Average Error: 0.0 → 0.0
Time: 3.7s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(b + a\right) \cdot \left(a - b\right)\]
a \cdot a - b \cdot b
↓
\left(b + a\right) \cdot \left(a - b\right)
double f(double a, double b) {
        double r68105 = a;
        double r68106 = r68105 * r68105;
        double r68107 = b;
        double r68108 = r68107 * r68107;
        double r68109 = r68106 - r68108;
        return r68109;
}
↓
double f(double a, double b) {
        double r68110 = b;
        double r68111 = a;
        double r68112 = r68110 + r68111;
        double r68113 = r68111 - r68110;
        double r68114 = r68112 * r68113;
        return r68114;
}

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. Using strategy rm

  3. Applied difference-of-squares0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019297 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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