto \color{blue}{\frac{z}{1} \cdot \frac{-0.5 \cdot z}{y}} \]

      8. /-rgt-identity 60.0%

         \[\leadsto \color{blue}{z} \cdot \frac{-0.5 \cdot z}{y} \]

      9. *-commutative 60.0%

         \[\leadsto z \cdot \frac{\color{blue}{z \cdot -0.5}}{y} \]

   7. Simplified 60.0%

      \[\leadsto \color{blue}{z \cdot \frac{z \cdot -0.5}{y}} \]

   if 1.8000000000000001e30 < x

   1. Initial program 68.3%

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

   2. Taylor expanded in x around inf 58.6%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 58.6%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 58.6%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 63.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{2}} \]

      2. div-inv 63.4%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 63.4%

         \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 63.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.5\right)} \]

   7. Taylor expanded in x around 0 58.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 58.6%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.5} \]

      2. unpow2 58.6%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y} \cdot 0.5 \]

      3. associate-*r/ 63.4%

         \[\leadsto \color{blue}{\left(x \cdot \frac{x}{y}\right)} \cdot 0.5 \]

      4. associate-*r* 63.4%

         \[\leadsto \color{blue}{x \cdot \left(\frac{x}{y} \cdot 0.5\right)} \]

      5. associate-*l/ 63.4%

         \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.5}{y}} \]

      6. *-lft-identity 63.4%

         \[\leadsto x \cdot \frac{x \cdot 0.5}{\color{blue}{1 \cdot y}} \]

      7. times-frac 63.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{0.5}{y}\right)} \]

      8. /-rgt-identity 63.4%

         \[\leadsto x \cdot \left(\color{blue}{x} \cdot \frac{0.5}{y}\right) \]

   9. Simplified 63.4%

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \frac{0.5}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{+79}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -8.8 \cdot 10^{-39}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-105}:\\ \;\;\;\;z \cdot \frac{z \cdot -0.5}{y}\\ \mathbf{elif}\;x \leq 1.8 \cdot 10^{+30}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \]

Alternative 6: 53.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+79}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-105}:\\ \;\;\;\;\frac{-0.5}{\frac{\frac{y}{z}}{z}}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e+79)
   (* 0.5 (/ x (/ y x)))
   (if (<= x -6.5e-40)
     (* y 0.5)
     (if (<= x 4.1e-105)
       (/ -0.5 (/ (/ y z) z))
       (if (<= x 6.2e+26) (* y 0.5) (* x (* x (/ 0.5 y))))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e+79) {
		tmp = 0.5 * (x / (y / x));
	} else if (x <= -6.5e-40) {
		tmp = y * 0.5;
	} else if (x <= 4.1e-105) {
		tmp = -0.5 / ((y / z) / z);
	} else if (x <= 6.2e+26) {
		tmp = y * 0.5;
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.5d+79)) then
        tmp = 0.5d0 * (x / (y / x))
    else if (x <= (-6.5d-40)) then
        tmp = y * 0.5d0
    else if (x <= 4.1d-105) then
        tmp = (-0.5d0) / ((y / z) / z)
    else if (x <= 6.2d+26) then
        tmp = y * 0.5d0
    else
        tmp = x * (x * (0.5d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e+79) {
		tmp = 0.5 * (x / (y / x));
	} else if (x <= -6.5e-40) {
		tmp = y * 0.5;
	} else if (x <= 4.1e-105) {
		tmp = -0.5 / ((y / z) / z);
	} else if (x <= 6.2e+26) {
		tmp = y * 0.5;
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e+79:
		tmp = 0.5 * (x / (y / x))
	elif x <= -6.5e-40:
		tmp = y * 0.5
	elif x <= 4.1e-105:
		tmp = -0.5 / ((y / z) / z)
	elif x <= 6.2e+26:
		tmp = y * 0.5
	else:
		tmp = x * (x * (0.5 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e+79)
		tmp = Float64(0.5 * Float64(x / Float64(y / x)));
	elseif (x <= -6.5e-40)
		tmp = Float64(y * 0.5);
	elseif (x <= 4.1e-105)
		tmp = Float64(-0.5 / Float64(Float64(y / z) / z));
	elseif (x <= 6.2e+26)
		tmp = Float64(y * 0.5);
	else
		tmp = Float64(x * Float64(x * Float64(0.5 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e+79)
		tmp = 0.5 * (x / (y / x));
	elseif (x <= -6.5e-40)
		tmp = y * 0.5;
	elseif (x <= 4.1e-105)
		tmp = -0.5 / ((y / z) / z);
	elseif (x <= 6.2e+26)
		tmp = y * 0.5;
	else
		tmp = x * (x * (0.5 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e+79], N[(0.5 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -6.5e-40], N[(y * 0.5), $MachinePrecision], If[LessEqual[x, 4.1e-105], N[(-0.5 / N[(N[(y / z), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.2e+26], N[(y * 0.5), $MachinePrecision], N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.49999999999999987e79

   1. Initial program 73.3%

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

   2. Taylor expanded in x around inf 69.0%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 69.0%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 69.0%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   5. Taylor expanded in x around 0 69.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   6. Step-by-step derivation

      1. unpow2 69.0%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x}}{y} \]

      2. *-commutative 69.0%

         \[\leadsto \color{blue}{\frac{x \cdot x}{y} \cdot 0.5} \]

      3. associate-/l* 74.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}}} \cdot 0.5 \]

   7. Simplified 74.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}} \cdot 0.5} \]

   if -1.49999999999999987e79 < x < -6.4999999999999999e-40 or 4.1000000000000003e-105 < x < 6.1999999999999999e26

   1. Initial program 66.9%

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

   2. Taylor expanded in y around inf 58.1%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
   3. Step-by-step derivation

      1. *-commutative 58.1%

         \[\leadsto \color{blue}{y \cdot 0.5} \]

   4. Simplified 58.1%

      \[\leadsto \color{blue}{y \cdot 0.5} \]

   if -6.4999999999999999e-40 < x < 4.1000000000000003e-105

   1. Initial program 74.9%

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

   2. Taylor expanded in z around inf 59.0%

      \[\leadsto \color{blue}{-0.5 \cdot \frac{{z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. unpow2 59.0%

         \[\leadsto -0.5 \cdot \frac{\color{blue}{z \cdot z}}{y} \]

      2. associate-*r/ 59.0%

         \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]

   4. Simplified 59.0%

      \[\leadsto \color{blue}{\frac{-0.5 \cdot \left(z \cdot z\right)}{y}} \]
   5. Step-by-step derivation

      1. clear-num 59.0%

         \[\leadsto \color{blue}{\frac{1}{\frac{y}{-0.5 \cdot \left(z \cdot z\right)}}} \]

      2. inv-pow 59.0%

         \[\leadsto \color{blue}{{\left(\frac{y}{-0.5 \cdot \left(z \cdot z\right)}\right)}^{-1}} \]

      3. *-un-lft-identity 59.0%

         \[\leadsto {\left(\frac{\color{blue}{1 \cdot y}}{-0.5 \cdot \left(z \cdot z\right)}\right)}^{-1} \]

      4. times-frac 59.0%

         \[\leadsto {\color{blue}{\left(\frac{1}{-0.5} \cdot \frac{y}{z \cdot z}\right)}}^{-1} \]

      5. metadata-eval 59.0%

         \[\leadsto {\left(\color{blue}{-2} \cdot \frac{y}{z \cdot z}\right)}^{-1} \]

