Average Error: 0.0 → 0.0
Time: 3.8s
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 r77636 = a;
        double r77637 = r77636 * r77636;
        double r77638 = b;
        double r77639 = r77638 * r77638;
        double r77640 = r77637 - r77639;
        return r77640;
}
↓
double f(double a, double b) {
        double r77641 = b;
        double r77642 = a;
        double r77643 = r77641 + r77642;
        double r77644 = r77642 - r77641;
        double r77645 = r77643 * r77644;
        return r77645;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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