Average Error: 45.7 → 0.1
Time: 17.4s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{1}{4}}{2 - \frac{\sqrt{1.0}}{i}} \cdot \frac{1}{2 + \frac{\sqrt{1.0}}{i}}\]
\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) - 1.0}
↓
\frac{\frac{1}{4}}{2 - \frac{\sqrt{1.0}}{i}} \cdot \frac{1}{2 + \frac{\sqrt{1.0}}{i}}
double f(double i) {
        double r2196877 = i;
        double r2196878 = r2196877 * r2196877;
        double r2196879 = r2196878 * r2196878;
        double r2196880 = 2.0;
        double r2196881 = r2196880 * r2196877;
        double r2196882 = r2196881 * r2196881;
        double r2196883 = r2196879 / r2196882;
        double r2196884 = 1.0;
        double r2196885 = r2196882 - r2196884;
        double r2196886 = r2196883 / r2196885;
        return r2196886;
}
↓
double f(double i) {
        double r2196887 = 0.25;
        double r2196888 = 2.0;
        double r2196889 = 1.0;
        double r2196890 = sqrt(r2196889);
        double r2196891 = i;
        double r2196892 = r2196890 / r2196891;
        double r2196893 = r2196888 - r2196892;
        double r2196894 = r2196887 / r2196893;
        double r2196895 = 1.0;
        double r2196896 = r2196888 + r2196892;
        double r2196897 = r2196895 / r2196896;
        double r2196898 = r2196894 * r2196897;
        return r2196898;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.7

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.3

    \[\leadsto \frac{\frac{1}{4}}{4 - \frac{\color{blue}{\sqrt{1.0} \cdot \sqrt{1.0}}}{i \cdot i}}\]

  5. Applied times-frac0.4

    \[\leadsto \frac{\frac{1}{4}}{4 - \color{blue}{\frac{\sqrt{1.0}}{i} \cdot \frac{\sqrt{1.0}}{i}}}\]

  6. Applied add-sqr-sqrt0.4

    \[\leadsto \frac{\frac{1}{4}}{\color{blue}{\sqrt{4} \cdot \sqrt{4}} - \frac{\sqrt{1.0}}{i} \cdot \frac{\sqrt{1.0}}{i}}\]

  7. Applied difference-of-squares0.4

    \[\leadsto \frac{\frac{1}{4}}{\color{blue}{\left(\sqrt{4} + \frac{\sqrt{1.0}}{i}\right) \cdot \left(\sqrt{4} - \frac{\sqrt{1.0}}{i}\right)}}\]

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

    \[\leadsto \frac{\color{blue}{1 \cdot \frac{1}{4}}}{\left(\sqrt{4} + \frac{\sqrt{1.0}}{i}\right) \cdot \left(\sqrt{4} - \frac{\sqrt{1.0}}{i}\right)}\]

  9. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1}{\sqrt{4} + \frac{\sqrt{1.0}}{i}} \cdot \frac{\frac{1}{4}}{\sqrt{4} - \frac{\sqrt{1.0}}{i}}}\]

  10. Final simplification0.1

    \[\leadsto \frac{\frac{1}{4}}{2 - \frac{\sqrt{1.0}}{i}} \cdot \frac{1}{2 + \frac{\sqrt{1.0}}{i}}\]

Reproduce

herbie shell --seed 2019130 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0)))