Average Error: 0.0 → 0.0
Time: 5.3s
Precision: 64
\[\left(x + y\right) \cdot \left(x - y\right)\]
↓
\[\mathsf{fma}\left(y, -y, x \cdot x\right)\]
\left(x + y\right) \cdot \left(x - y\right)
↓
\mathsf{fma}\left(y, -y, x \cdot x\right)
double f(double x, double y) {
        double r134920 = x;
        double r134921 = y;
        double r134922 = r134920 + r134921;
        double r134923 = r134920 - r134921;
        double r134924 = r134922 * r134923;
        return r134924;
}
↓
double f(double x, double y) {
        double r134925 = y;
        double r134926 = -r134925;
        double r134927 = x;
        double r134928 = r134927 * r134927;
        double r134929 = fma(r134925, r134926, r134928);
        return r134929;
}

Error

Bits error versus x

Bits error versus y

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(x - y\right)\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y)
  :name "Examples.Basics.BasicTests:f1 from sbv-4.4"
  (* (+ x y) (- x y)))