Average Error: 45.8 → 0.2
Time: 29.1s
Precision: 64
Internal Precision: 384
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{1 \cdot i}{2}}{\left(2 + 2\right) \cdot \left(i + i\right) - \frac{1.0 + 1.0}{i}}\]

Error

Bits error versus i

Derivation

  1. Initial program 45.8

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

  2. Applied simplify15.2

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

  4. Applied associate-/l*15.3

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

  5. Applied simplify0.2

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

Runtime

Time bar (total: 29.1s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' 
(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)))