Error

Derivation

1. Initial program 23.4

   \[\frac{\frac{\frac{\left(\alpha + \beta\right) \cdot \left(\beta - \alpha\right)}{\left(\alpha + \beta\right) + 2 \cdot i}}{\left(\left(\alpha + \beta\right) + 2 \cdot i\right) + 2.0} + 1.0}{2.0}\]

2. Applied simplify12.4

   \[\leadsto \color{blue}{\frac{(\left(\frac{\beta + \alpha}{(i \cdot 2 + \beta)_* + \left(2.0 + \alpha\right)}\right) \cdot \left(\frac{\beta - \alpha}{(2 \cdot i + \left(\beta + \alpha\right))_*}\right) + 1.0)_*}{2.0}}\]
3. Using strategy rm

4. Applied div-sub12.4

   \[\leadsto \frac{(\left(\frac{\beta + \alpha}{(i \cdot 2 + \beta)_* + \left(2.0 + \alpha\right)}\right) \cdot \color{blue}{\left(\frac{\beta}{(2 \cdot i + \left(\beta + \alpha\right))_*} - \frac{\alpha}{(2 \cdot i + \left(\beta + \alpha\right))_*}\right)} + 1.0)_*}{2.0}\]
5. Using strategy rm

6. Applied add-exp-log12.4

   \[\leadsto \frac{\color{blue}{e^{\log \left((\left(\frac{\beta + \alpha}{(i \cdot 2 + \beta)_* + \left(2.0 + \alpha\right)}\right) \cdot \left(\frac{\beta}{(2 \cdot i + \left(\beta + \alpha\right))_*} - \frac{\alpha}{(2 \cdot i + \left(\beta + \alpha\right))_*}\right) + 1.0)_*\right)}}}{2.0}\]
7. Using strategy rm

8. Applied add-log-exp12.4

   \[\leadsto \frac{e^{\log \left((\left(\frac{\beta + \alpha}{(i \cdot 2 + \beta)_* + \left(2.0 + \alpha\right)}\right) \cdot \left(\frac{\beta}{(2 \cdot i + \left(\beta + \alpha\right))_*} - \color{blue}{\log \left(e^{\frac{\alpha}{(2 \cdot i + \left(\beta + \alpha\right))_*}}\right)}\right) + 1.0)_*\right)}}{2.0}\]

Runtime

Time bar (total: 1.7m)Debug logProfile

herbie shell --seed '#(1070578969 3140398606 632207097 462683394 1189254563 964980650)' +o rules:numerics
(FPCore (alpha beta i)
  :name "Octave 3.8, jcobi/2"
  :pre (and (> alpha -1) (> beta -1) (> i 0))
  (/ (+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) 2.0)) 1.0) 2.0))