Average Error: 38.8 → 0.0
Time: 56.3s
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 r9592489 = x;
        double r9592490 = 1.0;
        double r9592491 = r9592489 + r9592490;
        double r9592492 = r9592491 * r9592491;
        double r9592493 = r9592492 - r9592490;
        return r9592493;
}
↓
double f(double x) {
        double r9592494 = x;
        double r9592495 = 2.0;
        double r9592496 = r9592494 + r9592495;
        double r9592497 = r9592496 * r9592494;
        return r9592497;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 38.8

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

  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 2019107 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))