Average Error: 45.6 → 0.1
Time: 1.3m
Precision: 64
Internal Precision: 576
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{-i}{2}}{\frac{1.0}{i} \cdot 2 - \left(i \cdot 2\right) \cdot \left(2 \cdot 2\right)}\]

Error

Bits error versus i

Derivation

  1. Initial program 45.6

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

  2. Applied simplify15.5

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

  4. Applied frac-2neg15.5

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

  5. Applied simplify15.5

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

  6. Applied simplify0.1

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

Runtime

Time bar (total: 1.3m)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' +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)))