Average Error: 0.0 → 0
Time: 4.1s
Precision: 64
\[x - y \cdot y\]
↓
\[\mathsf{fma}\left(y, -y, x\right)\]
x - y \cdot y
↓
\mathsf{fma}\left(y, -y, x\right)
double f(double x, double y) {
        double r86185 = x;
        double r86186 = y;
        double r86187 = r86186 * r86186;
        double r86188 = r86185 - r86187;
        return r86188;
}
↓
double f(double x, double y) {
        double r86189 = y;
        double r86190 = -r86189;
        double r86191 = x;
        double r86192 = fma(r86189, r86190, r86191);
        return r86192;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x - y \cdot y\]

  2. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{x - {y}^{2}}\]

  3. Simplified0

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, -y, x\right)}\]

  4. Final simplification0

    \[\leadsto \mathsf{fma}\left(y, -y, x\right)\]

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y)
  :name "Graphics.Rasterific.Shading:$sradialGradientWithFocusShader from Rasterific-0.6.1"
  :precision binary64
  (- x (* y y)))