   6. Applied egg-rr 59.0%

      \[\leadsto \color{blue}{{\left(-2 \cdot \frac{y}{z \cdot z}\right)}^{-1}} \]
   7. Step-by-step derivation

      1. unpow-1 59.0%

         \[\leadsto \color{blue}{\frac{1}{-2 \cdot \frac{y}{z \cdot z}}} \]

      2. associate-/r* 59.0%

         \[\leadsto \color{blue}{\frac{\frac{1}{-2}}{\frac{y}{z \cdot z}}} \]

      3. metadata-eval 59.0%

         \[\leadsto \frac{\color{blue}{-0.5}}{\frac{y}{z \cdot z}} \]

      4. associate-/r* 60.0%

         \[\leadsto \frac{-0.5}{\color{blue}{\frac{\frac{y}{z}}{z}}} \]

   8. Simplified 60.0%

      \[\leadsto \color{blue}{\frac{-0.5}{\frac{\frac{y}{z}}{z}}} \]

   if 6.1999999999999999e26 < x

   1. Initial program 68.3%

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

   2. Taylor expanded in x around inf 58.6%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 58.6%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 58.6%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 63.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{2}} \]

      2. div-inv 63.4%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 63.4%

         \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 63.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.5\right)} \]

   7. Taylor expanded in x around 0 58.6%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 58.6%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.5} \]

      2. unpow2 58.6%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y} \cdot 0.5 \]

      3. associate-*r/ 63.4%

         \[\leadsto \color{blue}{\left(x \cdot \frac{x}{y}\right)} \cdot 0.5 \]

      4. associate-*r* 63.4%

         \[\leadsto \color{blue}{x \cdot \left(\frac{x}{y} \cdot 0.5\right)} \]

      5. associate-*l/ 63.4%

         \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.5}{y}} \]

      6. *-lft-identity 63.4%

         \[\leadsto x \cdot \frac{x \cdot 0.5}{\color{blue}{1 \cdot y}} \]

      7. times-frac 63.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{0.5}{y}\right)} \]

      8. /-rgt-identity 63.4%

         \[\leadsto x \cdot \left(\color{blue}{x} \cdot \frac{0.5}{y}\right) \]

   9. Simplified 63.4%

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \frac{0.5}{y}\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+79}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq -6.5 \cdot 10^{-40}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-105}:\\ \;\;\;\;\frac{-0.5}{\frac{\frac{y}{z}}{z}}\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+26}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \]

Alternative 7: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+21} \lor \neg \left(y \leq 7.8 \cdot 10^{+68}\right):\\ \;\;\;\;-0.5 \cdot \left(x \cdot \frac{-x}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\left(x + z\right) \cdot \frac{x - z}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -1.05e+21) (not (<= y 7.8e+68)))
   (* -0.5 (- (* x (/ (- x) y)) y))
   (* 0.5 (* (+ x z) (/ (- x z) y)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e+21) || !(y <= 7.8e+68)) {
		tmp = -0.5 * ((x * (-x / y)) - y);
	} else {
		tmp = 0.5 * ((x + z) * ((x - z) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((y <= (-1.05d+21)) .or. (.not. (y <= 7.8d+68))) then
        tmp = (-0.5d0) * ((x * (-x / y)) - y)
    else
        tmp = 0.5d0 * ((x + z) * ((x - z) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -1.05e+21) || !(y <= 7.8e+68)) {
		tmp = -0.5 * ((x * (-x / y)) - y);
	} else {
		tmp = 0.5 * ((x + z) * ((x - z) / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -1.05e+21) or not (y <= 7.8e+68):
		tmp = -0.5 * ((x * (-x / y)) - y)
	else:
		tmp = 0.5 * ((x + z) * ((x - z) / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -1.05e+21) || !(y <= 7.8e+68))
		tmp = Float64(-0.5 * Float64(Float64(x * Float64(Float64(-x) / y)) - y));
	else
		tmp = Float64(0.5 * Float64(Float64(x + z) * Float64(Float64(x - z) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -1.05e+21) || ~((y <= 7.8e+68)))
		tmp = -0.5 * ((x * (-x / y)) - y);
	else
		tmp = 0.5 * ((x + z) * ((x - z) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -1.05e+21], N[Not[LessEqual[y, 7.8e+68]], $MachinePrecision]], N[(-0.5 * N[(N[(x * N[((-x) / y), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x + z), $MachinePrecision] * N[(N[(x - z), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e21 or 7.80000000000000037e68 < y

   1. Initial program 42.2%

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

      1. sub-neg 42.2%

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

      2. +-commutative 42.2%

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

      3. neg-sub0 42.2%

         \[\leadsto \frac{\color{blue}{\left(0 - z \cdot z\right)} + \left(x \cdot x + y \cdot y\right)}{y \cdot 2} \]

      4. associate-+l- 42.2%

         \[\leadsto \frac{\color{blue}{0 - \left(z \cdot z - \left(x \cdot x + y \cdot y\right)\right)}}{y \cdot 2} \]

      5. sub0-neg 42.2%

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

      6. neg-mul-1 42.2%

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

      7. *-commutative 42.2%

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

      8. times-frac 42.2%

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

      9. associate--r+ 42.2%

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

      10. div-sub 42.2%

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

      11. difference-of-squares 46.2%

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

      12. +-commutative 46.2%

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

      13. associate-*r/ 50.2%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot \color{blue}{-0.5} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot -0.5} \]
   4. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\frac{1}{\frac{y}{z - x}}} - y\right) \cdot -0.5 \]

      2. associate-/r/ 99.9%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]

   5. Applied egg-rr 99.9%

      \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]
   6. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + x\right)} \cdot \left(\frac{1}{y} \cdot \left(z - x\right)\right) - y\right) \cdot -0.5 \]

      2. *-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right) \cdot \left(z + x\right)} - y\right) \cdot -0.5 \]

      3. associate-*l/ 99.9%

         \[\leadsto \left(\color{blue}{\frac{1 \cdot \left(z - x\right)}{y}} \cdot \left(z + x\right) - y\right) \cdot -0.5 \]

      4. *-un-lft-identity 99.9%

         \[\leadsto \left(\frac{\color{blue}{z - x}}{y} \cdot \left(z + x\right) - y\right) \cdot -0.5 \]

      5. flip-+ 76.6%

         \[\leadsto \left(\frac{z - x}{y} \cdot \color{blue}{\frac{z \cdot z - x \cdot x}{z - x}} - y\right) \cdot -0.5 \]

      6. frac-times 52.6%

         \[\leadsto \left(\color{blue}{\frac{\left(z - x\right) \cdot \left(z \cdot z - x \cdot x\right)}{y \cdot \left(z - x\right)}} - y\right) \cdot -0.5 \]

   7. Applied egg-rr 52.6%

      \[\leadsto \left(\color{blue}{\frac{\left(z - x\right) \cdot \left(z \cdot z - x \cdot x\right)}{y \cdot \left(z - x\right)}} - y\right) \cdot -0.5 \]
   8. Step-by-step derivation

      1. associate-/l* 62.7%

         \[\leadsto \left(\color{blue}{\frac{z - x}{\frac{y \cdot \left(z - x\right)}{z \cdot z - x \cdot x}}} - y\right) \cdot -0.5 \]

      2. *-commutative 62.7%

         \[\leadsto \left(\frac{z - x}{\frac{\color{blue}{\left(z - x\right) \cdot y}}{z \cdot z - x \cdot x}} - y\right) \cdot -0.5 \]

   9. Simplified 62.7%

      \[\leadsto \left(\color{blue}{\frac{z - x}{\frac{\left(z - x\right) \cdot y}{z \cdot z - x \cdot x}}} - y\right) \cdot -0.5 \]

