Average Error: 0.0 → 0.0
Time: 7.4s
Precision: 64
\[a \cdot a - b \cdot b\]
↓
\[\left(b + a\right) \cdot \left(a - b\right)\]
a \cdot a - b \cdot b
↓
\left(b + a\right) \cdot \left(a - b\right)
double f(double a, double b) {
        double r2414761 = a;
        double r2414762 = r2414761 * r2414761;
        double r2414763 = b;
        double r2414764 = r2414763 * r2414763;
        double r2414765 = r2414762 - r2414764;
        return r2414765;
}
↓
double f(double a, double b) {
        double r2414766 = b;
        double r2414767 = a;
        double r2414768 = r2414766 + r2414767;
        double r2414769 = r2414767 - r2414766;
        double r2414770 = r2414768 * r2414769;
        return r2414770;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019144 
(FPCore (a b)
  :name "Difference of squares"

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

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