Average Error: 0.0 → 0.0
Time: 14.4s
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 r97914 = a;
        double r97915 = r97914 * r97914;
        double r97916 = b;
        double r97917 = r97916 * r97916;
        double r97918 = r97915 - r97917;
        return r97918;
}
↓
double f(double a, double b) {
        double r97919 = a;
        double r97920 = b;
        double r97921 = r97919 - r97920;
        double r97922 = r97919 + r97920;
        double r97923 = r97921 * r97922;
        return r97923;
}

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 2019303 
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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