Average Error: 0.0 → 0.0
Time: 809.0ms
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 r94732 = a;
        double r94733 = r94732 * r94732;
        double r94734 = b;
        double r94735 = r94734 * r94734;
        double r94736 = r94733 - r94735;
        return r94736;
}
↓
double f(double a, double b) {
        double r94737 = a;
        double r94738 = b;
        double r94739 = r94737 + r94738;
        double r94740 = r94737 - r94738;
        double r94741 = r94739 * r94740;
        return r94741;
}

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. Using strategy rm

  3. Applied difference-of-squares0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (a b)
  :name "Difference of squares"
  :precision binary64

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

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