Average Error: 46.7 → 0.1
Time: 3.0s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{2 \cdot i + \sqrt{1}} \cdot \left(\frac{i}{2 \cdot i - \sqrt{1}} \cdot \frac{i}{2 \cdot 2}\right)\]
\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{1}{2 \cdot i + \sqrt{1}} \cdot \left(\frac{i}{2 \cdot i - \sqrt{1}} \cdot \frac{i}{2 \cdot 2}\right)
double f(double i) {
        double r97733 = i;
        double r97734 = r97733 * r97733;
        double r97735 = r97734 * r97734;
        double r97736 = 2.0;
        double r97737 = r97736 * r97733;
        double r97738 = r97737 * r97737;
        double r97739 = r97735 / r97738;
        double r97740 = 1.0;
        double r97741 = r97738 - r97740;
        double r97742 = r97739 / r97741;
        return r97742;
}
↓
double f(double i) {
        double r97743 = 1.0;
        double r97744 = 2.0;
        double r97745 = i;
        double r97746 = r97744 * r97745;
        double r97747 = 1.0;
        double r97748 = sqrt(r97747);
        double r97749 = r97746 + r97748;
        double r97750 = r97743 / r97749;
        double r97751 = r97746 - r97748;
        double r97752 = r97745 / r97751;
        double r97753 = r97744 * r97744;
        double r97754 = r97745 / r97753;
        double r97755 = r97752 * r97754;
        double r97756 = r97750 * r97755;
        return r97756;
}

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. 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 times-frac15.5

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

  6. Applied add-sqr-sqrt15.5

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

  7. Applied difference-of-squares15.5

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

  8. Applied *-un-lft-identity15.5

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

  9. Applied times-frac0.1

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

  10. Applied associate-*l*0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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)))