Average Error: 39.1 → 0.0
Time: 5.5s
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 r312558 = x;
        double r312559 = 1.0;
        double r312560 = r312558 + r312559;
        double r312561 = r312560 * r312560;
        double r312562 = r312561 - r312559;
        return r312562;
}
↓
double f(double x) {
        double r312563 = x;
        double r312564 = 2.0;
        double r312565 = r312563 + r312564;
        double r312566 = r312565 * r312563;
        return r312566;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.1

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

  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 2019121 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))