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 r61034 = i;
        double r61035 = r61034 * r61034;
        double r61036 = r61035 * r61035;
        double r61037 = 2.0;
        double r61038 = r61037 * r61034;
        double r61039 = r61038 * r61038;
        double r61040 = r61036 / r61039;
        double r61041 = 1.0;
        double r61042 = r61039 - r61041;
        double r61043 = r61040 / r61042;
        return r61043;
}
↓
double f(double i) {
        double r61044 = 1.0;
        double r61045 = 2.0;
        double r61046 = r61045 * r61045;
        double r61047 = 1.0;
        double r61048 = i;
        double r61049 = r61048 * r61048;
        double r61050 = r61047 / r61049;
        double r61051 = r61046 - r61050;
        double r61052 = r61051 * r61046;
        double r61053 = r61044 / r61052;
        return r61053;
}

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)))