Average Error: 39.2 → 0.0
Time: 10.8s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[\left(x + 2\right) \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
\left(x + 2\right) \cdot x
double f(double x) {
        double r804589 = x;
        double r804590 = 1.0;
        double r804591 = r804589 + r804590;
        double r804592 = r804591 * r804591;
        double r804593 = r804592 - r804590;
        return r804593;
}
↓
double f(double x) {
        double r804594 = x;
        double r804595 = 2.0;
        double r804596 = r804594 + r804595;
        double r804597 = r804596 * r804594;
        return r804597;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 39.2

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

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(2 + x\right) \cdot x}\]

  3. Final simplification0.0

    \[\leadsto \left(x + 2\right) \cdot x\]

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))