Average Error: 0.0 → 0.0
Time: 4.0s
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 r1750940 = a;
        double r1750941 = r1750940 * r1750940;
        double r1750942 = b;
        double r1750943 = r1750942 * r1750942;
        double r1750944 = r1750941 - r1750943;
        return r1750944;
}
↓
double f(double a, double b) {
        double r1750945 = a;
        double r1750946 = b;
        double r1750947 = r1750945 + r1750946;
        double r1750948 = r1750945 - r1750946;
        double r1750949 = r1750947 * r1750948;
        return r1750949;
}

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. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{{a}^{2} - {b}^{2}}\]

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019154 
(FPCore (a b)
  :name "Difference of squares"

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

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