Average Error: 46.7 → 0.5
Time: 1.7s
Precision: binary64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{16 - 4 \cdot \frac{\frac{1}{i}}{{\left(\sqrt{i}\right)}^{2}}}\]
\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{1}{16 - 4 \cdot \frac{\frac{1}{i}}{{\left(\sqrt{i}\right)}^{2}}}
double code(double i) {
	return ((double) (((double) (((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) (1.0 / ((double) (16.0 - ((double) (4.0 * ((double) (((double) (1.0 / i)) / ((double) pow(((double) sqrt(i)), 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 46.7

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

  2. Simplified16.2

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

  4. Applied clear-num16.5

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

  5. Taylor expanded around 0 0.3

    \[\leadsto \frac{1}{\color{blue}{16 - 4 \cdot \frac{1}{{i}^{2}}}}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt0.5

    \[\leadsto \frac{1}{16 - 4 \cdot \frac{1}{{\color{blue}{\left(\sqrt{i} \cdot \sqrt{i}\right)}}^{2}}}\]

  8. Applied unpow-prod-down0.5

    \[\leadsto \frac{1}{16 - 4 \cdot \frac{1}{\color{blue}{{\left(\sqrt{i}\right)}^{2} \cdot {\left(\sqrt{i}\right)}^{2}}}}\]

  9. Applied associate-/r*0.5

    \[\leadsto \frac{1}{16 - 4 \cdot \color{blue}{\frac{\frac{1}{{\left(\sqrt{i}\right)}^{2}}}{{\left(\sqrt{i}\right)}^{2}}}}\]

  10. Simplified0.5

    \[\leadsto \frac{1}{16 - 4 \cdot \frac{\color{blue}{\frac{1}{i}}}{{\left(\sqrt{i}\right)}^{2}}}\]

  11. Final simplification0.5

    \[\leadsto \frac{1}{16 - 4 \cdot \frac{\frac{1}{i}}{{\left(\sqrt{i}\right)}^{2}}}\]

Reproduce

herbie shell --seed 2020153 
(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)))