Average Error: 46.2 → 0.2
Time: 1.5m
Precision: 64
Internal Precision: 320
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{1}{2} \cdot i}{\left(2 \cdot 2\right) \cdot \left(i \cdot 2\right) - 2 \cdot \frac{1.0}{i}}\]

Error

Bits error versus i

Derivation

  1. Initial program 46.2

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

  2. Applied simplify15.9

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

  4. Applied associate-/l*16.0

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

  5. Applied simplify0.2

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

Runtime

Time bar (total: 1.5m)Debug logProfile

herbie shell --seed '#(1071725047 233389029 2036512464 3988615230 2972226563 1111574017)' 
(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)))