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

Percentage Accurate: 68.6% → 96.0%

Time: 9.8s

Alternatives: 6

Speedup: 0.7×

• 42.3% 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: 68.6% 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: 96.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;y\_m \leq 8.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y\_m, y\_m, \mathsf{fma}\left(x, x, z \cdot \left(-z\right)\right)\right)}{y\_m \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\left(y\_m - \frac{z}{\frac{y\_m}{z}}\right) + x \cdot \frac{x}{y\_m}\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= y_m 8.2e+52)
    (/ (fma y_m y_m (fma x x (* z (- z)))) (* y_m 2.0))
    (* 0.5 (+ (- y_m (/ z (/ y_m z))) (* x (/ x y_m)))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (y_m <= 8.2e+52) {
		tmp = fma(y_m, y_m, fma(x, x, (z * -z))) / (y_m * 2.0);
	} else {
		tmp = 0.5 * ((y_m - (z / (y_m / z))) + (x * (x / y_m)));
	}
	return y_s * tmp;
}

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (y_m <= 8.2e+52)
		tmp = Float64(fma(y_m, y_m, fma(x, x, Float64(z * Float64(-z)))) / Float64(y_m * 2.0));
	else
		tmp = Float64(0.5 * Float64(Float64(y_m - Float64(z / Float64(y_m / z))) + Float64(x * Float64(x / y_m))));
	end
	return Float64(y_s * tmp)
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[y$95$m, 8.2e+52], N[(N[(y$95$m * y$95$m + N[(x * x + N[(z * (-z)), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(y$95$m * 2.0), $MachinePrecision]), $MachinePrecision], N[(0.5 * N[(N[(y$95$m - N[(z / N[(y$95$m / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 8.1999999999999999e52

   1. Initial program 70.8%

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

      1. div-sub 65.6%

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

      2. add0 65.6%

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

      3. associate--r+ 65.6%

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

      4. div-sub 70.8%

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

      5. div0 70.8%

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

      6. div-sub 70.8%

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

      7. --rgt-identity 70.8%

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

      8. sub-neg 70.8%

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

      9. +-commutative 70.8%

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

      10. cancel-sign-sub 70.8%

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

      11. associate-+l- 70.8%

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

   3. Simplified 76.1%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, y, \mathsf{fma}\left(x, x, z \cdot \left(-z\right)\right)\right)}{y \cdot 2}} \]
   4. Add Preprocessing

   if 8.1999999999999999e52 < y

   1. Initial program 38.5%

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

   3. Taylor expanded in x around 0 38.5%

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

      1. distribute-lft-out 38.5%

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

      2. div-sub 38.5%

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

      3. associate-+l- 38.5%

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

      4. unpow2 38.5%

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

      5. associate-/l* 67.8%

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

      6. *-inverses 67.8%

         \[\leadsto 0.5 \cdot \left(y \cdot \color{blue}{1} - \left(\frac{{z}^{2}}{y} - \frac{{x}^{2}}{y}\right)\right) \]

