Average Error: 0.0 → 0.0
Time: 864.0ms
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 r124754 = x;
        double r124755 = r124754 * r124754;
        double r124756 = y;
        double r124757 = r124756 * r124756;
        double r124758 = r124755 - r124757;
        return r124758;
}
↓
double f(double x, double y) {
        double r124759 = x;
        double r124760 = y;
        double r124761 = r124760 * r124760;
        double r124762 = -r124761;
        double r124763 = fma(r124759, r124759, r124762);
        return r124763;
}

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)))