Average Error: 38.8 → 0.0
Time: 4.5s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(2 + x\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot \left(2 + x\right)
double f(double x) {
        double r10547 = x;
        double r10548 = 1.0;
        double r10549 = r10547 + r10548;
        double r10550 = r10549 * r10549;
        double r10551 = r10550 - r10548;
        return r10551;
}
↓
double f(double x) {
        double r10552 = x;
        double r10553 = 2.0;
        double r10554 = r10553 + r10552;
        double r10555 = r10552 * r10554;
        return r10555;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.8

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

  2. Simplified38.8

    \[\leadsto \color{blue}{\mathsf{fma}\left(1 + x, 1 + x, -1\right)}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2 \cdot x + {x}^{2}}\]

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1.0) (+ x 1.0)) 1.0))