Average Error: 45.4 → 0.1
Time: 1.7m
Precision: 64
Internal Precision: 384
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{i}{2}}{8 \cdot i - \frac{2.0}{i}}\]

Error

Bits error versus i

Derivation

  1. Initial program 45.4

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

  2. Applied simplify15.5

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

  3. Taylor expanded around 0 0.1

    \[\leadsto \frac{\frac{i}{\frac{2}{1}}}{\color{blue}{8 \cdot i - 2.0 \cdot \frac{1}{i}}}\]

  4. Applied simplify0.1

    \[\leadsto \color{blue}{\frac{\frac{i}{2}}{8 \cdot i - \frac{2.0}{i}}}\]

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed '#(1070609872 3456127585 2380521889 2328837196 1765472538 734540918)' +o rules:numerics
(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)))