Data.Octree.Internal:octantDistance from Octree-0.5.4.2

Percentage Accurate: 54.0% → 100.0%

Time: 5.2s

Alternatives: 3

Speedup: 0.2×

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (sqrt (+ (* x x) (* y y))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 54.0% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (sqrt (+ (* x x) (* y y))))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \mathsf{hypot}\left(y, x\right) \end{array} \]

FPCore

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

C

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

Java

public static double code(double x, double y) {
	return Math.hypot(y, x);
}

Python

def code(x, y):
	return math.hypot(y, x)

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[Sqrt[y ^ 2 + x ^ 2], $MachinePrecision]

Derivation

1. Initial program 52.9%

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

   1. +-commutative N/A

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

   2. accelerator-lowering-hypot.f64 100.0

      \[\leadsto \color{blue}{\mathsf{hypot}\left(y, x\right)} \]

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{hypot}\left(y, x\right)} \]
5. Add Preprocessing

Alternative 2: 26.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, \frac{x}{y \cdot 2}, y\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x (/ x (* y 2.0)) y))

C

double code(double x, double y) {
	return fma(x, (x / (y * 2.0)), y);
}

Julia

function code(x, y)
	return fma(x, Float64(x / Float64(y * 2.0)), y)
end

Wolfram

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

Derivation

1. Initial program 52.9%

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

3. Taylor expanded in x around 0

   \[\leadsto \color{blue}{y + \frac{1}{2} \cdot \frac{{x}^{2}}{y}} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. *-lft-identity N/A

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

   3. associate-*l/ N/A

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

   4. associate-*l* N/A

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

   5. unpow2 N/A

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

   6. associate-*r* N/A

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

   7. *-commutative N/A

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

   8. accelerator-lowering-fma.f64 N/A

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

   9. associate-*r/ N/A

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

   10. metadata-eval N/A

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

   11. associate-*l/ N/A

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

   12. /-lowering-/.f64 N/A

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

   13. *-commutative N/A

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

   14. *-lowering-*.f64 24.5

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

5. Simplified 24.5%

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

   1. associate-/l* N/A

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

   2. clear-num N/A

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

   3. un-div-inv N/A

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

   4. /-lowering-/.f64 N/A

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

   5. div-inv N/A

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

   6. metadata-eval N/A

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

   7. *-lowering-*.f64 24.5

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

7. Applied egg-rr 24.5%

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

Alternative 3: 26.0% accurate, 24.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 52.9%

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

3. Taylor expanded in x around 0

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

5. Simplified 24.1%

   \[\leadsto \color{blue}{y} \]
6. Add Preprocessing

Developer Target 1: 74.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x < -1.1236950826599826 \cdot 10^{+145}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x < 1.116557621183362 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x \cdot x + y \cdot y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (< x -1.1236950826599826e+145)
   (- x)
   (if (< x 1.116557621183362e+93) (sqrt (+ (* x x) (* y y))) x)))

C

double code(double x, double y) {
	double tmp;
	if (x < -1.1236950826599826e+145) {
		tmp = -x;
	} else if (x < 1.116557621183362e+93) {
		tmp = sqrt(((x * x) + (y * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x < (-1.1236950826599826d+145)) then
        tmp = -x
    else if (x < 1.116557621183362d+93) then
        tmp = sqrt(((x * x) + (y * y)))
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x < -1.1236950826599826e+145) {
		tmp = -x;
	} else if (x < 1.116557621183362e+93) {
		tmp = Math.sqrt(((x * x) + (y * y)));
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x < -1.1236950826599826e+145:
		tmp = -x
	elif x < 1.116557621183362e+93:
		tmp = math.sqrt(((x * x) + (y * y)))
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x < -1.1236950826599826e+145)
		tmp = Float64(-x);
	elseif (x < 1.116557621183362e+93)
		tmp = sqrt(Float64(Float64(x * x) + Float64(y * y)));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x < -1.1236950826599826e+145)
		tmp = -x;
	elseif (x < 1.116557621183362e+93)
		tmp = sqrt(((x * x) + (y * y)));
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Less[x, -1.1236950826599826e+145], (-x), If[Less[x, 1.116557621183362e+93], N[Sqrt[N[(N[(x * x), $MachinePrecision] + N[(y * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], x]]

Reproduce

herbie shell --seed 2024196 
(FPCore (x y)
  :name "Data.Octree.Internal:octantDistance  from Octree-0.5.4.2"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -11236950826599826000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000) (- x) (if (< x 1116557621183362000000000000000000000000000000000000000000000000000000000000000000000000000000) (sqrt (+ (* x x) (* y y))) x)))

  (sqrt (+ (* x x) (* y y))))