Average Error: 0.0 → 0.0
Time: 7.7s
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 r4044867 = a;
        double r4044868 = r4044867 * r4044867;
        double r4044869 = b;
        double r4044870 = r4044869 * r4044869;
        double r4044871 = r4044868 - r4044870;
        return r4044871;
}
↓
double f(double a, double b) {
        double r4044872 = b;
        double r4044873 = a;
        double r4044874 = r4044872 + r4044873;
        double r4044875 = r4044873 - r4044872;
        double r4044876 = r4044874 * r4044875;
        return r4044876;
}

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

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

Reproduce

herbie shell --seed 2019151 
(FPCore (a b)
  :name "Difference of squares"

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

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