      7. *-rgt-identity 67.8%

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

      8. associate-+l- 67.8%

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

   5. Simplified 67.8%

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

      1. unpow2 67.8%

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

      2. associate-/l* 76.5%

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

   7. Applied egg-rr 76.5%

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

      1. unpow2 76.5%

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

      2. associate-/l* 99.9%

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

   9. Applied egg-rr 99.9%

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

       1. clear-num 99.9%

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

       2. un-div-inv 100.0%

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

   11. Applied egg-rr 100.0%

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

4. Final simplification 80.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8.2 \cdot 10^{+52}:\\ \;\;\;\;\frac{\mathsf{fma}\left(y, y, \mathsf{fma}\left(x, x, z \cdot \left(-z\right)\right)\right)}{y \cdot 2}\\ \mathbf{else}:\\ \;\;\;\;0.5 \cdot \left(\left(y - \frac{z}{\frac{y}{z}}\right) + x \cdot \frac{x}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 92.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+219}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{x}{y\_m} + \left(y\_m - z \cdot \frac{z}{y\_m}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y\_m}\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= x 1.5e+219)
    (* 0.5 (+ (* x (/ x y_m)) (- y_m (* z (/ z y_m)))))
    (* x (* x (/ 0.5 y_m))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 1.5e+219) {
		tmp = 0.5 * ((x * (x / y_m)) + (y_m - (z * (z / y_m))));
	} else {
		tmp = x * (x * (0.5 / y_m));
	}
	return y_s * tmp;
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 1.5d+219) then
        tmp = 0.5d0 * ((x * (x / y_m)) + (y_m - (z * (z / y_m))))
    else
        tmp = x * (x * (0.5d0 / y_m))
    end if
    code = y_s * tmp
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 1.5e+219) {
		tmp = 0.5 * ((x * (x / y_m)) + (y_m - (z * (z / y_m))));
	} else {
		tmp = x * (x * (0.5 / y_m));
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if x <= 1.5e+219:
		tmp = 0.5 * ((x * (x / y_m)) + (y_m - (z * (z / y_m))))
	else:
		tmp = x * (x * (0.5 / y_m))
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (x <= 1.5e+219)
		tmp = Float64(0.5 * Float64(Float64(x * Float64(x / y_m)) + Float64(y_m - Float64(z * Float64(z / y_m)))));
	else
		tmp = Float64(x * Float64(x * Float64(0.5 / y_m)));
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	tmp = 0.0;
	if (x <= 1.5e+219)
		tmp = 0.5 * ((x * (x / y_m)) + (y_m - (z * (z / y_m))));
	else
		tmp = x * (x * (0.5 / y_m));
	end
	tmp_2 = y_s * tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[x, 1.5e+219], N[(0.5 * N[(N[(x * N[(x / y$95$m), $MachinePrecision]), $MachinePrecision] + N[(y$95$m - N[(z * N[(z / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 1.4999999999999999e219

   1. Initial program 65.5%

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

   3. Taylor expanded in x around 0 61.3%

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

      1. distribute-lft-out 61.3%

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

      2. div-sub 61.3%

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

      3. associate-+l- 61.3%

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

      4. unpow2 61.3%

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

      5. associate-/l* 78.0%

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

      6. *-inverses 78.0%

         \[\leadsto 0.5 \cdot \left(y \cdot \color{blue}{1} - \left(\frac{{z}^{2}}{y} - \frac{{x}^{2}}{y}\right)\right) \]

      7. *-rgt-identity 78.0%

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

      8. associate-+l- 78.0%

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

   5. Simplified 78.0%

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

      1. unpow2 78.0%

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

      2. associate-/l* 83.8%

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

   7. Applied egg-rr 83.8%

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

      1. unpow2 83.8%

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

      2. associate-/l* 90.2%

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

   9. Applied egg-rr 90.2%

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

   if 1.4999999999999999e219 < x

   1. Initial program 60.7%

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

   3. Taylor expanded in x around inf 81.2%

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

      1. div-inv 81.2%

         \[\leadsto \color{blue}{{x}^{2} \cdot \frac{1}{y \cdot 2}} \]

      2. unpow2 81.2%

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

      3. associate-*l* 95.0%

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

      4. *-commutative 95.0%

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

      5. associate-/r* 95.0%

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

      6. metadata-eval 95.0%

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

   5. Applied egg-rr 95.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{+219}:\\ \;\;\;\;0.5 \cdot \left(x \cdot \frac{x}{y} + \left(y - z \cdot \frac{z}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 92.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;x \leq 7.5 \cdot 10^{+218}:\\ \;\;\;\;0.5 \cdot \left(\left(y\_m - z \cdot \frac{z}{y\_m}\right) + \frac{x}{\frac{y\_m}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y\_m}\right)\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (*
  y_s
  (if (<= x 7.5e+218)
    (* 0.5 (+ (- y_m (* z (/ z y_m))) (/ x (/ y_m x))))
    (* x (* x (/ 0.5 y_m))))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 7.5e+218) {
		tmp = 0.5 * ((y_m - (z * (z / y_m))) + (x / (y_m / x)));
	} else {
		tmp = x * (x * (0.5 / y_m));
	}
	return y_s * tmp;
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (x <= 7.5d+218) then
        tmp = 0.5d0 * ((y_m - (z * (z / y_m))) + (x / (y_m / x)))
    else
        tmp = x * (x * (0.5d0 / y_m))
    end if
    code = y_s * tmp
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (x <= 7.5e+218) {
		tmp = 0.5 * ((y_m - (z * (z / y_m))) + (x / (y_m / x)));
	} else {
		tmp = x * (x * (0.5 / y_m));
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if x <= 7.5e+218:
		tmp = 0.5 * ((y_m - (z * (z / y_m))) + (x / (y_m / x)))
	else:
		tmp = x * (x * (0.5 / y_m))
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (x <= 7.5e+218)
		tmp = Float64(0.5 * Float64(Float64(y_m - Float64(z * Float64(z / y_m))) + Float64(x / Float64(y_m / x))));
	else
		tmp = Float64(x * Float64(x * Float64(0.5 / y_m)));
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	tmp = 0.0;
	if (x <= 7.5e+218)
		tmp = 0.5 * ((y_m - (z * (z / y_m))) + (x / (y_m / x)));
	else
		tmp = x * (x * (0.5 / y_m));
	end
	tmp_2 = y_s * tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[x, 7.5e+218], N[(0.5 * N[(N[(y$95$m - N[(z * N[(z / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x / N[(y$95$m / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(x * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x < 7.4999999999999993e218

