Average Error: 0.0 → 0.0
Time: 13.2s
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 r4817566 = a;
        double r4817567 = r4817566 * r4817566;
        double r4817568 = b;
        double r4817569 = r4817568 * r4817568;
        double r4817570 = r4817567 - r4817569;
        return r4817570;
}
↓
double f(double a, double b) {
        double r4817571 = b;
        double r4817572 = a;
        double r4817573 = r4817571 + r4817572;
        double r4817574 = r4817572 - r4817571;
        double r4817575 = r4817573 * r4817574;
        return r4817575;
}

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 2019138 
(FPCore (a b)
  :name "Difference of squares"

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

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