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

Average Error: 0.0 → 0

Time: 394.0ms

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[x \cdot x + 1\]

↓

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

C

double f(double x) {
        double r115133 = x;
        double r115134 = r115133 * r115133;
        double r115135 = 1.0;
        double r115136 = r115134 + r115135;
        return r115136;
}

↓

double f(double x) {
        double r115137 = x;
        double r115138 = 1.0;
        double r115139 = fma(r115137, r115137, r115138);
        return r115139;
}

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 2019350 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  :precision binary64
  (+ (* x x) 1))