Average Error: 39.3 → 0.0
Time: 9.8s
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 r341462 = x;
        double r341463 = 1.0;
        double r341464 = r341462 + r341463;
        double r341465 = r341464 * r341464;
        double r341466 = r341465 - r341463;
        return r341466;
}
↓
double f(double x) {
        double r341467 = x;
        double r341468 = r341467 * r341467;
        double r341469 = 2.0;
        double r341470 = r341467 * r341469;
        double r341471 = r341468 + r341470;
        return r341471;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 39.3

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

  2. Simplified0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))