Average Error: 38.8 → 0.0
Time: 9.7s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot x + x \cdot 2\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot x + x \cdot 2
double f(double x) {
        double r341433 = x;
        double r341434 = 1.0;
        double r341435 = r341433 + r341434;
        double r341436 = r341435 * r341435;
        double r341437 = r341436 - r341434;
        return r341437;
}
↓
double f(double x) {
        double r341438 = x;
        double r341439 = r341438 * r341438;
        double r341440 = 2.0;
        double r341441 = r341438 * r341440;
        double r341442 = r341439 + r341441;
        return r341442;
}

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. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(x + 2\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

    \[\leadsto x \cdot x + x \cdot 2\]

Reproduce

herbie shell --seed 2019133 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))