Average Error: 46.3 → 0.5
Time: 8.3s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{1}{2}}{2 \cdot \frac{2 \cdot \left(i \cdot 2\right) - \frac{1}{i}}{i}}\]
\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{1}{2}}{2 \cdot \frac{2 \cdot \left(i \cdot 2\right) - \frac{1}{i}}{i}}
double f(double i) {
        double r61904 = i;
        double r61905 = r61904 * r61904;
        double r61906 = r61905 * r61905;
        double r61907 = 2.0;
        double r61908 = r61907 * r61904;
        double r61909 = r61908 * r61908;
        double r61910 = r61906 / r61909;
        double r61911 = 1.0;
        double r61912 = r61909 - r61911;
        double r61913 = r61910 / r61912;
        return r61913;
}
↓
double f(double i) {
        double r61914 = 1.0;
        double r61915 = 2.0;
        double r61916 = r61914 / r61915;
        double r61917 = i;
        double r61918 = r61917 * r61915;
        double r61919 = r61915 * r61918;
        double r61920 = 1.0;
        double r61921 = r61920 / r61917;
        double r61922 = r61919 - r61921;
        double r61923 = r61922 / r61917;
        double r61924 = r61915 * r61923;
        double r61925 = r61916 / r61924;
        return r61925;
}

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. Simplified0.1

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

  4. Applied *-un-lft-identity0.1

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

  5. Applied times-frac0.1

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

  6. Applied associate-/l*0.5

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

  7. Simplified0.5

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

  8. Final simplification0.5

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

Reproduce

herbie shell --seed 2019174 
(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)))