   10. Taylor expanded in z around 0 77.8%

       \[\leadsto \left(\color{blue}{-1 \cdot \frac{{x}^{2}}{y}} - y\right) \cdot -0.5 \]
   11. Step-by-step derivation

       1. mul-1-neg 77.8%

          \[\leadsto \left(\color{blue}{\left(-\frac{{x}^{2}}{y}\right)} - y\right) \cdot -0.5 \]

       2. unpow2 77.8%

          \[\leadsto \left(\left(-\frac{\color{blue}{x \cdot x}}{y}\right) - y\right) \cdot -0.5 \]

       3. associate-*l/ 88.9%

          \[\leadsto \left(\left(-\color{blue}{\frac{x}{y} \cdot x}\right) - y\right) \cdot -0.5 \]

       4. distribute-rgt-neg-out 88.9%

          \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot \left(-x\right)} - y\right) \cdot -0.5 \]

   12. Simplified 88.9%

       \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot \left(-x\right)} - y\right) \cdot -0.5 \]

   if -1.05e21 < y < 7.80000000000000037e68

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 90.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2} - {z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. unpow2 90.0%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x} - {z}^{2}}{y} \]

      2. unpow2 90.0%

         \[\leadsto 0.5 \cdot \frac{x \cdot x - \color{blue}{z \cdot z}}{y} \]

      3. difference-of-squares 96.1%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{\left(x + z\right) \cdot \left(x - z\right)}}{y} \]

      4. associate-/l* 96.7%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x + z}{\frac{y}{x - z}}} \]

      5. +-commutative 96.7%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{z + x}}{\frac{y}{x - z}} \]

   4. Simplified 96.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z + x}{\frac{y}{x - z}}} \]

   5. Taylor expanded in y around 0 96.1%

      \[\leadsto 0.5 \cdot \color{blue}{\frac{\left(x - z\right) \cdot \left(z + x\right)}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 96.1%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{\left(z + x\right) \cdot \left(x - z\right)}}{y} \]

      2. associate-*r/ 96.7%

         \[\leadsto 0.5 \cdot \color{blue}{\left(\left(z + x\right) \cdot \frac{x - z}{y}\right)} \]

   7. Simplified 96.7%

      \[\leadsto 0.5 \cdot \color{blue}{\left(\left(z + x\right) \cdot \frac{x - z}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{+21} \lor \neg \left(y \leq 7.8 \cdot 10^{+68}\right):\\ \;\;\;\;-0.5 \cdot \left(x \cdot \frac{-x}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\left(x + z\right) \cdot \frac{x - z}{y}\right)\\ \end{array} \]

Alternative 8: 85.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+20} \lor \neg \left(y \leq 3.3 \cdot 10^{+68}\right):\\ \;\;\;\;-0.5 \cdot \left(x \cdot \frac{-x}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + z}{\frac{y}{x - z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -9.6e+20) (not (<= y 3.3e+68)))
   (* -0.5 (- (* x (/ (- x) y)) y))
   (* 0.5 (/ (+ x z) (/ y (- x z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.6e+20) || !(y <= 3.3e+68)) {
		tmp = -0.5 * ((x * (-x / y)) - y);
	} else {
		tmp = 0.5 * ((x + z) / (y / (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 ((y <= (-9.6d+20)) .or. (.not. (y <= 3.3d+68))) then
        tmp = (-0.5d0) * ((x * (-x / y)) - y)
    else
        tmp = 0.5d0 * ((x + z) / (y / (x - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((y <= -9.6e+20) || !(y <= 3.3e+68)) {
		tmp = -0.5 * ((x * (-x / y)) - y);
	} else {
		tmp = 0.5 * ((x + z) / (y / (x - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -9.6e+20) or not (y <= 3.3e+68):
		tmp = -0.5 * ((x * (-x / y)) - y)
	else:
		tmp = 0.5 * ((x + z) / (y / (x - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -9.6e+20) || !(y <= 3.3e+68))
		tmp = Float64(-0.5 * Float64(Float64(x * Float64(Float64(-x) / y)) - y));
	else
		tmp = Float64(0.5 * Float64(Float64(x + z) / Float64(y / Float64(x - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((y <= -9.6e+20) || ~((y <= 3.3e+68)))
		tmp = -0.5 * ((x * (-x / y)) - y);
	else
		tmp = 0.5 * ((x + z) / (y / (x - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -9.6e+20], N[Not[LessEqual[y, 3.3e+68]], $MachinePrecision]], N[(-0.5 * N[(N[(x * N[((-x) / y), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(x + z), $MachinePrecision] / N[(y / N[(x - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.6e20 or 3.3e68 < y

   1. Initial program 42.2%

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

      1. sub-neg 42.2%

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

      2. +-commutative 42.2%

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

      3. neg-sub0 42.2%

         \[\leadsto \frac{\color{blue}{\left(0 - z \cdot z\right)} + \left(x \cdot x + y \cdot y\right)}{y \cdot 2} \]

      4. associate-+l- 42.2%

         \[\leadsto \frac{\color{blue}{0 - \left(z \cdot z - \left(x \cdot x + y \cdot y\right)\right)}}{y \cdot 2} \]

      5. sub0-neg 42.2%

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

      6. neg-mul-1 42.2%

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

      7. *-commutative 42.2%

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

      8. times-frac 42.2%

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

      9. associate--r+ 42.2%

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

      10. div-sub 42.2%

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

      11. difference-of-squares 46.2%

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

      12. +-commutative 46.2%

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

      13. associate-*r/ 50.2%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot \color{blue}{-0.5} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot -0.5} \]
   4. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\frac{1}{\frac{y}{z - x}}} - y\right) \cdot -0.5 \]

      2. associate-/r/ 99.9%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]

   5. Applied egg-rr 99.9%

      \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]
   6. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + x\right)} \cdot \left(\frac{1}{y} \cdot \left(z - x\right)\right) - y\right) \cdot -0.5 \]

      2. *-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right) \cdot \left(z + x\right)} - y\right) \cdot -0.5 \]

      3. associate-*l/ 99.9%

         \[\leadsto \left(\color{blue}{\frac{1 \cdot \left(z - x\right)}{y}} \cdot \left(z + x\right) - y\right) \cdot -0.5 \]

      4. *-un-lft-identity 99.9%

         \[\leadsto \left(\frac{\color{blue}{z - x}}{y} \cdot \left(z + x\right) - y\right) \cdot -0.5 \]

      5. flip-+ 76.6%

         \[\leadsto \left(\frac{z - x}{y} \cdot \color{blue}{\frac{z \cdot z - x \cdot x}{z - x}} - y\right) \cdot -0.5 \]

      6. frac-times 52.6%

         \[\leadsto \left(\color{blue}{\frac{\left(z - x\right) \cdot \left(z \cdot z - x \cdot x\right)}{y \cdot \left(z - x\right)}} - y\right) \cdot -0.5 \]

   7. Applied egg-rr 52.6%

      \[\leadsto \left(\color{blue}{\frac{\left(z - x\right) \cdot \left(z \cdot z - x \cdot x\right)}{y \cdot \left(z - x\right)}} - y\right) \cdot -0.5 \]
   8. Step-by-step derivation

      1. associate-/l* 62.7%

         \[\leadsto \left(\color{blue}{\frac{z - x}{\frac{y \cdot \left(z - x\right)}{z \cdot z - x \cdot x}}} - y\right) \cdot -0.5 \]

