Average Error: 39.6 → 0.0
Time: 9.4s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[\left(x + x\right) + x \cdot x\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
\left(x + x\right) + x \cdot x
double f(double x) {
        double r531603 = x;
        double r531604 = 1.0;
        double r531605 = r531603 + r531604;
        double r531606 = r531605 * r531605;
        double r531607 = r531606 - r531604;
        return r531607;
}
↓
double f(double x) {
        double r531608 = x;
        double r531609 = r531608 + r531608;
        double r531610 = r531608 * r531608;
        double r531611 = r531609 + r531610;
        return r531611;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.6

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

  2. Simplified0.0

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

  4. Applied associate-+r+0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))