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

Average Error: 0.0 → 0

Time: 4.2s

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 r200796 = x;
        double r200797 = y;
        double r200798 = r200797 * r200797;
        double r200799 = r200796 - r200798;
        return r200799;
}

↓

double f(double x, double y) {
        double r200800 = y;
        double r200801 = -r200800;
        double r200802 = x;
        double r200803 = fma(r200801, r200800, r200802);
        return r200803;
}

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 2020047 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1"
  :precision binary64
  (- x (* y y)))