Average Error: 0.0 → 0.0
Time: 6.1s
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 r107564 = a;
        double r107565 = r107564 * r107564;
        double r107566 = b;
        double r107567 = r107566 * r107566;
        double r107568 = r107565 - r107567;
        return r107568;
}
↓
double f(double a, double b) {
        double r107569 = a;
        double r107570 = b;
        double r107571 = r107569 - r107570;
        double r107572 = r107569 + r107570;
        double r107573 = r107571 * r107572;
        return r107573;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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