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

Average Error: 0.0 → 0

Time: 913.0ms

Precision: 64

Math

\[x \cdot x + 1.0\]

↓

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

C

double f(double x) {
        double r8254540 = x;
        double r8254541 = r8254540 * r8254540;
        double r8254542 = 1.0;
        double r8254543 = r8254541 + r8254542;
        return r8254543;
}

↓

double f(double x) {
        double r8254544 = x;
        double r8254545 = 1.0;
        double r8254546 = fma(r8254544, r8254544, r8254545);
        return r8254546;
}

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 2019162 +o rules:numerics
(FPCore (x)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1, A"
  (+ (* x x) 1.0))