Average Error: 47.1 → 0.2
Time: 10.3s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(\left(2 \cdot 2\right) \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}\]
\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(\left(2 \cdot 2\right) \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r51817 = i;
        double r51818 = r51817 * r51817;
        double r51819 = r51818 * r51818;
        double r51820 = 2.0;
        double r51821 = r51820 * r51817;
        double r51822 = r51821 * r51821;
        double r51823 = r51819 / r51822;
        double r51824 = 1.0;
        double r51825 = r51822 - r51824;
        double r51826 = r51823 / r51825;
        return r51826;
}
↓
double f(double i) {
        double r51827 = i;
        double r51828 = 2.0;
        double r51829 = r51828 * r51828;
        double r51830 = r51829 * r51827;
        double r51831 = 1.0;
        double r51832 = r51831 / r51827;
        double r51833 = r51830 - r51832;
        double r51834 = r51833 * r51829;
        double r51835 = r51827 / r51834;
        return r51835;
}

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

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2020047 +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)))