Average Error: 39.2 → 0.0
Time: 5.8s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot \left(x + 2\right)\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot \left(x + 2\right)
double f(double x) {
        double r10859 = x;
        double r10860 = 1.0;
        double r10861 = r10859 + r10860;
        double r10862 = r10861 * r10861;
        double r10863 = r10862 - r10860;
        return r10863;
}
↓
double f(double x) {
        double r10864 = x;
        double r10865 = 2.0;
        double r10866 = r10864 + r10865;
        double r10867 = r10864 * r10866;
        return r10867;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 39.2

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

  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. Using strategy rm

  5. Applied distribute-lft-in0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))