      2. *-commutative 62.7%

         \[\leadsto \left(\frac{z - x}{\frac{\color{blue}{\left(z - x\right) \cdot y}}{z \cdot z - x \cdot x}} - y\right) \cdot -0.5 \]

   9. Simplified 62.7%

      \[\leadsto \left(\color{blue}{\frac{z - x}{\frac{\left(z - x\right) \cdot y}{z \cdot z - x \cdot x}}} - y\right) \cdot -0.5 \]

   10. Taylor expanded in z around 0 77.8%

       \[\leadsto \left(\color{blue}{-1 \cdot \frac{{x}^{2}}{y}} - y\right) \cdot -0.5 \]
   11. Step-by-step derivation

       1. mul-1-neg 77.8%

          \[\leadsto \left(\color{blue}{\left(-\frac{{x}^{2}}{y}\right)} - y\right) \cdot -0.5 \]

       2. unpow2 77.8%

          \[\leadsto \left(\left(-\frac{\color{blue}{x \cdot x}}{y}\right) - y\right) \cdot -0.5 \]

       3. associate-*l/ 88.9%

          \[\leadsto \left(\left(-\color{blue}{\frac{x}{y} \cdot x}\right) - y\right) \cdot -0.5 \]

       4. distribute-rgt-neg-out 88.9%

          \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot \left(-x\right)} - y\right) \cdot -0.5 \]

   12. Simplified 88.9%

       \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot \left(-x\right)} - y\right) \cdot -0.5 \]

   if -9.6e20 < y < 3.3e68

   1. Initial program 92.6%

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

   2. Taylor expanded in y around 0 90.0%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2} - {z}^{2}}{y}} \]
   3. Step-by-step derivation

      1. unpow2 90.0%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x} - {z}^{2}}{y} \]

      2. unpow2 90.0%

         \[\leadsto 0.5 \cdot \frac{x \cdot x - \color{blue}{z \cdot z}}{y} \]

      3. difference-of-squares 96.1%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{\left(x + z\right) \cdot \left(x - z\right)}}{y} \]

      4. associate-/l* 96.7%

         \[\leadsto 0.5 \cdot \color{blue}{\frac{x + z}{\frac{y}{x - z}}} \]

      5. +-commutative 96.7%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{z + x}}{\frac{y}{x - z}} \]

   4. Simplified 96.7%

      \[\leadsto \color{blue}{0.5 \cdot \frac{z + x}{\frac{y}{x - z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 93.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9.6 \cdot 10^{+20} \lor \neg \left(y \leq 3.3 \cdot 10^{+68}\right):\\ \;\;\;\;-0.5 \cdot \left(x \cdot \frac{-x}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \frac{x + z}{\frac{y}{x - z}}\\ \end{array} \]

Alternative 9: 86.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 10^{+72}:\\ \;\;\;\;-0.5 \cdot \left(\frac{z}{\frac{y}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(x \cdot \frac{-x}{y} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* x x) 1e+72)
   (* -0.5 (- (/ z (/ y z)) y))
   (* -0.5 (- (* x (/ (- x) y)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 1e+72) {
		tmp = -0.5 * ((z / (y / z)) - y);
	} else {
		tmp = -0.5 * ((x * (-x / y)) - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x * x) <= 1d+72) then
        tmp = (-0.5d0) * ((z / (y / z)) - y)
    else
        tmp = (-0.5d0) * ((x * (-x / y)) - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 1e+72) {
		tmp = -0.5 * ((z / (y / z)) - y);
	} else {
		tmp = -0.5 * ((x * (-x / y)) - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x * x) <= 1e+72:
		tmp = -0.5 * ((z / (y / z)) - y)
	else:
		tmp = -0.5 * ((x * (-x / y)) - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x * x) <= 1e+72)
		tmp = Float64(-0.5 * Float64(Float64(z / Float64(y / z)) - y));
	else
		tmp = Float64(-0.5 * Float64(Float64(x * Float64(Float64(-x) / y)) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x * x) <= 1e+72)
		tmp = -0.5 * ((z / (y / z)) - y);
	else
		tmp = -0.5 * ((x * (-x / y)) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x * x), $MachinePrecision], 1e+72], N[(-0.5 * N[(N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[(x * N[((-x) / y), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 9.99999999999999944e71

   1. Initial program 72.5%

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

      1. sub-neg 72.5%

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

      2. +-commutative 72.5%

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

      3. neg-sub0 72.5%

         \[\leadsto \frac{\color{blue}{\left(0 - z \cdot z\right)} + \left(x \cdot x + y \cdot y\right)}{y \cdot 2} \]

      4. associate-+l- 72.5%

         \[\leadsto \frac{\color{blue}{0 - \left(z \cdot z - \left(x \cdot x + y \cdot y\right)\right)}}{y \cdot 2} \]

      5. sub0-neg 72.5%

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

      6. neg-mul-1 72.5%

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

      7. *-commutative 72.5%

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

      8. times-frac 72.5%

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

      9. associate--r+ 72.5%

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

      10. div-sub 72.5%

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

      11. difference-of-squares 72.5%

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

      12. +-commutative 72.5%

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

      13. associate-*r/ 73.5%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot \color{blue}{-0.5} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot -0.5} \]

   4. Taylor expanded in x around 0 87.6%

      \[\leadsto \left(\color{blue}{\frac{{z}^{2}}{y}} - y\right) \cdot -0.5 \]
   5. Step-by-step derivation

      1. unpow2 87.6%

         \[\leadsto \left(\frac{\color{blue}{z \cdot z}}{y} - y\right) \cdot -0.5 \]

      2. associate-/l* 92.7%

         \[\leadsto \left(\color{blue}{\frac{z}{\frac{y}{z}}} - y\right) \cdot -0.5 \]

   6. Simplified 92.7%

      \[\leadsto \left(\color{blue}{\frac{z}{\frac{y}{z}}} - y\right) \cdot -0.5 \]

   if 9.99999999999999944e71 < (*.f64 x x)

   1. Initial program 70.4%

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

      1. sub-neg 70.4%

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

      2. +-commutative 70.4%

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

      3. neg-sub0 70.4%

         \[\leadsto \frac{\color{blue}{\left(0 - z \cdot z\right)} + \left(x \cdot x + y \cdot y\right)}{y \cdot 2} \]

      4. associate-+l- 70.4%

         \[\leadsto \frac{\color{blue}{0 - \left(z \cdot z - \left(x \cdot x + y \cdot y\right)\right)}}{y \cdot 2} \]

      5. sub0-neg 70.4%

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

      6. neg-mul-1 70.4%

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

      7. *-commutative 70.4%

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

      8. times-frac 70.4%

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

      9. associate--r+ 70.4%

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

      10. div-sub 70.4%

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

      11. difference-of-squares 81.4%

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

      12. +-commutative 81.4%

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

      13. associate-*r/ 84.5%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot \color{blue}{-0.5} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot -0.5} \]
   4. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\frac{1}{\frac{y}{z - x}}} - y\right) \cdot -0.5 \]

      2. associate-/r/ 99.9%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]

   5. Applied egg-rr 99.9%

      \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]
   6. Step-by-step derivation

      1. +-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(z + x\right)} \cdot \left(\frac{1}{y} \cdot \left(z - x\right)\right) - y\right) \cdot -0.5 \]

      2. *-commutative 99.9%

         \[\leadsto \left(\color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right) \cdot \left(z + x\right)} - y\right) \cdot -0.5 \]

      3. associate-*l/ 99.9%

         \[\leadsto \left(\color{blue}{\frac{1 \cdot \left(z - x\right)}{y}} \cdot \left(z + x\right) - y\right) \cdot -0.5 \]

