Average Error: 47.1 → 0.2
Time: 8.6s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(2 \cdot 2\right) \cdot \left(\left(2 \cdot 2\right) \cdot i - \frac{1}{i}\right)}\]
\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{i}{\left(2 \cdot 2\right) \cdot \left(\left(2 \cdot 2\right) \cdot i - \frac{1}{i}\right)}
double f(double i) {
        double r49791 = i;
        double r49792 = r49791 * r49791;
        double r49793 = r49792 * r49792;
        double r49794 = 2.0;
        double r49795 = r49794 * r49791;
        double r49796 = r49795 * r49795;
        double r49797 = r49793 / r49796;
        double r49798 = 1.0;
        double r49799 = r49796 - r49798;
        double r49800 = r49797 / r49799;
        return r49800;
}
↓
double f(double i) {
        double r49801 = i;
        double r49802 = 2.0;
        double r49803 = r49802 * r49802;
        double r49804 = r49803 * r49801;
        double r49805 = 1.0;
        double r49806 = r49805 / r49801;
        double r49807 = r49804 - r49806;
        double r49808 = r49803 * r49807;
        double r49809 = r49801 / r49808;
        return r49809;
}

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. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 
(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)))