Average Error: 38.6 → 0.0
Time: 1.1s
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 r1283 = x;
        double r1284 = 1.0;
        double r1285 = r1283 + r1284;
        double r1286 = r1285 * r1285;
        double r1287 = r1286 - r1284;
        return r1287;
}
↓
double f(double x) {
        double r1288 = x;
        double r1289 = 2.0;
        double r1290 = r1289 + r1288;
        double r1291 = r1288 * r1290;
        return r1291;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.6

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

  2. Taylor expanded around 0 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020064 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))