Average Error: 39.0 → 0.0
Time: 15.2s
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 r924509 = x;
        double r924510 = 1.0;
        double r924511 = r924509 + r924510;
        double r924512 = r924511 * r924511;
        double r924513 = r924512 - r924510;
        return r924513;
}
↓
double f(double x) {
        double r924514 = x;
        double r924515 = 2.0;
        double r924516 = r924514 + r924515;
        double r924517 = r924516 * r924514;
        return r924517;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 39.0

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

  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 2019120 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))