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

Average Error: 0.0 → 0

Time: 3.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x - y \cdot y\]

↓

\[\mathsf{fma}\left(y, -y, x\right)\]

C

double f(double x, double y) {
        double r171780 = x;
        double r171781 = y;
        double r171782 = r171781 * r171781;
        double r171783 = r171780 - r171782;
        return r171783;
}

↓

double f(double x, double y) {
        double r171784 = y;
        double r171785 = -r171784;
        double r171786 = x;
        double r171787 = fma(r171784, r171785, r171786);
        return r171787;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.0

   \[x - y \cdot y\]

2. Taylor expanded around 0 0.0

   \[\leadsto \color{blue}{x - {y}^{2}}\]

3. Simplified 0

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

4. Final simplification 0

   \[\leadsto \mathsf{fma}\left(y, -y, x\right)\]

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1"
  :precision binary64
  (- x (* y y)))