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

Percentage Accurate: 66.7% → 99.4%

Time: 9.7s

Alternatives: 3

Speedup: 4.8×

Specification

Math

\[\begin{array}{l} \\ x \cdot \sqrt{y \cdot y - z \cdot z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x * math.sqrt(((y * y) - (z * z)))

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x \cdot \sqrt{y \cdot y - z \cdot z} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y, z):
	return x * math.sqrt(((y * y) - (z * z)))

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ \left(x \cdot \sqrt{y\_m \cdot \left(1 + \frac{z\_m}{y\_m}\right)}\right) \cdot \sqrt{y\_m - z\_m} \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
(FPCore (x y_m z_m)
 :precision binary64
 (* (* x (sqrt (* y_m (+ 1.0 (/ z_m y_m))))) (sqrt (- y_m z_m))))

C

z_m = fabs(z);
y_m = fabs(y);
double code(double x, double y_m, double z_m) {
	return (x * sqrt((y_m * (1.0 + (z_m / y_m))))) * sqrt((y_m - z_m));
}

Fortran

z_m = abs(z)
y_m = abs(y)
real(8) function code(x, y_m, z_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z_m
    code = (x * sqrt((y_m * (1.0d0 + (z_m / y_m))))) * sqrt((y_m - z_m))
end function

Java

z_m = Math.abs(z);
y_m = Math.abs(y);
public static double code(double x, double y_m, double z_m) {
	return (x * Math.sqrt((y_m * (1.0 + (z_m / y_m))))) * Math.sqrt((y_m - z_m));
}

Python

z_m = math.fabs(z)
y_m = math.fabs(y)
def code(x, y_m, z_m):
	return (x * math.sqrt((y_m * (1.0 + (z_m / y_m))))) * math.sqrt((y_m - z_m))

Julia

z_m = abs(z)
y_m = abs(y)
function code(x, y_m, z_m)
	return Float64(Float64(x * sqrt(Float64(y_m * Float64(1.0 + Float64(z_m / y_m))))) * sqrt(Float64(y_m - z_m)))
end

MATLAB

z_m = abs(z);
y_m = abs(y);
function tmp = code(x, y_m, z_m)
	tmp = (x * sqrt((y_m * (1.0 + (z_m / y_m))))) * sqrt((y_m - z_m));
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z$95$m_] := N[(N[(x * N[Sqrt[N[(y$95$m * N[(1.0 + N[(z$95$m / y$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(y$95$m - z$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.8%

   \[x \cdot \sqrt{y \cdot y - z \cdot z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow1/2 N/A

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

   2. difference-of-squares N/A

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

   3. unpow-prod-down N/A

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

   4. associate-*r* N/A

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

   5. *-lowering-*.f64 N/A

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

   6. *-lowering-*.f64 N/A

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

   7. pow1/2 N/A

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

   8. sqrt-lowering-sqrt.f64 N/A

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

   9. +-lowering-+.f64 N/A

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

   10. pow1/2 N/A

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

   11. sqrt-lowering-sqrt.f64 N/A

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

   12. --lowering--.f64 51.2

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

4. Applied egg-rr 51.2%

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

5. Taylor expanded in y around -inf

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

   1. mul-1-neg N/A

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

   2. neg-lowering-neg.f64 N/A

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

   3. *-lowering-*.f64 N/A

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

   4. sub-neg N/A

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

   5. metadata-eval N/A

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

   6. +-lowering-+.f64 N/A

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

   7. mul-1-neg N/A

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

   8. distribute-neg-frac2 N/A

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

   9. mul-1-neg N/A

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

   10. /-lowering-/.f64 N/A

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

   11. mul-1-neg N/A

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

   12. neg-lowering-neg.f64 51.3

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

7. Simplified 51.3%

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

   1. distribute-rgt-neg-in N/A

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

   2. neg-mul-1 N/A

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

   3. +-commutative N/A

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

   4. distribute-rgt-in N/A

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

   5. *-commutative N/A

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

   6. *-lowering-*.f64 N/A

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

   7. distribute-rgt-in N/A

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

   8. +-commutative N/A

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

   9. neg-mul-1 N/A

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

   10. neg-sub0 N/A

       \[\leadsto \left(x \cdot \sqrt{\color{blue}{\left(0 - \left(\frac{z}{\mathsf{neg}\left(y\right)} + -1\right)\right)} \cdot y}\right) \cdot \sqrt{y - z} \]

