Average Error: 0.0 → 0.0
Time: 4.4s
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 r1718192 = a;
        double r1718193 = r1718192 * r1718192;
        double r1718194 = b;
        double r1718195 = r1718194 * r1718194;
        double r1718196 = r1718193 - r1718195;
        return r1718196;
}
↓
double f(double a, double b) {
        double r1718197 = a;
        double r1718198 = b;
        double r1718199 = r1718197 + r1718198;
        double r1718200 = r1718197 - r1718198;
        double r1718201 = r1718199 * r1718200;
        return r1718201;
}

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 inf 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 2019151 
(FPCore (a b)
  :name "Difference of squares"

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

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