Average Error: 0.0 → 0.0
Time: 11.0s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(a + b\right) \cdot \left(a - b\right)\]
a \cdot a - b \cdot b
↓
\left(a + b\right) \cdot \left(a - b\right)
double f(double a, double b) {
        double r77684 = a;
        double r77685 = r77684 * r77684;
        double r77686 = b;
        double r77687 = r77686 * r77686;
        double r77688 = r77685 - r77687;
        return r77688;
}
↓
double f(double a, double b) {
        double r77689 = a;
        double r77690 = b;
        double r77691 = r77689 + r77690;
        double r77692 = r77689 - r77690;
        double r77693 = r77691 * r77692;
        return r77693;
}

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

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

Reproduce

herbie shell --seed 2019351 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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