Average Error: 0.0 → 0.0
Time: 6.2s
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 r137068 = a;
        double r137069 = r137068 * r137068;
        double r137070 = b;
        double r137071 = r137070 * r137070;
        double r137072 = r137069 - r137071;
        return r137072;
}
↓
double f(double a, double b) {
        double r137073 = a;
        double r137074 = b;
        double r137075 = r137073 - r137074;
        double r137076 = r137073 + r137074;
        double r137077 = r137075 * r137076;
        return r137077;
}

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 2020042 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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