Average Error: 38.5 → 0.0
Time: 9.4s
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 r326411 = x;
        double r326412 = 1.0;
        double r326413 = r326411 + r326412;
        double r326414 = r326413 * r326413;
        double r326415 = r326414 - r326412;
        return r326415;
}
↓
double f(double x) {
        double r326416 = x;
        double r326417 = r326416 * r326416;
        double r326418 = 2.0;
        double r326419 = r326418 * r326416;
        double r326420 = r326417 + r326419;
        return r326420;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 38.5

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

  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 2019129 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))