Average Error: 39.4 → 0.0
Time: 3.6s
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 r173521 = x;
        double r173522 = 1.0;
        double r173523 = r173521 + r173522;
        double r173524 = r173523 * r173523;
        double r173525 = r173524 - r173522;
        return r173525;
}
↓
double f(double x) {
        double r173526 = x;
        double r173527 = r173526 * r173526;
        double r173528 = 2.0;
        double r173529 = r173526 * r173528;
        double r173530 = r173527 + r173529;
        return r173530;
}

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-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

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