Average Error: 45.6 → 0.3
Time: 27.4s
Precision: 64
Internal Precision: 576
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{1}{16 - \frac{4.0}{i \cdot i}}\]

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.6

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

  2. Initial simplification15.5

    \[\leadsto \frac{\left(\frac{i}{2} \cdot 1\right) \cdot \left(\frac{i}{2} \cdot 1\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
  3. Using strategy rm

  4. Applied clear-num15.8

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}{\left(\frac{i}{2} \cdot 1\right) \cdot \left(\frac{i}{2} \cdot 1\right)}}}\]

  5. Taylor expanded around inf 0.3

    \[\leadsto \frac{1}{\color{blue}{16 - 4.0 \cdot \frac{1}{{i}^{2}}}}\]

  6. Simplified0.3

    \[\leadsto \frac{1}{\color{blue}{16 - \frac{4.0}{i \cdot i}}}\]

  7. Final simplification0.3

    \[\leadsto \frac{1}{16 - \frac{4.0}{i \cdot i}}\]

Runtime

Time bar (total: 27.4s)Debug logProfile

herbie shell --seed 2018225 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0)))