Average Error: 39.8 → 0.0
Time: 11.3s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot x + 2 \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot x + 2 \cdot x
double f(double x) {
        double r258346 = x;
        double r258347 = 1.0;
        double r258348 = r258346 + r258347;
        double r258349 = r258348 * r258348;
        double r258350 = r258349 - r258347;
        return r258350;
}
↓
double f(double x) {
        double r258351 = x;
        double r258352 = r258351 * r258351;
        double r258353 = 2.0;
        double r258354 = r258353 * r258351;
        double r258355 = r258352 + r258354;
        return r258355;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 39.8

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

  2. Simplified0.0

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

  4. Applied distribute-rgt-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019146 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))