Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1

Percentage Accurate: 100.0% → 100.0%

Time: 1.9s

Alternatives: 3

Speedup: 1.0×

• 24.4% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[x - y \cdot y \]

2. Final simplification 100.0%

   \[\leadsto x - y \cdot y \]

Alternative 2: 68.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 1.12e-8) x (* y (- y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 1.12e-8) {
		tmp = x;
	} else {
		tmp = y * -y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 1.12d-8) then
        tmp = x
    else
        tmp = y * -y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 1.12e-8) {
		tmp = x;
	} else {
		tmp = y * -y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 1.12e-8:
		tmp = x
	else:
		tmp = y * -y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 1.12e-8)
		tmp = x;
	else
		tmp = Float64(y * Float64(-y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 1.12e-8)
		tmp = x;
	else
		tmp = y * -y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 1.12e-8], x, N[(y * (-y)), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.11999999999999994e-8

   1. Initial program 100.0%

      \[x - y \cdot y \]

   2. Taylor expanded in x around inf 69.9%

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

   if 1.11999999999999994e-8 < y

   1. Initial program 100.0%

      \[x - y \cdot y \]

   2. Taylor expanded in x around 0 90.0%

      \[\leadsto \color{blue}{-1 \cdot {y}^{2}} \]
   3. Step-by-step derivation

      1. unpow2 90.0%

         \[\leadsto -1 \cdot \color{blue}{\left(y \cdot y\right)} \]

      2. neg-mul-1 90.0%

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

      3. distribute-rgt-neg-in 90.0%

         \[\leadsto \color{blue}{y \cdot \left(-y\right)} \]

   4. Simplified 90.0%

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

4. Final simplification 75.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 1.12 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(-y\right)\\ \end{array} \]

Alternative 3: 50.9% accurate, 5.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 100.0%

   \[x - y \cdot y \]

2. Taylor expanded in x around inf 55.0%

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

3. Final simplification 55.0%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023222 
(FPCore (x y)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1"
  :precision binary64
  (- x (* y y)))