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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 simplification15.4

   \[\leadsto \frac{i \cdot \frac{i}{4}}{i \cdot \left(4 \cdot i\right) - 1.0}\]
3. Using strategy rm

4. Applied clear-num15.8

   \[\leadsto \color{blue}{\frac{1}{\frac{i \cdot \left(4 \cdot i\right) - 1.0}{i \cdot \frac{i}{4}}}}\]

5. Taylor expanded around -inf 0.4

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

6. Simplified0.4

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

7. Final simplification0.4

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

Runtime

Time bar (total: 23.6s)Debug logProfile

herbie shell --seed 2018352 
(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)))