Average Error: 46.7 → 0.2
Time: 20.5s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[i \cdot \frac{\frac{1}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}\]
\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}
↓
i \cdot \frac{\frac{1}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}
double f(double i) {
        double r59756 = i;
        double r59757 = r59756 * r59756;
        double r59758 = r59757 * r59757;
        double r59759 = 2.0;
        double r59760 = r59759 * r59756;
        double r59761 = r59760 * r59760;
        double r59762 = r59758 / r59761;
        double r59763 = 1.0;
        double r59764 = r59761 - r59763;
        double r59765 = r59762 / r59764;
        return r59765;
}
↓
double f(double i) {
        double r59766 = i;
        double r59767 = 1.0;
        double r59768 = 2.0;
        double r59769 = r59768 * r59768;
        double r59770 = r59767 / r59769;
        double r59771 = r59768 * r59766;
        double r59772 = r59768 * r59771;
        double r59773 = 1.0;
        double r59774 = r59773 / r59766;
        double r59775 = r59772 - r59774;
        double r59776 = r59770 / r59775;
        double r59777 = r59766 * r59776;
        return r59777;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.7

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

  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

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

  5. Applied div-inv0.1

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

  6. Applied times-frac0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 
(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)))