Average Error: 39.2 → 0.0
Time: 13.0s
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 r344380 = x;
        double r344381 = 1.0;
        double r344382 = r344380 + r344381;
        double r344383 = r344382 * r344382;
        double r344384 = r344383 - r344381;
        return r344384;
}
↓
double f(double x) {
        double r344385 = x;
        double r344386 = r344385 * r344385;
        double r344387 = 2.0;
        double r344388 = r344387 * r344385;
        double r344389 = r344386 + r344388;
        return r344389;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 39.2

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

  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 2019144 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))