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

Average Error: 0.0 → 0

Time: 340.0ms

Precision: 64

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

Math

\[x \cdot x + 1\]

↓

\[\mathsf{fma}\left(x, x, 1\right)\]

C

double f(double x) {
        double r140412 = x;
        double r140413 = r140412 * r140412;
        double r140414 = 1.0;
        double r140415 = r140413 + r140414;
        return r140415;
}

↓

double f(double x) {
        double r140416 = x;
        double r140417 = 1.0;
        double r140418 = fma(r140416, r140416, r140417);
        return r140418;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[x \cdot x + 1\]

2. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, 1\right)}\]

3. Final simplification 0

   \[\leadsto \mathsf{fma}\left(x, x, 1\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  :precision binary64
  (+ (* x x) 1))