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

Average Error: 0 → 0

Time: 744.0ms

Precision: 64

Math

\[x \cdot x + 1.0\]

↓

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

C

double f(double x) {
        double r2757556 = x;
        double r2757557 = r2757556 * r2757556;
        double r2757558 = 1.0;
        double r2757559 = r2757557 + r2757558;
        return r2757559;
}

↓

double f(double x) {
        double r2757560 = x;
        double r2757561 = 1.0;
        double r2757562 = fma(r2757560, r2757560, r2757561);
        return r2757562;
}

Error

Bits error versus x

Derivation

1. Initial program 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 2019156 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  (+ (* x x) 1.0))