Average Error: 46.5 → 0.3
Time: 15.5s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot \left(2 \cdot 2\right)}\]
\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{1}{i \cdot i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r43407 = i;
        double r43408 = r43407 * r43407;
        double r43409 = r43408 * r43408;
        double r43410 = 2.0;
        double r43411 = r43410 * r43407;
        double r43412 = r43411 * r43411;
        double r43413 = r43409 / r43412;
        double r43414 = 1.0;
        double r43415 = r43412 - r43414;
        double r43416 = r43413 / r43415;
        return r43416;
}
↓
double f(double i) {
        double r43417 = 1.0;
        double r43418 = 2.0;
        double r43419 = r43418 * r43418;
        double r43420 = 1.0;
        double r43421 = i;
        double r43422 = r43421 * r43421;
        double r43423 = r43420 / r43422;
        double r43424 = r43419 - r43423;
        double r43425 = r43424 * r43419;
        double r43426 = r43417 / r43425;
        return r43426;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.5

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

  2. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019323 +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)))