Average Error: 0.0 → 0.0
Time: 3.8s
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 r1743523 = a;
        double r1743524 = r1743523 * r1743523;
        double r1743525 = b;
        double r1743526 = r1743525 * r1743525;
        double r1743527 = r1743524 - r1743526;
        return r1743527;
}
↓
double f(double a, double b) {
        double r1743528 = a;
        double r1743529 = b;
        double r1743530 = r1743528 + r1743529;
        double r1743531 = r1743528 - r1743529;
        double r1743532 = r1743530 * r1743531;
        return r1743532;
}

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 2019153 
(FPCore (a b)
  :name "Difference of squares"

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

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