      4. *-un-lft-identity 99.9%

         \[\leadsto \left(\frac{\color{blue}{z - x}}{y} \cdot \left(z + x\right) - y\right) \cdot -0.5 \]

      5. flip-+ 77.5%

         \[\leadsto \left(\frac{z - x}{y} \cdot \color{blue}{\frac{z \cdot z - x \cdot x}{z - x}} - y\right) \cdot -0.5 \]

      6. frac-times 61.5%

         \[\leadsto \left(\color{blue}{\frac{\left(z - x\right) \cdot \left(z \cdot z - x \cdot x\right)}{y \cdot \left(z - x\right)}} - y\right) \cdot -0.5 \]

   7. Applied egg-rr 61.5%

      \[\leadsto \left(\color{blue}{\frac{\left(z - x\right) \cdot \left(z \cdot z - x \cdot x\right)}{y \cdot \left(z - x\right)}} - y\right) \cdot -0.5 \]
   8. Step-by-step derivation

      1. associate-/l* 68.7%

         \[\leadsto \left(\color{blue}{\frac{z - x}{\frac{y \cdot \left(z - x\right)}{z \cdot z - x \cdot x}}} - y\right) \cdot -0.5 \]

      2. *-commutative 68.7%

         \[\leadsto \left(\frac{z - x}{\frac{\color{blue}{\left(z - x\right) \cdot y}}{z \cdot z - x \cdot x}} - y\right) \cdot -0.5 \]

   9. Simplified 68.7%

      \[\leadsto \left(\color{blue}{\frac{z - x}{\frac{\left(z - x\right) \cdot y}{z \cdot z - x \cdot x}}} - y\right) \cdot -0.5 \]

   10. Taylor expanded in z around 0 72.0%

       \[\leadsto \left(\color{blue}{-1 \cdot \frac{{x}^{2}}{y}} - y\right) \cdot -0.5 \]
   11. Step-by-step derivation

       1. mul-1-neg 72.0%

          \[\leadsto \left(\color{blue}{\left(-\frac{{x}^{2}}{y}\right)} - y\right) \cdot -0.5 \]

       2. unpow2 72.0%

          \[\leadsto \left(\left(-\frac{\color{blue}{x \cdot x}}{y}\right) - y\right) \cdot -0.5 \]

       3. associate-*l/ 81.8%

          \[\leadsto \left(\left(-\color{blue}{\frac{x}{y} \cdot x}\right) - y\right) \cdot -0.5 \]

       4. distribute-rgt-neg-out 81.8%

          \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot \left(-x\right)} - y\right) \cdot -0.5 \]

   12. Simplified 81.8%

       \[\leadsto \left(\color{blue}{\frac{x}{y} \cdot \left(-x\right)} - y\right) \cdot -0.5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 10^{+72}:\\ \;\;\;\;-0.5 \cdot \left(\frac{z}{\frac{y}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(x \cdot \frac{-x}{y} - y\right)\\ \end{array} \]

Alternative 10: 86.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \cdot x \leq 10^{+72}:\\ \;\;\;\;-0.5 \cdot \left(\frac{z}{\frac{y}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(\frac{-x}{\frac{y}{x}} - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* x x) 1e+72)
   (* -0.5 (- (/ z (/ y z)) y))
   (* -0.5 (- (/ (- x) (/ y x)) y))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 1e+72) {
		tmp = -0.5 * ((z / (y / z)) - y);
	} else {
		tmp = -0.5 * ((-x / (y / x)) - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x * x) <= 1d+72) then
        tmp = (-0.5d0) * ((z / (y / z)) - y)
    else
        tmp = (-0.5d0) * ((-x / (y / x)) - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x * x) <= 1e+72) {
		tmp = -0.5 * ((z / (y / z)) - y);
	} else {
		tmp = -0.5 * ((-x / (y / x)) - y);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x * x) <= 1e+72:
		tmp = -0.5 * ((z / (y / z)) - y)
	else:
		tmp = -0.5 * ((-x / (y / x)) - y)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(x * x) <= 1e+72)
		tmp = Float64(-0.5 * Float64(Float64(z / Float64(y / z)) - y));
	else
		tmp = Float64(-0.5 * Float64(Float64(Float64(-x) / Float64(y / x)) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x * x) <= 1e+72)
		tmp = -0.5 * ((z / (y / z)) - y);
	else
		tmp = -0.5 * ((-x / (y / x)) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(x * x), $MachinePrecision], 1e+72], N[(-0.5 * N[(N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(-0.5 * N[(N[((-x) / N[(y / x), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 x x) < 9.99999999999999944e71

   1. Initial program 72.5%

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

      1. sub-neg 72.5%

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

      2. +-commutative 72.5%

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

      3. neg-sub0 72.5%

         \[\leadsto \frac{\color{blue}{\left(0 - z \cdot z\right)} + \left(x \cdot x + y \cdot y\right)}{y \cdot 2} \]

      4. associate-+l- 72.5%

         \[\leadsto \frac{\color{blue}{0 - \left(z \cdot z - \left(x \cdot x + y \cdot y\right)\right)}}{y \cdot 2} \]

      5. sub0-neg 72.5%

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

      6. neg-mul-1 72.5%

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

      7. *-commutative 72.5%

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

      8. times-frac 72.5%

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

      9. associate--r+ 72.5%

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

      10. div-sub 72.5%

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

      11. difference-of-squares 72.5%

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

      12. +-commutative 72.5%

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

      13. associate-*r/ 73.5%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot \color{blue}{-0.5} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot -0.5} \]

   4. Taylor expanded in x around 0 87.6%

      \[\leadsto \left(\color{blue}{\frac{{z}^{2}}{y}} - y\right) \cdot -0.5 \]
   5. Step-by-step derivation

      1. unpow2 87.6%

         \[\leadsto \left(\frac{\color{blue}{z \cdot z}}{y} - y\right) \cdot -0.5 \]

      2. associate-/l* 92.7%

         \[\leadsto \left(\color{blue}{\frac{z}{\frac{y}{z}}} - y\right) \cdot -0.5 \]

   6. Simplified 92.7%

      \[\leadsto \left(\color{blue}{\frac{z}{\frac{y}{z}}} - y\right) \cdot -0.5 \]

   if 9.99999999999999944e71 < (*.f64 x x)

   1. Initial program 70.4%

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

      1. sub-neg 70.4%

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

      2. +-commutative 70.4%

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

      3. neg-sub0 70.4%

         \[\leadsto \frac{\color{blue}{\left(0 - z \cdot z\right)} + \left(x \cdot x + y \cdot y\right)}{y \cdot 2} \]

      4. associate-+l- 70.4%

         \[\leadsto \frac{\color{blue}{0 - \left(z \cdot z - \left(x \cdot x + y \cdot y\right)\right)}}{y \cdot 2} \]

      5. sub0-neg 70.4%

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

      6. neg-mul-1 70.4%

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

      7. *-commutative 70.4%

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

      8. times-frac 70.4%

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

      9. associate--r+ 70.4%

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

      10. div-sub 70.4%

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

      11. difference-of-squares 81.4%

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

      12. +-commutative 81.4%

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

      13. associate-*r/ 84.5%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot \color{blue}{-0.5} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot -0.5} \]
   4. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\frac{1}{\frac{y}{z - x}}} - y\right) \cdot -0.5 \]

      2. associate-/r/ 99.9%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]

   5. Applied egg-rr 99.9%

      \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]

