Average Error: 46.7 → 0.2
Time: 16.6s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}\]
\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{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r3834681 = i;
        double r3834682 = r3834681 * r3834681;
        double r3834683 = r3834682 * r3834682;
        double r3834684 = 2.0;
        double r3834685 = r3834684 * r3834681;
        double r3834686 = r3834685 * r3834685;
        double r3834687 = r3834683 / r3834686;
        double r3834688 = 1.0;
        double r3834689 = r3834686 - r3834688;
        double r3834690 = r3834687 / r3834689;
        return r3834690;
}
↓
double f(double i) {
        double r3834691 = i;
        double r3834692 = 4.0;
        double r3834693 = r3834692 * r3834691;
        double r3834694 = 1.0;
        double r3834695 = r3834694 / r3834691;
        double r3834696 = r3834693 - r3834695;
        double r3834697 = 2.0;
        double r3834698 = r3834697 * r3834697;
        double r3834699 = r3834696 * r3834698;
        double r3834700 = r3834691 / r3834699;
        return r3834700;
}

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. Simplified0.2

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

  3. Taylor expanded around 0 0.2

    \[\leadsto \frac{i}{\left(2 \cdot 2\right) \cdot \color{blue}{\left(4 \cdot i - 1 \cdot \frac{1}{i}\right)}}\]

  4. Simplified0.2

    \[\leadsto \frac{i}{\left(2 \cdot 2\right) \cdot \color{blue}{\left(4 \cdot i - \frac{1}{i}\right)}}\]

  5. Final simplification0.2

    \[\leadsto \frac{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}\]

Reproduce

herbie shell --seed 2019172 
(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)))