Average Error: 0.0 → 0.0
Time: 2.5s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(b + a\right) \cdot \left(a - b\right)\]
double f(double a, double b) {
        double r27831196 = a;
        double r27831197 = r27831196 * r27831196;
        double r27831198 = b;
        double r27831199 = r27831198 * r27831198;
        double r27831200 = r27831197 - r27831199;
        return r27831200;
}
↓
double f(double a, double b) {
        double r27831201 = b;
        double r27831202 = a;
        double r27831203 = r27831201 + r27831202;
        double r27831204 = r27831202 - r27831201;
        double r27831205 = r27831203 * r27831204;
        return r27831205;
}


a \cdot a - b \cdot b
↓
\left(b + a\right) \cdot \left(a - b\right)

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 difference-of-squares0.0

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

  4. Final simplification0.0

    \[\leadsto \left(b + a\right) \cdot \left(a - b\right)\]

Reproduce

herbie shell --seed 2019101 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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