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

Percentage Accurate: 100.0% → 100.0%

Time: 1.2s

Alternatives: 3

Speedup: 1.0×

• 24.0% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-45} \lor \neg \left(y \leq 1.05 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 2.15e-57)
   x
   (if (or (<= y 1.35e-45) (not (<= y 1.05e+24))) (* y (- y)) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.15e-57) {
		tmp = x;
	} else if ((y <= 1.35e-45) || !(y <= 1.05e+24)) {
		tmp = 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 (y <= 2.15d-57) then
        tmp = x
    else if ((y <= 1.35d-45) .or. (.not. (y <= 1.05d+24))) then
        tmp = y * -y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 2.15e-57) {
		tmp = x;
	} else if ((y <= 1.35e-45) || !(y <= 1.05e+24)) {
		tmp = y * -y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.15e-57:
		tmp = x
	elif (y <= 1.35e-45) or not (y <= 1.05e+24):
		tmp = y * -y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.15e-57)
		tmp = x;
	elseif ((y <= 1.35e-45) || !(y <= 1.05e+24))
		tmp = Float64(y * Float64(-y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 2.15e-57)
		tmp = x;
	elseif ((y <= 1.35e-45) || ~((y <= 1.05e+24)))
		tmp = y * -y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.15e-57], x, If[Or[LessEqual[y, 1.35e-45], N[Not[LessEqual[y, 1.05e+24]], $MachinePrecision]], N[(y * (-y)), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < 2.15000000000000011e-57 or 1.34999999999999992e-45 < y < 1.0500000000000001e24

   1. Initial program 100.0%

      \[x - y \cdot y \]

   2. Taylor expanded in x around inf 59.9%

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

   if 2.15000000000000011e-57 < y < 1.34999999999999992e-45 or 1.0500000000000001e24 < y

   1. Initial program 100.0%

      \[x - y \cdot y \]

   2. Taylor expanded in x around 0 88.7%

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

      1. unpow2 88.7%

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

      2. neg-mul-1 88.7%

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

      3. distribute-rgt-neg-in 88.7%

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

   4. Simplified 88.7%

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

4. Final simplification 66.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 2.15 \cdot 10^{-57}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-45} \lor \neg \left(y \leq 1.05 \cdot 10^{+24}\right):\\ \;\;\;\;y \cdot \left(-y\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 3: 51.4% 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 48.9%

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

3. Final simplification 48.9%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023255 
(FPCore (x y)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1"
  :precision binary64
  (- x (* y y)))