Average Error: 0.0 → 0.0
Time: 10.1s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(a - b\right) \cdot a + b \cdot \left(a - b\right)\]
a \cdot a - b \cdot b
↓
\left(a - b\right) \cdot a + b \cdot \left(a - b\right)
double f(double a, double b) {
        double r129289 = a;
        double r129290 = r129289 * r129289;
        double r129291 = b;
        double r129292 = r129291 * r129291;
        double r129293 = r129290 - r129292;
        return r129293;
}
↓
double f(double a, double b) {
        double r129294 = a;
        double r129295 = b;
        double r129296 = r129294 - r129295;
        double r129297 = r129296 * r129294;
        double r129298 = r129295 * r129296;
        double r129299 = r129297 + r129298;
        return r129299;
}

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. Using strategy rm

  4. Applied distribute-lft-in0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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