Average Error: 0.0 → 0.0
Time: 14.5s
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 r85483 = a;
        double r85484 = r85483 * r85483;
        double r85485 = b;
        double r85486 = r85485 * r85485;
        double r85487 = r85484 - r85486;
        return r85487;
}
↓
double f(double a, double b) {
        double r85488 = a;
        double r85489 = b;
        double r85490 = r85489 * r85489;
        double r85491 = -r85490;
        double r85492 = fma(r85488, r85488, r85491);
        return r85492;
}

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 2019326 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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