Average Error: 46.5 → 0.1
Time: 1.5s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{16 \cdot i - 4 \cdot \frac{1}{i}}\]
\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{i}{16 \cdot i - 4 \cdot \frac{1}{i}}
double f(double i) {
        double r36923 = i;
        double r36924 = r36923 * r36923;
        double r36925 = r36924 * r36924;
        double r36926 = 2.0;
        double r36927 = r36926 * r36923;
        double r36928 = r36927 * r36927;
        double r36929 = r36925 / r36928;
        double r36930 = 1.0;
        double r36931 = r36928 - r36930;
        double r36932 = r36929 / r36931;
        return r36932;
}
↓
double f(double i) {
        double r36933 = i;
        double r36934 = 16.0;
        double r36935 = r36934 * r36933;
        double r36936 = 4.0;
        double r36937 = 1.0;
        double r36938 = r36937 / r36933;
        double r36939 = r36936 * r36938;
        double r36940 = r36935 - r36939;
        double r36941 = r36933 / r36940;
        return r36941;
}

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. Simplified15.9

    \[\leadsto \color{blue}{\frac{i \cdot i}{\left(\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1\right) \cdot \left(2 \cdot 2\right)}}\]
  3. Using strategy rm

  4. Applied associate-/l*15.5

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

  5. Taylor expanded around 0 0.1

    \[\leadsto \frac{i}{\color{blue}{16 \cdot i - 4 \cdot \frac{1}{i}}}\]

  6. Final simplification0.1

    \[\leadsto \frac{i}{16 \cdot i - 4 \cdot \frac{1}{i}}\]

Reproduce

herbie shell --seed 2020027 
(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)))