Average Error: 46.7 → 0.4
Time: 16.4s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{\left(2 \cdot 2 - \frac{\frac{1}{i}}{i}\right) \cdot \left(2 \cdot 2\right)}\]
\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{1}{\left(2 \cdot 2 - \frac{\frac{1}{i}}{i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r47202 = i;
        double r47203 = r47202 * r47202;
        double r47204 = r47203 * r47203;
        double r47205 = 2.0;
        double r47206 = r47205 * r47202;
        double r47207 = r47206 * r47206;
        double r47208 = r47204 / r47207;
        double r47209 = 1.0;
        double r47210 = r47207 - r47209;
        double r47211 = r47208 / r47210;
        return r47211;
}
↓
double f(double i) {
        double r47212 = 1.0;
        double r47213 = 2.0;
        double r47214 = r47213 * r47213;
        double r47215 = 1.0;
        double r47216 = i;
        double r47217 = r47215 / r47216;
        double r47218 = r47217 / r47216;
        double r47219 = r47214 - r47218;
        double r47220 = r47219 * r47214;
        double r47221 = r47212 / r47220;
        return r47221;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.7

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

  2. Simplified0.4

    \[\leadsto \color{blue}{\frac{1}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot \left(2 \cdot 2\right)}}\]
  3. Using strategy rm

  4. Applied associate-/r*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :precision binary64
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1)))