Average Error: 39.0 → 0.0
Time: 4.3s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot x + x \cdot 2\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot x + x \cdot 2
double f(double x) {
        double r164256 = x;
        double r164257 = 1.0;
        double r164258 = r164256 + r164257;
        double r164259 = r164258 * r164258;
        double r164260 = r164259 - r164257;
        return r164260;
}
↓
double f(double x) {
        double r164261 = x;
        double r164262 = r164261 * r164261;
        double r164263 = 2.0;
        double r164264 = r164261 * r164263;
        double r164265 = r164262 + r164264;
        return r164265;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.0

    \[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]

  2. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(x + 2\right)}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in0.0

    \[\leadsto \color{blue}{x \cdot x + 2 \cdot x}\]

  5. Final simplification0.0

    \[\leadsto x \cdot x + x \cdot 2\]

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))