Average Error: 39.1 → 0.0
Time: 1.7s
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 r15746 = x;
        double r15747 = 1.0;
        double r15748 = r15746 + r15747;
        double r15749 = r15748 * r15748;
        double r15750 = r15749 - r15747;
        return r15750;
}
↓
double f(double x) {
        double r15751 = x;
        double r15752 = 2.0;
        double r15753 = r15751 + r15752;
        double r15754 = r15753 * r15751;
        return r15754;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.1

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

  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 2019128 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))