Average Error: 0.0 → 0.0
Time: 18.7s
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 r5153127 = a;
        double r5153128 = r5153127 * r5153127;
        double r5153129 = b;
        double r5153130 = r5153129 * r5153129;
        double r5153131 = r5153128 - r5153130;
        return r5153131;
}
↓
double f(double a, double b) {
        double r5153132 = a;
        double r5153133 = b;
        double r5153134 = r5153132 - r5153133;
        double r5153135 = r5153132 + r5153133;
        double r5153136 = r5153134 * r5153135;
        return r5153136;
}

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

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"

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

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