Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1

Percentage Accurate: 100.0% → 100.0%

Time: 3.0s

Alternatives: 2

Speedup: 1.0×

• 43.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x * x) + (y * y)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (x * x) + (y * y)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ [x_m, y_m] = \mathsf{sort}([x_m, y_m])\\ \\ \mathsf{fma}\left(y\_m, y\_m, x\_m \cdot x\_m\right) \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
(FPCore (x_m y_m) :precision binary64 (fma y_m y_m (* x_m x_m)))

C

x_m = fabs(x);
y_m = fabs(y);
assert(x_m < y_m);
double code(double x_m, double y_m) {
	return fma(y_m, y_m, (x_m * x_m));
}

Julia

x_m = abs(x)
y_m = abs(y)
x_m, y_m = sort([x_m, y_m])
function code(x_m, y_m)
	return fma(y_m, y_m, Float64(x_m * x_m))
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
code[x$95$m_, y$95$m_] := N[(y$95$m * y$95$m + N[(x$95$m * x$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

   1. +-commutative 100.0%

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

   2. fma-define 100.0%

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

   3. pow2 100.0%

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

4. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y, y, {x}^{2}\right)} \]
5. Step-by-step derivation

   1. unpow2 100.0%

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

6. Applied egg-rr 100.0%

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

Alternative 2: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} x_m = \left|x\right| \\ y_m = \left|y\right| \\ [x_m, y_m] = \mathsf{sort}([x_m, y_m])\\ \\ x\_m \cdot x\_m + y\_m \cdot y\_m \end{array} \]

FPCore

x_m = (fabs.f64 x)
y_m = (fabs.f64 y)
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
(FPCore (x_m y_m) :precision binary64 (+ (* x_m x_m) (* y_m y_m)))

C

x_m = fabs(x);
y_m = fabs(y);
assert(x_m < y_m);
double code(double x_m, double y_m) {
	return (x_m * x_m) + (y_m * y_m);
}

Fortran

x_m = abs(x)
y_m = abs(y)
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
real(8) function code(x_m, y_m)
    real(8), intent (in) :: x_m
    real(8), intent (in) :: y_m
    code = (x_m * x_m) + (y_m * y_m)
end function

Java

x_m = Math.abs(x);
y_m = Math.abs(y);
assert x_m < y_m;
public static double code(double x_m, double y_m) {
	return (x_m * x_m) + (y_m * y_m);
}

Python

x_m = math.fabs(x)
y_m = math.fabs(y)
[x_m, y_m] = sort([x_m, y_m])
def code(x_m, y_m):
	return (x_m * x_m) + (y_m * y_m)

Julia

x_m = abs(x)
y_m = abs(y)
x_m, y_m = sort([x_m, y_m])
function code(x_m, y_m)
	return Float64(Float64(x_m * x_m) + Float64(y_m * y_m))
end

MATLAB

x_m = abs(x);
y_m = abs(y);
x_m, y_m = num2cell(sort([x_m, y_m])){:}
function tmp = code(x_m, y_m)
	tmp = (x_m * x_m) + (y_m * y_m);
end

Wolfram

x_m = N[Abs[x], $MachinePrecision]
y_m = N[Abs[y], $MachinePrecision]
NOTE: x_m and y_m should be sorted in increasing order before calling this function.
code[x$95$m_, y$95$m_] := N[(N[(x$95$m * x$95$m), $MachinePrecision] + N[(y$95$m * y$95$m), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

   \[x \cdot x + y \cdot y \]
2. Add Preprocessing
3. Add Preprocessing

Reproduce

herbie shell --seed 2024180 
(FPCore (x y)
  :name "Graphics.Rasterific.Linear:$cquadrance from Rasterific-0.6.1"
  :precision binary64
  (+ (* x x) (* y y)))