Average Error: 38.8 → 0.0
Time: 9.9s
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 r338302 = x;
        double r338303 = 1.0;
        double r338304 = r338302 + r338303;
        double r338305 = r338304 * r338304;
        double r338306 = r338305 - r338303;
        return r338306;
}
↓
double f(double x) {
        double r338307 = x;
        double r338308 = r338307 * r338307;
        double r338309 = 2.0;
        double r338310 = r338307 * r338309;
        double r338311 = r338308 + r338310;
        return r338311;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.8

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

  2. Simplified0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019135 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))