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

Average Error: 0.0 → 0

Time: 337.0ms

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 r166688 = x;
        double r166689 = r166688 * r166688;
        double r166690 = 1.0;
        double r166691 = r166689 + r166690;
        return r166691;
}

↓

double f(double x) {
        double r166692 = x;
        double r166693 = 1.0;
        double r166694 = fma(r166692, r166692, r166693);
        return r166694;
}

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 2020045 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  :precision binary64
  (+ (* x x) 1))