Error

Derivation

1. Initial program 52.9

   \[\frac{\frac{\left(i \cdot \left(\left(\alpha + \beta\right) + i\right)\right) \cdot \left(\beta \cdot \alpha + i \cdot \left(\left(\alpha + \beta\right) + i\right)\right)}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right)}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]
2. Using strategy rm

3. Applied times-frac38.6

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

4. Applied simplify38.6

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

6. Applied *-un-lft-identity38.6

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

7. Applied associate-/r*38.6

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

8. Applied simplify38.6

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

10. Applied add-cube-cbrt39.0

    \[\leadsto \frac{\frac{i}{\frac{\color{blue}{\left(\sqrt[3]{\left(\alpha + \beta\right) + i \cdot 2} \cdot \sqrt[3]{\left(\alpha + \beta\right) + i \cdot 2}\right) \cdot \sqrt[3]{\left(\alpha + \beta\right) + i \cdot 2}}}{\left(i + \beta\right) \cdot \left(\alpha + i\right)}} \cdot \frac{\left(i + \beta\right) + \alpha}{\left(\alpha + \beta\right) + i \cdot 2}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]

11. Applied times-frac36.7

    \[\leadsto \frac{\frac{i}{\color{blue}{\frac{\sqrt[3]{\left(\alpha + \beta\right) + i \cdot 2} \cdot \sqrt[3]{\left(\alpha + \beta\right) + i \cdot 2}}{i + \beta} \cdot \frac{\sqrt[3]{\left(\alpha + \beta\right) + i \cdot 2}}{\alpha + i}}} \cdot \frac{\left(i + \beta\right) + \alpha}{\left(\alpha + \beta\right) + i \cdot 2}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) \cdot \left(\left(\alpha + \beta\right) + 2 \cdot i\right) - 1.0}\]

Runtime

Time bar (total: 4.0m)Debug logProfile

herbie shell --seed '#(1071246582 2318319007 2683472949 3810440501 3233274817 2724848749)' 
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/4"
  :pre (and (> alpha -1) (> beta -1) (> i 1))
  (/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i)))) (- (* (+ (+ alpha beta) (* 2 i)) (+ (+ alpha beta) (* 2 i))) 1.0)))