Error

Derivation

1. Split input into 2 regimes

2. if i < 240.0194711557849

   1. Initial program 44.0

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

   2. Applied simplify0.0

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

   4. Applied *-un-lft-identity0.0

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

   5. Applied times-frac0.0

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

   6. Applied simplify0.0

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

   if 240.0194711557849 < i

   1. Initial program 47.6

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

   2. Applied simplify32.6

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

   3. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{0.00390625 \cdot \frac{1}{{i}^{4}} + \left(\frac{1}{16} + 0.015625 \cdot \frac{1}{{i}^{2}}\right)}\]

   4. Applied simplify0.0

      \[\leadsto \color{blue}{\left(\frac{0.00390625}{{i}^{4}} + \frac{\frac{0.015625}{i}}{i}\right) + \frac{1}{16}}\]
3. Recombined 2 regimes into one program.
4. Removed slow pow expressions.

Runtime

Time bar (total: 2.3m)Debug logProfile

herbie shell --seed '#(1063185673 2139736501 2393378123 1907444849 1070993796 1007244912)' 
(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)))