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

Average Error: 0.0 → 0

Time: 812.0ms

Precision: 64

Math

\[x \cdot x + 1\]

↓

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

C

double f(double x) {
        double r8483891 = x;
        double r8483892 = r8483891 * r8483891;
        double r8483893 = 1.0;
        double r8483894 = r8483892 + r8483893;
        return r8483894;
}

↓

double f(double x) {
        double r8483895 = x;
        double r8483896 = 1.0;
        double r8483897 = fma(r8483895, r8483895, r8483896);
        return r8483897;
}

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 2019174 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  (+ (* x x) 1.0))