Average Error: 46.2 → 0.1
Time: 5.1s
Precision: binary64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2}}{2 \cdot i + \sqrt{1}} \cdot \frac{\frac{i}{2 \cdot i - \sqrt{1}}}{2}\]
\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{i}{2}}{2 \cdot i + \sqrt{1}} \cdot \frac{\frac{i}{2 \cdot i - \sqrt{1}}}{2}
double code(double i) {
	return ((((double) (((double) (i * i)) * ((double) (i * i)))) / ((double) (((double) (2.0 * i)) * ((double) (2.0 * i))))) / ((double) (((double) (((double) (2.0 * i)) * ((double) (2.0 * i)))) - 1.0)));
}
↓
double code(double i) {
	return ((double) (((i / 2.0) / ((double) (((double) (2.0 * i)) + ((double) sqrt(1.0))))) * ((i / ((double) (((double) (2.0 * i)) - ((double) sqrt(1.0))))) / 2.0)));
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.2

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

  2. Simplified15.1

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

  4. Applied *-un-lft-identity15.1

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

  5. Applied add-sqr-sqrt15.1

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

  6. Applied difference-of-squares15.1

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

  7. Applied *-un-lft-identity15.1

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

  8. Applied times-frac0.1

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

  9. Applied times-frac0.1

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

  10. Applied associate-*r*0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020182 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :precision binary64
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0)))