Average Error: 47.0 → 0.1
Time: 12.0s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{4 \cdot i - \frac{1}{i}}\]
\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}
↓
\frac{\frac{i}{2 \cdot 2}}{4 \cdot i - \frac{1}{i}}
double f(double i) {
        double r47470 = i;
        double r47471 = r47470 * r47470;
        double r47472 = r47471 * r47471;
        double r47473 = 2.0;
        double r47474 = r47473 * r47470;
        double r47475 = r47474 * r47474;
        double r47476 = r47472 / r47475;
        double r47477 = 1.0;
        double r47478 = r47475 - r47477;
        double r47479 = r47476 / r47478;
        return r47479;
}
↓
double f(double i) {
        double r47480 = i;
        double r47481 = 2.0;
        double r47482 = r47481 * r47481;
        double r47483 = r47480 / r47482;
        double r47484 = 4.0;
        double r47485 = r47484 * r47480;
        double r47486 = 1.0;
        double r47487 = r47486 / r47480;
        double r47488 = r47485 - r47487;
        double r47489 = r47483 / r47488;
        return r47489;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 47.0

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}}\]

  3. Taylor expanded around 0 0.1

    \[\leadsto \frac{\frac{i}{2 \cdot 2}}{\color{blue}{4 \cdot i - 1 \cdot \frac{1}{i}}}\]

  4. Simplified0.1

    \[\leadsto \frac{\frac{i}{2 \cdot 2}}{\color{blue}{i \cdot 4 - \frac{1}{i}}}\]

  5. Final simplification0.1

    \[\leadsto \frac{\frac{i}{2 \cdot 2}}{4 \cdot i - \frac{1}{i}}\]

Reproduce

herbie shell --seed 2019196 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0)))