Average Error: 0.0 → 0.0
Time: 8.7s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(b + a\right) \cdot \left(a - b\right)\]
a \cdot a - b \cdot b
↓
\left(b + a\right) \cdot \left(a - b\right)
double f(double a, double b) {
        double r67620 = a;
        double r67621 = r67620 * r67620;
        double r67622 = b;
        double r67623 = r67622 * r67622;
        double r67624 = r67621 - r67623;
        return r67624;
}
↓
double f(double a, double b) {
        double r67625 = b;
        double r67626 = a;
        double r67627 = r67625 + r67626;
        double r67628 = r67626 - r67625;
        double r67629 = r67627 * r67628;
        return r67629;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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 2019194 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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