Average Error: 39.3 → 0.0
Time: 5.8s
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 r297460 = x;
        double r297461 = 1.0;
        double r297462 = r297460 + r297461;
        double r297463 = r297462 * r297462;
        double r297464 = r297463 - r297461;
        return r297464;
}
↓
double f(double x) {
        double r297465 = x;
        double r297466 = 2.0;
        double r297467 = r297465 + r297466;
        double r297468 = r297467 * r297465;
        return r297468;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Derivation

  1. Initial program 39.3

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

  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 2019104 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))