Average Error: 38.9 → 0.0
Time: 2.1s
Precision: 64
\[\left(x + 1\right) \cdot \left(x + 1\right) - 1\]
↓
\[x \cdot 2 + {x}^{2}\]
\left(x + 1\right) \cdot \left(x + 1\right) - 1
↓
x \cdot 2 + {x}^{2}
double f(double x) {
        double r7851 = x;
        double r7852 = 1.0;
        double r7853 = r7851 + r7852;
        double r7854 = r7853 * r7853;
        double r7855 = r7854 - r7852;
        return r7855;
}
↓
double f(double x) {
        double r7856 = x;
        double r7857 = 2.0;
        double r7858 = r7856 * r7857;
        double r7859 = 2.0;
        double r7860 = pow(r7856, r7859);
        double r7861 = r7858 + r7860;
        return r7861;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 38.9

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

  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

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

Reproduce

herbie shell --seed 2020056 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))