Average Error: 46.3 → 0.1
Time: 12.5s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{\left(2 \cdot 2\right) \cdot i - \frac{1}{i}}\]
\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{\frac{i}{2 \cdot 2}}{\left(2 \cdot 2\right) \cdot i - \frac{1}{i}}
double f(double i) {
        double r86034 = i;
        double r86035 = r86034 * r86034;
        double r86036 = r86035 * r86035;
        double r86037 = 2.0;
        double r86038 = r86037 * r86034;
        double r86039 = r86038 * r86038;
        double r86040 = r86036 / r86039;
        double r86041 = 1.0;
        double r86042 = r86039 - r86041;
        double r86043 = r86040 / r86042;
        return r86043;
}
↓
double f(double i) {
        double r86044 = i;
        double r86045 = 2.0;
        double r86046 = r86045 * r86045;
        double r86047 = r86044 / r86046;
        double r86048 = r86046 * r86044;
        double r86049 = 1.0;
        double r86050 = r86049 / r86044;
        double r86051 = r86048 - r86050;
        double r86052 = r86047 / r86051;
        return r86052;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.3

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

  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. Using strategy rm

  4. Applied associate-/r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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)))