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

Average Error: 0.0 → 0

Time: 805.0ms

Precision: 64

Math

\[x \cdot x + 1.0\]

↓

\[\mathsf{fma}\left(x, x, 1.0\right)\]

C

double f(double x) {
        double r8213907 = x;
        double r8213908 = r8213907 * r8213907;
        double r8213909 = 1.0;
        double r8213910 = r8213908 + r8213909;
        return r8213910;
}

↓

double f(double x) {
        double r8213911 = x;
        double r8213912 = 1.0;
        double r8213913 = fma(r8213911, r8213911, r8213912);
        return r8213913;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[x \cdot x + 1.0\]

2. Simplified 0

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, 1.0\right)}\]

3. Final simplification 0

   \[\leadsto \mathsf{fma}\left(x, x, 1.0\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  (+ (* x x) 1.0))