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

Percentage Accurate: 67.3% → 99.4%

Time: 3.4s

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: 67.3% 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, 0.8× speedup

Math

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

FPCore

z_m = (fabs.f64 z)
y_m = (fabs.f64 y)
(FPCore (x y_m z_m)
 :precision binary64
 (* (* x (sqrt (+ 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((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((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((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((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(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((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[(z$95$m + y$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(y$95$m - z$95$m), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 63.0%

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

   1. lift-*.f64 N/A

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

   2. lift-sqrt.f64 N/A

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

   3. pow1/2 N/A

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

   4. lift--.f64 N/A

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

   5. lift-*.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. difference-of-squares N/A

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

   8. unpow-prod-down N/A

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

   9. associate-*r* N/A

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

   10. lower-*.f64 N/A

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

   11. lower-*.f64 N/A

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

   12. pow1/2 N/A

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

   13. lower-sqrt.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-+.f64 N/A

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

   16. pow1/2 N/A

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

   17. lower-sqrt.f64 N/A

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

   18. lower--.f64 49.7

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

4. Applied rewrites 49.7%

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

Alternative 2: 99.4% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

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((z_m + y_m)) * (sqrt((y_m - z_m)) * x)
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((z_m + y_m)) * (Math.sqrt((y_m - z_m)) * x);
}

Python

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

Julia

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

MATLAB

z_m = abs(z);
y_m = abs(y);
function tmp = code(x, y_m, z_m)
	tmp = sqrt((z_m + y_m)) * (sqrt((y_m - z_m)) * x);
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[(z$95$m + y$95$m), $MachinePrecision]], $MachinePrecision] * N[(N[Sqrt[N[(y$95$m - z$95$m), $MachinePrecision]], $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 63.0%

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

   1. lift-*.f64 N/A

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

   2. *-commutative N/A

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

   3. lift-sqrt.f64 N/A

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

   4. pow1/2 N/A

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

   5. lift--.f64 N/A

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

   6. lift-*.f64 N/A

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

   7. lift-*.f64 N/A

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

   8. difference-of-squares N/A

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

   9. unpow-prod-down N/A

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

   10. associate-*l* N/A

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

   11. lower-*.f64 N/A

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

   12. pow1/2 N/A

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

   13. lower-sqrt.f64 N/A

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

   14. +-commutative N/A

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

   15. lower-+.f64 N/A

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

   16. lower-*.f64 N/A

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

   17. pow1/2 N/A

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

   18. lower-sqrt.f64 N/A

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

   19. lower--.f64 49.7

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

4. Applied rewrites 49.7%

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

Alternative 3: 99.3% accurate, 4.8× speedup

Math

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

FPCore

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

C

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

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 = y_m * x
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 y_m * x;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 63.0%

   \[x \cdot \sqrt{y \cdot y - z \cdot z} \]
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. lower-*.f64 51.5

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

5. Applied rewrites 51.5%

   \[\leadsto \color{blue}{y \cdot x} \]
6. 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 2024329 
(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)))))