Average Error: 0.0 → 0.0
Time: 903.0ms
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\mathsf{fma}\left(a, a, -b \cdot b\right)\]
a \cdot a - b \cdot b
↓
\mathsf{fma}\left(a, a, -b \cdot b\right)
double f(double a, double b) {
        double r110268 = a;
        double r110269 = r110268 * r110268;
        double r110270 = b;
        double r110271 = r110270 * r110270;
        double r110272 = r110269 - r110271;
        return r110272;
}
↓
double f(double a, double b) {
        double r110273 = a;
        double r110274 = b;
        double r110275 = r110274 * r110274;
        double r110276 = -r110275;
        double r110277 = fma(r110273, r110273, r110276);
        return r110277;
}

Error

Bits error versus a

Bits error versus b

Target

Original0.0
Target0.0
Herbie0.0
\[\left(a + b\right) \cdot \left(a - b\right)\]

Derivation

  1. Initial program 0.0

    \[a \cdot a - b \cdot b\]
  2. Using strategy rm

  3. Applied fma-neg0.0

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

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(a, a, -b \cdot b\right)\]

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

  :herbie-target
  (* (+ a b) (- a b))

  (- (* a a) (* b b)))