   6. Taylor expanded in x around inf 72.0%

      \[\leadsto \left(\color{blue}{-1 \cdot \frac{{x}^{2}}{y}} - y\right) \cdot -0.5 \]
   7. Step-by-step derivation

      1. mul-1-neg 72.0%

         \[\leadsto \left(\color{blue}{\left(-\frac{{x}^{2}}{y}\right)} - y\right) \cdot -0.5 \]

      2. unpow2 72.0%

         \[\leadsto \left(\left(-\frac{\color{blue}{x \cdot x}}{y}\right) - y\right) \cdot -0.5 \]

      3. associate-/l* 81.8%

         \[\leadsto \left(\left(-\color{blue}{\frac{x}{\frac{y}{x}}}\right) - y\right) \cdot -0.5 \]

      4. distribute-neg-frac 81.8%

         \[\leadsto \left(\color{blue}{\frac{-x}{\frac{y}{x}}} - y\right) \cdot -0.5 \]

   8. Simplified 81.8%

      \[\leadsto \left(\color{blue}{\frac{-x}{\frac{y}{x}}} - y\right) \cdot -0.5 \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x \leq 10^{+72}:\\ \;\;\;\;-0.5 \cdot \left(\frac{z}{\frac{y}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;-0.5 \cdot \left(\frac{-x}{\frac{y}{x}} - y\right)\\ \end{array} \]

Alternative 11: 80.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+128}:\\ \;\;\;\;-0.5 \cdot \left(z \cdot \frac{z}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.46e+80)
   (* 0.5 (/ x (/ y x)))
   (if (<= x 1.3e+128) (* -0.5 (- (* z (/ z y)) y)) (* x (* x (/ 0.5 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.46e+80) {
		tmp = 0.5 * (x / (y / x));
	} else if (x <= 1.3e+128) {
		tmp = -0.5 * ((z * (z / y)) - y);
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.46d+80)) then
        tmp = 0.5d0 * (x / (y / x))
    else if (x <= 1.3d+128) then
        tmp = (-0.5d0) * ((z * (z / y)) - y)
    else
        tmp = x * (x * (0.5d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.46e+80) {
		tmp = 0.5 * (x / (y / x));
	} else if (x <= 1.3e+128) {
		tmp = -0.5 * ((z * (z / y)) - y);
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.46e+80:
		tmp = 0.5 * (x / (y / x))
	elif x <= 1.3e+128:
		tmp = -0.5 * ((z * (z / y)) - y)
	else:
		tmp = x * (x * (0.5 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.46e+80)
		tmp = Float64(0.5 * Float64(x / Float64(y / x)));
	elseif (x <= 1.3e+128)
		tmp = Float64(-0.5 * Float64(Float64(z * Float64(z / y)) - y));
	else
		tmp = Float64(x * Float64(x * Float64(0.5 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.46e+80)
		tmp = 0.5 * (x / (y / x));
	elseif (x <= 1.3e+128)
		tmp = -0.5 * ((z * (z / y)) - y);
	else
		tmp = x * (x * (0.5 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.46e+80], N[(0.5 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.3e+128], N[(-0.5 * N[(N[(z * N[(z / y), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.4599999999999999e80

   1. Initial program 72.2%

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

   2. Taylor expanded in x around inf 69.8%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 69.8%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 69.8%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   5. Taylor expanded in x around 0 69.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   6. Step-by-step derivation

      1. unpow2 69.8%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x}}{y} \]

      2. *-commutative 69.8%

         \[\leadsto \color{blue}{\frac{x \cdot x}{y} \cdot 0.5} \]

      3. associate-/l* 75.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}}} \cdot 0.5 \]

   7. Simplified 75.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}} \cdot 0.5} \]

   if -1.4599999999999999e80 < x < 1.3e128

   1. Initial program 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. neg-sub0 73.9%

         \[\leadsto \frac{\color{blue}{\left(0 - z \cdot z\right)} + \left(x \cdot x + y \cdot y\right)}{y \cdot 2} \]

      4. associate-+l- 73.9%

         \[\leadsto \frac{\color{blue}{0 - \left(z \cdot z - \left(x \cdot x + y \cdot y\right)\right)}}{y \cdot 2} \]

      5. sub0-neg 73.9%

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

      6. neg-mul-1 73.9%

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

      7. *-commutative 73.9%

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

      8. times-frac 73.9%

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

      9. associate--r+ 73.9%

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

      10. div-sub 73.9%

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

      11. difference-of-squares 73.9%

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

      12. +-commutative 73.9%

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

      13. associate-*r/ 74.8%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot \color{blue}{-0.5} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot -0.5} \]
   4. Step-by-step derivation

      1. clear-num 99.9%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\frac{1}{\frac{y}{z - x}}} - y\right) \cdot -0.5 \]

      2. associate-/r/ 99.8%

         \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]

   5. Applied egg-rr 99.8%

      \[\leadsto \left(\left(x + z\right) \cdot \color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right)} - y\right) \cdot -0.5 \]
   6. Step-by-step derivation

      1. +-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(z + x\right)} \cdot \left(\frac{1}{y} \cdot \left(z - x\right)\right) - y\right) \cdot -0.5 \]

      2. *-commutative 99.8%

         \[\leadsto \left(\color{blue}{\left(\frac{1}{y} \cdot \left(z - x\right)\right) \cdot \left(z + x\right)} - y\right) \cdot -0.5 \]

      3. associate-*l/ 99.9%

         \[\leadsto \left(\color{blue}{\frac{1 \cdot \left(z - x\right)}{y}} \cdot \left(z + x\right) - y\right) \cdot -0.5 \]

      4. *-un-lft-identity 99.9%

         \[\leadsto \left(\frac{\color{blue}{z - x}}{y} \cdot \left(z + x\right) - y\right) \cdot -0.5 \]

      5. flip-+ 94.7%

         \[\leadsto \left(\frac{z - x}{y} \cdot \color{blue}{\frac{z \cdot z - x \cdot x}{z - x}} - y\right) \cdot -0.5 \]

      6. frac-times 79.7%

         \[\leadsto \left(\color{blue}{\frac{\left(z - x\right) \cdot \left(z \cdot z - x \cdot x\right)}{y \cdot \left(z - x\right)}} - y\right) \cdot -0.5 \]

   7. Applied egg-rr 79.7%

      \[\leadsto \left(\color{blue}{\frac{\left(z - x\right) \cdot \left(z \cdot z - x \cdot x\right)}{y \cdot \left(z - x\right)}} - y\right) \cdot -0.5 \]
   8. Step-by-step derivation

      1. associate-/l* 85.6%

         \[\leadsto \left(\color{blue}{\frac{z - x}{\frac{y \cdot \left(z - x\right)}{z \cdot z - x \cdot x}}} - y\right) \cdot -0.5 \]

      2. *-commutative 85.6%

         \[\leadsto \left(\frac{z - x}{\frac{\color{blue}{\left(z - x\right) \cdot y}}{z \cdot z - x \cdot x}} - y\right) \cdot -0.5 \]

   9. Simplified 85.6%

      \[\leadsto \left(\color{blue}{\frac{z - x}{\frac{\left(z - x\right) \cdot y}{z \cdot z - x \cdot x}}} - y\right) \cdot -0.5 \]

   10. Taylor expanded in z around inf 80.9%

       \[\leadsto \left(\color{blue}{\frac{{z}^{2}}{y}} - y\right) \cdot -0.5 \]
   11. Step-by-step derivation

       1. unpow2 80.9%

          \[\leadsto \left(\frac{\color{blue}{z \cdot z}}{y} - y\right) \cdot -0.5 \]

