Average Error: 39.4 → 0.0
Time: 5.0s
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 r223446 = x;
        double r223447 = 1.0;
        double r223448 = r223446 + r223447;
        double r223449 = r223448 * r223448;
        double r223450 = r223449 - r223447;
        return r223450;
}
↓
double f(double x) {
        double r223451 = x;
        double r223452 = 2.0;
        double r223453 = r223451 + r223452;
        double r223454 = r223453 * r223451;
        return r223454;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.4

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

  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 2019119 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))