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

Average Error: 0.0 → 0

Time: 1.2s

Precision: 64

Math

\[x \cdot x + 1.0\]

↓

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

C

double f(double x) {
        double r8313384 = x;
        double r8313385 = r8313384 * r8313384;
        double r8313386 = 1.0;
        double r8313387 = r8313385 + r8313386;
        return r8313387;
}

↓

double f(double x) {
        double r8313388 = x;
        double r8313389 = 1.0;
        double r8313390 = fma(r8313388, r8313388, r8313389);
        return r8313390;
}

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 2019158 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  (+ (* x x) 1.0))