Average Error: 39.0 → 0.0
Time: 15.3s
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 r292643 = x;
        double r292644 = 1.0;
        double r292645 = r292643 + r292644;
        double r292646 = r292645 * r292645;
        double r292647 = r292646 - r292644;
        return r292647;
}
↓
double f(double x) {
        double r292648 = x;
        double r292649 = 2.0;
        double r292650 = r292648 + r292649;
        double r292651 = r292650 * r292648;
        return r292651;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.0

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

  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 2019138 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))