Average Error: 46.1 → 0.4
Time: 27.6s
Precision: 64
Internal Precision: 128
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{1}{\frac{i \cdot 4 - \frac{1.0}{i}}{\frac{i}{4}}}\]

Error

Bits error versus i

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.1

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

  2. Initial simplification15.7

    \[\leadsto \frac{i \cdot \frac{i}{4}}{i \cdot \left(4 \cdot i\right) - 1.0}\]
  3. Using strategy rm

  4. Applied associate-/l*15.8

    \[\leadsto \color{blue}{\frac{i}{\frac{i \cdot \left(4 \cdot i\right) - 1.0}{\frac{i}{4}}}}\]
  5. Using strategy rm

  6. Applied clear-num16.1

    \[\leadsto \color{blue}{\frac{1}{\frac{\frac{i \cdot \left(4 \cdot i\right) - 1.0}{\frac{i}{4}}}{i}}}\]
  7. Using strategy rm

  8. Applied associate-/r/16.1

    \[\leadsto \frac{1}{\frac{\color{blue}{\frac{i \cdot \left(4 \cdot i\right) - 1.0}{i} \cdot 4}}{i}}\]

  9. Applied associate-/l*16.1

    \[\leadsto \frac{1}{\color{blue}{\frac{\frac{i \cdot \left(4 \cdot i\right) - 1.0}{i}}{\frac{i}{4}}}}\]

  10. Simplified0.4

    \[\leadsto \frac{1}{\frac{\color{blue}{4 \cdot i - \frac{1.0}{i}}}{\frac{i}{4}}}\]

  11. Final simplification0.4

    \[\leadsto \frac{1}{\frac{i \cdot 4 - \frac{1.0}{i}}{\frac{i}{4}}}\]

Runtime

Time bar (total: 27.6s)Debug logProfile

herbie shell --seed 2018278 
(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)))