Average Error: 39.4 → 0.0
Time: 3.8s
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 r163004 = x;
        double r163005 = 1.0;
        double r163006 = r163004 + r163005;
        double r163007 = r163006 * r163006;
        double r163008 = r163007 - r163005;
        return r163008;
}
↓
double f(double x) {
        double r163009 = x;
        double r163010 = r163009 * r163009;
        double r163011 = 2.0;
        double r163012 = r163009 * r163011;
        double r163013 = r163010 + r163012;
        return r163013;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 39.4

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

  2. Simplified0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))