Average Error: 45.5 → 0.4
Time: 12.4s
Precision: 64
Internal Precision: 576
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{1}{16 - \frac{4.0}{i \cdot i}}\]

Error

Bits error versus i

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.5

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

  2. Initial simplification15.5

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

  4. Applied clear-num15.9

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

  5. Taylor expanded around 0 0.4

    \[\leadsto \frac{1}{\color{blue}{16 - 4.0 \cdot \frac{1}{{i}^{2}}}}\]

  6. Simplified0.4

    \[\leadsto \frac{1}{\color{blue}{16 - \frac{4.0}{i \cdot i}}}\]

  7. Final simplification0.4

    \[\leadsto \frac{1}{16 - \frac{4.0}{i \cdot i}}\]

Runtime

Time bar (total: 12.4s)Debug logProfile

herbie shell --seed 2018251 +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)))