       2. *-lft-identity 80.9%

          \[\leadsto \left(\frac{z \cdot z}{\color{blue}{1 \cdot y}} - y\right) \cdot -0.5 \]

       3. times-frac 85.5%

          \[\leadsto \left(\color{blue}{\frac{z}{1} \cdot \frac{z}{y}} - y\right) \cdot -0.5 \]

       4. /-rgt-identity 85.5%

          \[\leadsto \left(\color{blue}{z} \cdot \frac{z}{y} - y\right) \cdot -0.5 \]

   12. Simplified 85.5%

       \[\leadsto \left(\color{blue}{z \cdot \frac{z}{y}} - y\right) \cdot -0.5 \]

   if 1.3e128 < x

   1. Initial program 60.3%

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

   2. Taylor expanded in x around inf 66.5%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 66.5%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 66.5%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 74.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{2}} \]

      2. div-inv 74.8%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 74.8%

         \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 74.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.5\right)} \]

   7. Taylor expanded in x around 0 66.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 66.5%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.5} \]

      2. unpow2 66.5%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y} \cdot 0.5 \]

      3. associate-*r/ 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \frac{x}{y}\right)} \cdot 0.5 \]

      4. associate-*r* 74.8%

         \[\leadsto \color{blue}{x \cdot \left(\frac{x}{y} \cdot 0.5\right)} \]

      5. associate-*l/ 74.8%

         \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.5}{y}} \]

      6. *-lft-identity 74.8%

         \[\leadsto x \cdot \frac{x \cdot 0.5}{\color{blue}{1 \cdot y}} \]

      7. times-frac 74.8%

         \[\leadsto x \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{0.5}{y}\right)} \]

      8. /-rgt-identity 74.8%

         \[\leadsto x \cdot \left(\color{blue}{x} \cdot \frac{0.5}{y}\right) \]

   9. Simplified 74.8%

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \frac{0.5}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.46 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+128}:\\ \;\;\;\;-0.5 \cdot \left(z \cdot \frac{z}{y} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \]

Alternative 12: 80.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+122}:\\ \;\;\;\;-0.5 \cdot \left(\frac{z}{\frac{y}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.5e+80)
   (* 0.5 (/ x (/ y x)))
   (if (<= x 7.5e+122) (* -0.5 (- (/ z (/ y z)) y)) (* x (* x (/ 0.5 y))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e+80) {
		tmp = 0.5 * (x / (y / x));
	} else if (x <= 7.5e+122) {
		tmp = -0.5 * ((z / (y / z)) - y);
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= (-1.5d+80)) then
        tmp = 0.5d0 * (x / (y / x))
    else if (x <= 7.5d+122) then
        tmp = (-0.5d0) * ((z / (y / z)) - y)
    else
        tmp = x * (x * (0.5d0 / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.5e+80) {
		tmp = 0.5 * (x / (y / x));
	} else if (x <= 7.5e+122) {
		tmp = -0.5 * ((z / (y / z)) - y);
	} else {
		tmp = x * (x * (0.5 / y));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.5e+80:
		tmp = 0.5 * (x / (y / x))
	elif x <= 7.5e+122:
		tmp = -0.5 * ((z / (y / z)) - y)
	else:
		tmp = x * (x * (0.5 / y))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.5e+80)
		tmp = Float64(0.5 * Float64(x / Float64(y / x)));
	elseif (x <= 7.5e+122)
		tmp = Float64(-0.5 * Float64(Float64(z / Float64(y / z)) - y));
	else
		tmp = Float64(x * Float64(x * Float64(0.5 / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.5e+80)
		tmp = 0.5 * (x / (y / x));
	elseif (x <= 7.5e+122)
		tmp = -0.5 * ((z / (y / z)) - y);
	else
		tmp = x * (x * (0.5 / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.5e+80], N[(0.5 * N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e+122], N[(-0.5 * N[(N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.49999999999999993e80

   1. Initial program 72.2%

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

   2. Taylor expanded in x around inf 69.8%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 69.8%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 69.8%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   5. Taylor expanded in x around 0 69.8%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   6. Step-by-step derivation

      1. unpow2 69.8%

         \[\leadsto 0.5 \cdot \frac{\color{blue}{x \cdot x}}{y} \]

      2. *-commutative 69.8%

         \[\leadsto \color{blue}{\frac{x \cdot x}{y} \cdot 0.5} \]

      3. associate-/l* 75.5%

         \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}}} \cdot 0.5 \]

   7. Simplified 75.5%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}} \cdot 0.5} \]

   if -1.49999999999999993e80 < x < 7.5000000000000002e122

   1. Initial program 73.9%

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

      1. sub-neg 73.9%

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

      2. +-commutative 73.9%

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

      3. neg-sub0 73.9%

         \[\leadsto \frac{\color{blue}{\left(0 - z \cdot z\right)} + \left(x \cdot x + y \cdot y\right)}{y \cdot 2} \]

      4. associate-+l- 73.9%

         \[\leadsto \frac{\color{blue}{0 - \left(z \cdot z - \left(x \cdot x + y \cdot y\right)\right)}}{y \cdot 2} \]

      5. sub0-neg 73.9%

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

      6. neg-mul-1 73.9%

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

      7. *-commutative 73.9%

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

      8. times-frac 73.9%

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

      9. associate--r+ 73.9%

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

      10. div-sub 73.9%

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

      11. difference-of-squares 73.9%

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

      12. +-commutative 73.9%

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

      13. associate-*r/ 74.8%

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

      14. associate-/l* 99.9%

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

      15. *-inverses 99.9%

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

      16. /-rgt-identity 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot \color{blue}{-0.5} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\left(\left(x + z\right) \cdot \frac{z - x}{y} - y\right) \cdot -0.5} \]

   4. Taylor expanded in x around 0 80.9%

      \[\leadsto \left(\color{blue}{\frac{{z}^{2}}{y}} - y\right) \cdot -0.5 \]
   5. Step-by-step derivation

      1. unpow2 80.9%

         \[\leadsto \left(\frac{\color{blue}{z \cdot z}}{y} - y\right) \cdot -0.5 \]

      2. associate-/l* 85.5%

         \[\leadsto \left(\color{blue}{\frac{z}{\frac{y}{z}}} - y\right) \cdot -0.5 \]

   6. Simplified 85.5%

      \[\leadsto \left(\color{blue}{\frac{z}{\frac{y}{z}}} - y\right) \cdot -0.5 \]

   if 7.5000000000000002e122 < x

   1. Initial program 60.3%

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

   2. Taylor expanded in x around inf 66.5%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 66.5%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 66.5%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 74.8%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{2}} \]

      2. div-inv 74.8%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 74.8%

         \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 74.8%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.5\right)} \]

   7. Taylor expanded in x around 0 66.5%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 66.5%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.5} \]

      2. unpow2 66.5%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y} \cdot 0.5 \]

      3. associate-*r/ 74.8%

         \[\leadsto \color{blue}{\left(x \cdot \frac{x}{y}\right)} \cdot 0.5 \]

      4. associate-*r* 74.8%

         \[\leadsto \color{blue}{x \cdot \left(\frac{x}{y} \cdot 0.5\right)} \]

      5. associate-*l/ 74.8%

         \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.5}{y}} \]

      6. *-lft-identity 74.8%

         \[\leadsto x \cdot \frac{x \cdot 0.5}{\color{blue}{1 \cdot y}} \]

      7. times-frac 74.8%

         \[\leadsto x \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{0.5}{y}\right)} \]