   1. Initial program 65.5%

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

   3. Taylor expanded in x around 0 61.3%

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

      1. distribute-lft-out 61.3%

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

      2. div-sub 61.3%

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

      3. associate-+l- 61.3%

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

      4. unpow2 61.3%

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

      5. associate-/l* 78.0%

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

      6. *-inverses 78.0%

         \[\leadsto 0.5 \cdot \left(y \cdot \color{blue}{1} - \left(\frac{{z}^{2}}{y} - \frac{{x}^{2}}{y}\right)\right) \]

      7. *-rgt-identity 78.0%

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

      8. associate-+l- 78.0%

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

   5. Simplified 78.0%

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

      1. unpow2 78.0%

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

      2. associate-/l* 83.8%

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

   7. Applied egg-rr 83.8%

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

      1. unpow2 83.8%

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

      2. associate-/l* 90.2%

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

   9. Applied egg-rr 90.2%

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

       1. clear-num 90.2%

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

       2. un-div-inv 90.2%

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

   11. Applied egg-rr 90.2%

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

   if 7.4999999999999993e218 < x

   1. Initial program 60.7%

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

   3. Taylor expanded in x around inf 81.2%

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

      1. div-inv 81.2%

         \[\leadsto \color{blue}{{x}^{2} \cdot \frac{1}{y \cdot 2}} \]

      2. unpow2 81.2%

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

      3. associate-*l* 95.0%

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

      4. *-commutative 95.0%

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

      5. associate-/r* 95.0%

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

      6. metadata-eval 95.0%

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

   5. Applied egg-rr 95.0%

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

4. Final simplification 90.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.5 \cdot 10^{+218}:\\ \;\;\;\;0.5 \cdot \left(\left(y - z \cdot \frac{z}{y}\right) + \frac{x}{\frac{y}{x}}\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 53.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;y\_m \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y\_m}\right)\\ \mathbf{else}:\\ \;\;\;\;y\_m \cdot 0.5\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (* y_s (if (<= y_m 5.4e+44) (* x (* x (/ 0.5 y_m))) (* y_m 0.5))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (y_m <= 5.4e+44) {
		tmp = x * (x * (0.5 / y_m));
	} else {
		tmp = y_m * 0.5;
	}
	return y_s * tmp;
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y_m <= 5.4d+44) then
        tmp = x * (x * (0.5d0 / y_m))
    else
        tmp = y_m * 0.5d0
    end if
    code = y_s * tmp
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (y_m <= 5.4e+44) {
		tmp = x * (x * (0.5 / y_m));
	} else {
		tmp = y_m * 0.5;
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if y_m <= 5.4e+44:
		tmp = x * (x * (0.5 / y_m))
	else:
		tmp = y_m * 0.5
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (y_m <= 5.4e+44)
		tmp = Float64(x * Float64(x * Float64(0.5 / y_m)));
	else
		tmp = Float64(y_m * 0.5);
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	tmp = 0.0;
	if (y_m <= 5.4e+44)
		tmp = x * (x * (0.5 / y_m));
	else
		tmp = y_m * 0.5;
	end
	tmp_2 = y_s * tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[y$95$m, 5.4e+44], N[(x * N[(x * N[(0.5 / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y$95$m * 0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 5.4e44

   1. Initial program 70.7%

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

   3. Taylor expanded in x around inf 36.3%

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

      1. div-inv 36.3%

         \[\leadsto \color{blue}{{x}^{2} \cdot \frac{1}{y \cdot 2}} \]

