Average Error: 0.0 → 0.0
Time: 5.2s
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 r98934 = a;
        double r98935 = r98934 * r98934;
        double r98936 = b;
        double r98937 = r98936 * r98936;
        double r98938 = r98935 - r98937;
        return r98938;
}
↓
double f(double a, double b) {
        double r98939 = a;
        double r98940 = b;
        double r98941 = r98939 - r98940;
        double r98942 = r98939 + r98940;
        double r98943 = r98941 * r98942;
        return r98943;
}

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 2019209 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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