      8. /-rgt-identity 74.8%

         \[\leadsto x \cdot \left(\color{blue}{x} \cdot \frac{0.5}{y}\right) \]

   9. Simplified 74.8%

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \frac{0.5}{y}\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 82.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.5 \cdot 10^{+80}:\\ \;\;\;\;0.5 \cdot \frac{x}{\frac{y}{x}}\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+122}:\\ \;\;\;\;-0.5 \cdot \left(\frac{z}{\frac{y}{z}} - y\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \]

Alternative 13: 52.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+91}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -3.15e+91)
   (* y 0.5)
   (if (<= y 2e+117) (* x (* x (/ 0.5 y))) (* y 0.5))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.15e+91) {
		tmp = y * 0.5;
	} else if (y <= 2e+117) {
		tmp = x * (x * (0.5 / y));
	} else {
		tmp = y * 0.5;
	}
	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 <= (-3.15d+91)) then
        tmp = y * 0.5d0
    else if (y <= 2d+117) then
        tmp = x * (x * (0.5d0 / y))
    else
        tmp = y * 0.5d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -3.15e+91) {
		tmp = y * 0.5;
	} else if (y <= 2e+117) {
		tmp = x * (x * (0.5 / y));
	} else {
		tmp = y * 0.5;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -3.15e+91:
		tmp = y * 0.5
	elif y <= 2e+117:
		tmp = x * (x * (0.5 / y))
	else:
		tmp = y * 0.5
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -3.15e+91)
		tmp = Float64(y * 0.5);
	elseif (y <= 2e+117)
		tmp = Float64(x * Float64(x * Float64(0.5 / y)));
	else
		tmp = Float64(y * 0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -3.15e+91)
		tmp = y * 0.5;
	elseif (y <= 2e+117)
		tmp = x * (x * (0.5 / y));
	else
		tmp = y * 0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -3.15e+91], N[(y * 0.5), $MachinePrecision], If[LessEqual[y, 2e+117], N[(x * N[(x * N[(0.5 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 0.5), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.15e91 or 2.0000000000000001e117 < y

   1. Initial program 27.9%

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

   2. Taylor expanded in y around inf 79.3%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
   3. Step-by-step derivation

      1. *-commutative 79.3%

         \[\leadsto \color{blue}{y \cdot 0.5} \]

   4. Simplified 79.3%

      \[\leadsto \color{blue}{y \cdot 0.5} \]

   if -3.15e91 < y < 2.0000000000000001e117

   1. Initial program 91.0%

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

   2. Taylor expanded in x around inf 45.4%

      \[\leadsto \frac{\color{blue}{{x}^{2}}}{y \cdot 2} \]
   3. Step-by-step derivation

      1. unpow2 45.4%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]

   4. Simplified 45.4%

      \[\leadsto \frac{\color{blue}{x \cdot x}}{y \cdot 2} \]
   5. Step-by-step derivation

      1. times-frac 47.4%

         \[\leadsto \color{blue}{\frac{x}{y} \cdot \frac{x}{2}} \]

      2. div-inv 47.4%

         \[\leadsto \frac{x}{y} \cdot \color{blue}{\left(x \cdot \frac{1}{2}\right)} \]

      3. metadata-eval 47.4%

         \[\leadsto \frac{x}{y} \cdot \left(x \cdot \color{blue}{0.5}\right) \]

   6. Applied egg-rr 47.4%

      \[\leadsto \color{blue}{\frac{x}{y} \cdot \left(x \cdot 0.5\right)} \]

   7. Taylor expanded in x around 0 45.4%

      \[\leadsto \color{blue}{0.5 \cdot \frac{{x}^{2}}{y}} \]
   8. Step-by-step derivation

      1. *-commutative 45.4%

         \[\leadsto \color{blue}{\frac{{x}^{2}}{y} \cdot 0.5} \]

      2. unpow2 45.4%

         \[\leadsto \frac{\color{blue}{x \cdot x}}{y} \cdot 0.5 \]

      3. associate-*r/ 47.4%

         \[\leadsto \color{blue}{\left(x \cdot \frac{x}{y}\right)} \cdot 0.5 \]

      4. associate-*r* 47.4%

         \[\leadsto \color{blue}{x \cdot \left(\frac{x}{y} \cdot 0.5\right)} \]

      5. associate-*l/ 47.4%

         \[\leadsto x \cdot \color{blue}{\frac{x \cdot 0.5}{y}} \]

      6. *-lft-identity 47.4%

         \[\leadsto x \cdot \frac{x \cdot 0.5}{\color{blue}{1 \cdot y}} \]

      7. times-frac 47.4%

         \[\leadsto x \cdot \color{blue}{\left(\frac{x}{1} \cdot \frac{0.5}{y}\right)} \]

      8. /-rgt-identity 47.4%

         \[\leadsto x \cdot \left(\color{blue}{x} \cdot \frac{0.5}{y}\right) \]

   9. Simplified 47.4%

      \[\leadsto \color{blue}{x \cdot \left(x \cdot \frac{0.5}{y}\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 57.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.15 \cdot 10^{+91}:\\ \;\;\;\;y \cdot 0.5\\ \mathbf{elif}\;y \leq 2 \cdot 10^{+117}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]

Alternative 14: 34.6% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ y \cdot 0.5 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* y 0.5))

C

double code(double x, double y, double z) {
	return y * 0.5;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = y * 0.5d0
end function

Java

public static double code(double x, double y, double z) {
	return y * 0.5;
}

Python

def code(x, y, z):
	return y * 0.5

Julia

function code(x, y, z)
	return Float64(y * 0.5)
end

MATLAB

function tmp = code(x, y, z)
	tmp = y * 0.5;
end

Wolfram

code[x_, y_, z_] := N[(y * 0.5), $MachinePrecision]

Derivation

1. Initial program 71.5%

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

2. Taylor expanded in y around inf 30.8%

   \[\leadsto \color{blue}{0.5 \cdot y} \]
3. Step-by-step derivation

   1. *-commutative 30.8%

      \[\leadsto \color{blue}{y \cdot 0.5} \]

4. Simplified 30.8%

   \[\leadsto \color{blue}{y \cdot 0.5} \]

5. Final simplification 30.8%

   \[\leadsto y \cdot 0.5 \]

Developer target: 99.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y \cdot 0.5 - \left(\frac{0.5}{y} \cdot \left(z + x\right)\right) \cdot \left(z - x\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x))))

C

double code(double x, double y, double z) {
	return (y * 0.5) - (((0.5 / y) * (z + x)) * (z - 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 = (y * 0.5d0) - (((0.5d0 / y) * (z + x)) * (z - x))
end function

Java

public static double code(double x, double y, double z) {
	return (y * 0.5) - (((0.5 / y) * (z + x)) * (z - x));
}

Python

def code(x, y, z):
	return (y * 0.5) - (((0.5 / y) * (z + x)) * (z - x))

Julia

function code(x, y, z)
	return Float64(Float64(y * 0.5) - Float64(Float64(Float64(0.5 / y) * Float64(z + x)) * Float64(z - x)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = (y * 0.5) - (((0.5 / y) * (z + x)) * (z - x));
end

Wolfram

code[x_, y_, z_] := N[(N[(y * 0.5), $MachinePrecision] - N[(N[(N[(0.5 / y), $MachinePrecision] * N[(z + x), $MachinePrecision]), $MachinePrecision] * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023176 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"
  :precision binary64

  :herbie-target
  (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x)))

  (/ (- (+ (* x x) (* y y)) (* z z)) (* y 2.0)))