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

Average Error: 0.0 → 0

Time: 923.0ms

Precision: 64

Math

\[x \cdot x + 1\]

↓

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

C

double f(double x) {
        double r19044988 = x;
        double r19044989 = r19044988 * r19044988;
        double r19044990 = 1.0;
        double r19044991 = r19044989 + r19044990;
        return r19044991;
}

↓

double f(double x) {
        double r19044992 = x;
        double r19044993 = 1.0;
        double r19044994 = fma(r19044992, r19044992, r19044993);
        return r19044994;
}

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 2019173 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  (+ (* x x) 1.0))