Average Error: 39.2 → 0.0
Time: 8.1s
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 r25515 = x;
        double r25516 = 1.0;
        double r25517 = r25515 + r25516;
        double r25518 = r25517 * r25517;
        double r25519 = r25518 - r25516;
        return r25519;
}
↓
double f(double x) {
        double r25520 = x;
        double r25521 = 2.0;
        double r25522 = r25521 + r25520;
        double r25523 = r25520 * r25522;
        return r25523;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.2

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

  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 2019212 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))