Average Error: 39.4 → 0.0
Time: 4.6s
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 r191523 = x;
        double r191524 = 1.0;
        double r191525 = r191523 + r191524;
        double r191526 = r191525 * r191525;
        double r191527 = r191526 - r191524;
        return r191527;
}
↓
double f(double x) {
        double r191528 = x;
        double r191529 = 2.0;
        double r191530 = r191528 + r191529;
        double r191531 = r191530 * r191528;
        return r191531;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 39.4

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

  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 2019119 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))