Average Error: 39.2 → 0.0
Time: 16.0s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[\left(x + 2\right) \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
\left(x + 2\right) \cdot x
double f(double x) {
        double r886263 = x;
        double r886264 = 1.0;
        double r886265 = r886263 + r886264;
        double r886266 = r886265 * r886265;
        double r886267 = r886266 - r886264;
        return r886267;
}
↓
double f(double x) {
        double r886268 = x;
        double r886269 = 2.0;
        double r886270 = r886268 + r886269;
        double r886271 = r886270 * r886268;
        return r886271;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.2

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(2 + x\right) \cdot x}\]

  3. Final simplification0.0

    \[\leadsto \left(x + 2\right) \cdot x\]

Reproduce

herbie shell --seed 2019112 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))