Average Error: 38.9 → 0.0
Time: 8.6s
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 r892631 = x;
        double r892632 = 1.0;
        double r892633 = r892631 + r892632;
        double r892634 = r892633 * r892633;
        double r892635 = r892634 - r892632;
        return r892635;
}
↓
double f(double x) {
        double r892636 = x;
        double r892637 = r892636 * r892636;
        double r892638 = 2.0;
        double r892639 = r892636 * r892638;
        double r892640 = r892637 + r892639;
        return r892640;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 38.9

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

  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 2019168 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))