Average Error: 0.0 → 0.0
Time: 1.6s
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 r107897 = a;
        double r107898 = r107897 * r107897;
        double r107899 = b;
        double r107900 = r107899 * r107899;
        double r107901 = r107898 - r107900;
        return r107901;
}
↓
double f(double a, double b) {
        double r107902 = a;
        double r107903 = b;
        double r107904 = r107902 + r107903;
        double r107905 = r107902 - r107903;
        double r107906 = r107904 * r107905;
        return r107906;
}

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 2020083 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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