Average Error: 46.0 → 0.1
Time: 1.9m
Precision: 64
Internal Precision: 320
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{i}{2} \cdot 1}{\left(i \cdot 2\right) \cdot \left(2 \cdot 2\right) - \frac{1.0}{\frac{i}{2}}}\]

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.0

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

  2. Applied simplify15.4

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

  4. Applied associate-/l*15.5

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

  5. Applied simplify0.1

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

Runtime

Time bar (total: 1.9m)Debug logProfile

herbie shell --seed 2020178 
(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)))