Average Error: 38.3 → 0.0
Time: 13.2s
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 r356533 = x;
        double r356534 = 1.0;
        double r356535 = r356533 + r356534;
        double r356536 = r356535 * r356535;
        double r356537 = r356536 - r356534;
        return r356537;
}
↓
double f(double x) {
        double r356538 = x;
        double r356539 = 2.0;
        double r356540 = r356539 + r356538;
        double r356541 = r356538 * r356540;
        return r356541;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.3

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(FPCore (x)
  :name "Expanding a square"
  (- (* (+ x 1) (+ x 1)) 1))