Average Error: 47.1 → 0.1
Time: 13.5s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{2 \cdot \left(i \cdot 2\right) - \frac{1}{i}}\]
\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}}{2 \cdot \left(i \cdot 2\right) - \frac{1}{i}}
double f(double i) {
        double r47381 = i;
        double r47382 = r47381 * r47381;
        double r47383 = r47382 * r47382;
        double r47384 = 2.0;
        double r47385 = r47384 * r47381;
        double r47386 = r47385 * r47385;
        double r47387 = r47383 / r47386;
        double r47388 = 1.0;
        double r47389 = r47386 - r47388;
        double r47390 = r47387 / r47389;
        return r47390;
}
↓
double f(double i) {
        double r47391 = i;
        double r47392 = 2.0;
        double r47393 = r47392 * r47392;
        double r47394 = r47391 / r47393;
        double r47395 = r47391 * r47392;
        double r47396 = r47392 * r47395;
        double r47397 = 1.0;
        double r47398 = r47397 / r47391;
        double r47399 = r47396 - r47398;
        double r47400 = r47394 / r47399;
        return r47400;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 47.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019194 
(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)))