Average Error: 0.0 → 0.0
Time: 1.9s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(b + a\right) \cdot \left(a - b\right)\]
double f(double a, double b) {
        double r11990329 = a;
        double r11990330 = r11990329 * r11990329;
        double r11990331 = b;
        double r11990332 = r11990331 * r11990331;
        double r11990333 = r11990330 - r11990332;
        return r11990333;
}
↓
double f(double a, double b) {
        double r11990334 = b;
        double r11990335 = a;
        double r11990336 = r11990334 + r11990335;
        double r11990337 = r11990335 - r11990334;
        double r11990338 = r11990336 * r11990337;
        return r11990338;
}


a \cdot a - b \cdot b
↓
\left(b + a\right) \cdot \left(a - b\right)

Error

Bits error versus a

Bits error versus b

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

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

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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