Average Error: 0.0 → 0.0
Time: 818.0ms
Precision: 64
\[x \cdot x - y \cdot y\]
↓
\[\mathsf{fma}\left(x, x, -y \cdot y\right)\]
x \cdot x - y \cdot y
↓
\mathsf{fma}\left(x, x, -y \cdot y\right)
double f(double x, double y) {
        double r173388 = x;
        double r173389 = r173388 * r173388;
        double r173390 = y;
        double r173391 = r173390 * r173390;
        double r173392 = r173389 - r173391;
        return r173392;
}
↓
double f(double x, double y) {
        double r173393 = x;
        double r173394 = y;
        double r173395 = r173394 * r173394;
        double r173396 = -r173395;
        double r173397 = fma(r173393, r173393, r173396);
        return r173397;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[x \cdot x - y \cdot y\]
  2. Using strategy rm

  3. Applied fma-neg0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f2 from sbv-4.4"
  :precision binary64
  (- (* x x) (* y y)))