Average Error: 39.2 → 0.0
Time: 1.5s
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 r2677 = x;
        double r2678 = 1.0;
        double r2679 = r2677 + r2678;
        double r2680 = r2679 * r2679;
        double r2681 = r2680 - r2678;
        return r2681;
}
↓
double f(double x) {
        double r2682 = x;
        double r2683 = 2.0;
        double r2684 = r2682 * r2683;
        double r2685 = 2.0;
        double r2686 = pow(r2682, r2685);
        double r2687 = r2684 + r2686;
        return r2687;
}

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

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

Reproduce

herbie shell --seed 2020020 
(FPCore (x)
  :name "Expanding a square"
  :precision binary64
  (- (* (+ x 1) (+ x 1)) 1))