   11. +-commutative N/A

       \[\leadsto \left(x \cdot \sqrt{\left(0 - \color{blue}{\left(-1 + \frac{z}{\mathsf{neg}\left(y\right)}\right)}\right) \cdot y}\right) \cdot \sqrt{y - z} \]

   12. distribute-frac-neg2 N/A

       \[\leadsto \left(x \cdot \sqrt{\left(0 - \left(-1 + \color{blue}{\left(\mathsf{neg}\left(\frac{z}{y}\right)\right)}\right)\right) \cdot y}\right) \cdot \sqrt{y - z} \]

   13. unsub-neg N/A

       \[\leadsto \left(x \cdot \sqrt{\left(0 - \color{blue}{\left(-1 - \frac{z}{y}\right)}\right) \cdot y}\right) \cdot \sqrt{y - z} \]

   14. associate--r- N/A

       \[\leadsto \left(x \cdot \sqrt{\color{blue}{\left(\left(0 - -1\right) + \frac{z}{y}\right)} \cdot y}\right) \cdot \sqrt{y - z} \]

   15. metadata-eval N/A

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

   16. metadata-eval N/A

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

   17. +-lowering-+.f64 N/A

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

   18. metadata-eval N/A

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

   19. /-lowering-/.f64 51.3

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

9. Applied egg-rr 51.3%

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

10. Final simplification 51.3%

    \[\leadsto \left(x \cdot \sqrt{y \cdot \left(1 + \frac{z}{y}\right)}\right) \cdot \sqrt{y - z} \]
11. Add Preprocessing

Alternative 2: 99.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ \sqrt{y\_m - z\_m} \cdot \left(x \cdot \sqrt{z\_m + y\_m}\right) \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
(FPCore (x y_m z_m)
 :precision binary64
 (* (sqrt (- y_m z_m)) (* x (sqrt (+ z_m y_m)))))

C

z_m = fabs(z);
y_m = fabs(y);
double code(double x, double y_m, double z_m) {
	return sqrt((y_m - z_m)) * (x * sqrt((z_m + y_m)));
}

Fortran

z_m = abs(z)
y_m = abs(y)
real(8) function code(x, y_m, z_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z_m
    code = sqrt((y_m - z_m)) * (x * sqrt((z_m + y_m)))
end function

Java

z_m = Math.abs(z);
y_m = Math.abs(y);
public static double code(double x, double y_m, double z_m) {
	return Math.sqrt((y_m - z_m)) * (x * Math.sqrt((z_m + y_m)));
}

Python

z_m = math.fabs(z)
y_m = math.fabs(y)
def code(x, y_m, z_m):
	return math.sqrt((y_m - z_m)) * (x * math.sqrt((z_m + y_m)))

Julia

z_m = abs(z)
y_m = abs(y)
function code(x, y_m, z_m)
	return Float64(sqrt(Float64(y_m - z_m)) * Float64(x * sqrt(Float64(z_m + y_m))))
end

MATLAB

z_m = abs(z);
y_m = abs(y);
function tmp = code(x, y_m, z_m)
	tmp = sqrt((y_m - z_m)) * (x * sqrt((z_m + y_m)));
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z$95$m_] := N[(N[Sqrt[N[(y$95$m - z$95$m), $MachinePrecision]], $MachinePrecision] * N[(x * N[Sqrt[N[(z$95$m + y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 66.8%

   \[x \cdot \sqrt{y \cdot y - z \cdot z} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow1/2 N/A

