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

Average Error: 0.0 → 0

Time: 752.0ms

Precision: 64

Math

\[x \cdot x + 1\]

↓

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

C

double f(double x) {
        double r7387076 = x;
        double r7387077 = r7387076 * r7387076;
        double r7387078 = 1.0;
        double r7387079 = r7387077 + r7387078;
        return r7387079;
}

↓

double f(double x) {
        double r7387080 = x;
        double r7387081 = 1.0;
        double r7387082 = fma(r7387080, r7387080, r7387081);
        return r7387082;
}

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 2019169 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  (+ (* x x) 1.0))