Average Error: 0.0 → 0.0
Time: 17.7s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(a - b\right) \cdot \left(b + a\right)\]
a \cdot a - b \cdot b
↓
\left(a - b\right) \cdot \left(b + a\right)
double f(double a, double b) {
        double r5670830 = a;
        double r5670831 = r5670830 * r5670830;
        double r5670832 = b;
        double r5670833 = r5670832 * r5670832;
        double r5670834 = r5670831 - r5670833;
        return r5670834;
}
↓
double f(double a, double b) {
        double r5670835 = a;
        double r5670836 = b;
        double r5670837 = r5670835 - r5670836;
        double r5670838 = r5670836 + r5670835;
        double r5670839 = r5670837 * r5670838;
        return r5670839;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{a}^{2} - {b}^{2}}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019165 
(FPCore (a b)
  :name "Difference of squares"

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

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