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

   2. difference-of-squares N/A

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

   3. unpow-prod-down N/A

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

   4. associate-*r* N/A

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

   5. *-lowering-*.f64 N/A

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

   6. *-lowering-*.f64 N/A

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

   7. pow1/2 N/A

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

   8. sqrt-lowering-sqrt.f64 N/A

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

   9. +-lowering-+.f64 N/A

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

   10. pow1/2 N/A

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

   11. sqrt-lowering-sqrt.f64 N/A

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

   12. --lowering--.f64 51.2

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

4. Applied egg-rr 51.2%

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

5. Final simplification 51.2%

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

Alternative 3: 99.2% accurate, 4.8× speedup

Math

\[\begin{array}{l} z_m = \left|z\right| \\ y_m = \left|y\right| \\ x \cdot y\_m \end{array} \]

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
(FPCore (x y_m z_m) :precision binary64 (* x y_m))

C

z_m = fabs(z);
y_m = fabs(y);
double code(double x, double y_m, double z_m) {
	return x * y_m;
}

Fortran

z_m = abs(z)
y_m = abs(y)
real(8) function code(x, y_m, z_m)
    real(8), intent (in) :: x
    real(8), intent (in) :: y_m
    real(8), intent (in) :: z_m
    code = x * y_m
end function

Java

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

Python

z_m = math.fabs(z)
y_m = math.fabs(y)
def code(x, y_m, z_m):
	return x * y_m

Julia

z_m = abs(z)
y_m = abs(y)
function code(x, y_m, z_m)
	return Float64(x * y_m)
end

MATLAB

z_m = abs(z);
y_m = abs(y);
function tmp = code(x, y_m, z_m)
	tmp = x * y_m;
end

Wolfram

z_m = N[Abs[z], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
code[x_, y$95$m_, z$95$m_] := N[(x * y$95$m), $MachinePrecision]

Derivation

1. Initial program 66.8%

   \[x \cdot \sqrt{y \cdot y - z \cdot z} \]
2. Add Preprocessing

3. Taylor expanded in y around inf

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

   1. *-commutative N/A

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

   2. *-lowering-*.f64 55.2

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

5. Simplified 55.2%

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

6. Final simplification 55.2%

   \[\leadsto x \cdot y \]
7. Add Preprocessing

Developer Target 1: 99.3% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y < 2.5816096488251695 \cdot 10^{-278}:\\ \;\;\;\;-x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\sqrt{y + z} \cdot \sqrt{y - z}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (< y 2.5816096488251695e-278)
   (- (* x y))
   (* x (* (sqrt (+ y z)) (sqrt (- y z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y < 2.5816096488251695e-278) {
		tmp = -(x * y);
	} else {
		tmp = x * (sqrt((y + z)) * sqrt((y - 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 < 2.5816096488251695d-278) then
        tmp = -(x * y)
    else
        tmp = x * (sqrt((y + z)) * sqrt((y - z)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y < 2.5816096488251695e-278) {
		tmp = -(x * y);
	} else {
		tmp = x * (Math.sqrt((y + z)) * Math.sqrt((y - z)));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y < 2.5816096488251695e-278:
		tmp = -(x * y)
	else:
		tmp = x * (math.sqrt((y + z)) * math.sqrt((y - z)))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y < 2.5816096488251695e-278)
		tmp = Float64(-Float64(x * y));
	else
		tmp = Float64(x * Float64(sqrt(Float64(y + z)) * sqrt(Float64(y - z))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y < 2.5816096488251695e-278)
		tmp = -(x * y);
	else
		tmp = x * (sqrt((y + z)) * sqrt((y - z)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Less[y, 2.5816096488251695e-278], (-N[(x * y), $MachinePrecision]), N[(x * N[(N[Sqrt[N[(y + z), $MachinePrecision]], $MachinePrecision] * N[Sqrt[N[(y - z), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024204 
(FPCore (x y z)
  :name "Diagrams.TwoD.Apollonian:initialConfig from diagrams-contrib-1.3.0.5, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y 5163219297650339/200000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- (* x y)) (* x (* (sqrt (+ y z)) (sqrt (- y z))))))

  (* x (sqrt (- (* y y) (* z z)))))