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

Average Error: 0.0 → 0

Time: 4.3s

Precision: 64

Math

\[x \cdot x + 1\]

↓

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

C

double f(double x) {
        double r8039613 = x;
        double r8039614 = r8039613 * r8039613;
        double r8039615 = 1.0;
        double r8039616 = r8039614 + r8039615;
        return r8039616;
}

↓

double f(double x) {
        double r8039617 = x;
        double r8039618 = 1.0;
        double r8039619 = fma(r8039617, r8039617, r8039618);
        return r8039619;
}

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 2019200 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  (+ (* x x) 1.0))