      2. unpow2 36.3%

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

      3. associate-*l* 38.0%

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

      4. *-commutative 38.0%

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

      5. associate-/r* 38.0%

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

      6. metadata-eval 38.0%

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

   5. Applied egg-rr 38.0%

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

   if 5.4e44 < y

   1. Initial program 39.9%

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

   3. Taylor expanded in y around inf 58.1%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.4 \cdot 10^{+44}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{0.5}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 53.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y\_s \cdot \begin{array}{l} \mathbf{if}\;y\_m \leq 4.4 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y\_m} \cdot \frac{x}{2}\\ \mathbf{else}:\\ \;\;\;\;y\_m \cdot 0.5\\ \end{array} \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z)
 :precision binary64
 (* y_s (if (<= y_m 4.4e+44) (* (/ x y_m) (/ x 2.0)) (* y_m 0.5))))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (y_m <= 4.4e+44) {
		tmp = (x / y_m) * (x / 2.0);
	} else {
		tmp = y_m * 0.5;
	}
	return y_s * tmp;
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y_m <= 4.4d+44) then
        tmp = (x / y_m) * (x / 2.0d0)
    else
        tmp = y_m * 0.5d0
    end if
    code = y_s * tmp
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	double tmp;
	if (y_m <= 4.4e+44) {
		tmp = (x / y_m) * (x / 2.0);
	} else {
		tmp = y_m * 0.5;
	}
	return y_s * tmp;
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	tmp = 0
	if y_m <= 4.4e+44:
		tmp = (x / y_m) * (x / 2.0)
	else:
		tmp = y_m * 0.5
	return y_s * tmp

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	tmp = 0.0
	if (y_m <= 4.4e+44)
		tmp = Float64(Float64(x / y_m) * Float64(x / 2.0));
	else
		tmp = Float64(y_m * 0.5);
	end
	return Float64(y_s * tmp)
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp_2 = code(y_s, x, y_m, z)
	tmp = 0.0;
	if (y_m <= 4.4e+44)
		tmp = (x / y_m) * (x / 2.0);
	else
		tmp = y_m * 0.5;
	end
	tmp_2 = y_s * tmp;
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * If[LessEqual[y$95$m, 4.4e+44], N[(N[(x / y$95$m), $MachinePrecision] * N[(x / 2.0), $MachinePrecision]), $MachinePrecision], N[(y$95$m * 0.5), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if y < 4.39999999999999991e44

   1. Initial program 70.7%

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

   3. Taylor expanded in x around inf 36.3%

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

      1. unpow2 36.3%

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

      2. times-frac 38.0%

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

   5. Applied egg-rr 38.0%

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

   if 4.39999999999999991e44 < y

   1. Initial program 39.9%

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

   3. Taylor expanded in y around inf 58.1%

      \[\leadsto \color{blue}{0.5 \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 41.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 4.4 \cdot 10^{+44}:\\ \;\;\;\;\frac{x}{y} \cdot \frac{x}{2}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 0.5\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 34.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} y_m = \left|y\right| \\ y_s = \mathsf{copysign}\left(1, y\right) \\ y\_s \cdot \left(y\_m \cdot 0.5\right) \end{array} \]

FPCore

y_m = (fabs.f64 y)
y_s = (copysign.f64 1 y)
(FPCore (y_s x y_m z) :precision binary64 (* y_s (* y_m 0.5)))

C

y_m = fabs(y);
y_s = copysign(1.0, y);
double code(double y_s, double x, double y_m, double z) {
	return y_s * (y_m * 0.5);
}

Fortran

y_m = abs(y)
y_s = copysign(1.0d0, y)
real(8) function code(y_s, x, y_m, z)
    real(8), intent (in) :: y_s
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z
    code = y_s * (y_m * 0.5d0)
end function

Java

y_m = Math.abs(y);
y_s = Math.copySign(1.0, y);
public static double code(double y_s, double x, double y_m, double z) {
	return y_s * (y_m * 0.5);
}

Python

y_m = math.fabs(y)
y_s = math.copysign(1.0, y)
def code(y_s, x, y_m, z):
	return y_s * (y_m * 0.5)

Julia

y_m = abs(y)
y_s = copysign(1.0, y)
function code(y_s, x, y_m, z)
	return Float64(y_s * Float64(y_m * 0.5))
end

MATLAB

y_m = abs(y);
y_s = sign(y) * abs(1.0);
function tmp = code(y_s, x, y_m, z)
	tmp = y_s * (y_m * 0.5);
end

Wolfram

y_m = N[Abs[y], $MachinePrecision]
y_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[y]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[y$95$s_, x_, y$95$m_, z_] := N[(y$95$s * N[(y$95$m * 0.5), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 65.1%

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

3. Taylor expanded in y around inf 33.4%

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

4. Final simplification 33.4%

   \[\leadsto y \cdot 0.5 \]
5. Add Preprocessing

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 2024046 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, A"
  :precision binary64

  :alt
  (- (* y 0.5) (* (* (/ 0.5 y) (+ z x)) (- z x)))

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