Average Error: 46.4 → 0.5
Time: 14.7s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\sqrt{\frac{i}{2 \cdot 2}} \cdot \frac{\sqrt{\frac{i}{2 \cdot 2}}}{\left(i \cdot 2\right) \cdot 2 - \frac{1}{i}}\]
\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}
↓
\sqrt{\frac{i}{2 \cdot 2}} \cdot \frac{\sqrt{\frac{i}{2 \cdot 2}}}{\left(i \cdot 2\right) \cdot 2 - \frac{1}{i}}
double f(double i) {
        double r57757 = i;
        double r57758 = r57757 * r57757;
        double r57759 = r57758 * r57758;
        double r57760 = 2.0;
        double r57761 = r57760 * r57757;
        double r57762 = r57761 * r57761;
        double r57763 = r57759 / r57762;
        double r57764 = 1.0;
        double r57765 = r57762 - r57764;
        double r57766 = r57763 / r57765;
        return r57766;
}
↓
double f(double i) {
        double r57767 = i;
        double r57768 = 2.0;
        double r57769 = r57768 * r57768;
        double r57770 = r57767 / r57769;
        double r57771 = sqrt(r57770);
        double r57772 = r57767 * r57768;
        double r57773 = r57772 * r57768;
        double r57774 = 1.0;
        double r57775 = r57774 / r57767;
        double r57776 = r57773 - r57775;
        double r57777 = r57771 / r57776;
        double r57778 = r57771 * r57777;
        return r57778;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.4

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

  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 add-sqr-sqrt0.5

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

  6. Applied times-frac0.5

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

  7. Simplified0.5

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

  8. Simplified0.5

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

  9. Final simplification0.5

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

Reproduce

herbie shell --seed 2019179 
(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)))