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 r62368 = a;
        double r62369 = r62368 * r62368;
        double r62370 = b;
        double r62371 = r62370 * r62370;
        double r62372 = r62369 - r62371;
        return r62372;
}
↓
double f(double a, double b) {
        double r62373 = a;
        double r62374 = b;
        double r62375 = r62373 - r62374;
        double r62376 = r62373 + r62374;
        double r62377 = r62375 * r62376;
        return r62377;
}

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 2020047 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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