Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(b + a\right) \cdot \left(a - b\right)\]
double f(double a, double b) {
        double r29413124 = a;
        double r29413125 = r29413124 * r29413124;
        double r29413126 = b;
        double r29413127 = r29413126 * r29413126;
        double r29413128 = r29413125 - r29413127;
        return r29413128;
}
↓
double f(double a, double b) {
        double r29413129 = b;
        double r29413130 = a;
        double r29413131 = r29413129 + r29413130;
        double r29413132 = r29413130 - r29413129;
        double r29413133 = r29413131 * r29413132;
        return r29413133;
}


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 2019101 
(FPCore (a b)
  :name "Difference of squares"

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

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