Average Error: 46.0 → 0.4
Time: 2.2m
Precision: 64
Internal Precision: 320
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{1}{\left(2 \cdot 2\right) \cdot \left(2 \cdot 2 - \frac{1.0}{i \cdot i}\right)}\]

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. Using strategy rm

  3. Applied clear-num46.0

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

  4. Applied simplify0.4

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

  5. Applied simplify0.4

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

  6. Applied simplify0.4

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

Runtime

Time bar (total: 2.2m)Debug logProfile

herbie shell --seed 2020178 +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)))