Error

Derivation

1. Initial program 26.3

   \[\left(a - \frac{1.0}{3.0}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}} \cdot rand\right)\]

2. Initial simplification26.3

   \[\leadsto (\left(\frac{a - \frac{1.0}{3.0}}{\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]
3. Using strategy rm

4. Applied add-exp-log26.3

   \[\leadsto (\left(\frac{a - \frac{1.0}{3.0}}{\color{blue}{e^{\log \left(\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}\right)}}}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

5. Applied add-exp-log26.3

   \[\leadsto (\left(\frac{\color{blue}{e^{\log \left(a - \frac{1.0}{3.0}\right)}}}{e^{\log \left(\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}\right)}}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

6. Applied div-exp26.3

   \[\leadsto (\color{blue}{\left(e^{\log \left(a - \frac{1.0}{3.0}\right) - \log \left(\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}\right)}\right)} \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]
7. Using strategy rm

8. Applied expm1-log1p-u26.4

   \[\leadsto (\left(e^{\color{blue}{(e^{\log_* (1 + \left(\log \left(a - \frac{1.0}{3.0}\right) - \log \left(\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}\right)\right))} - 1)^*}}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

9. Final simplification26.4

   \[\leadsto (\left(e^{(e^{\log_* (1 + \left(\log \left(a - \frac{1.0}{3.0}\right) - \log \left(\sqrt{9 \cdot \left(a - \frac{1.0}{3.0}\right)}\right)\right))} - 1)^*}\right) \cdot rand + \left(a - \frac{1.0}{3.0}\right))_*\]

Runtime

Time bar (total: 1.1m)Debug logProfile

herbie shell --seed 2018255 +o rules:numerics
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  (* (- a (/ 1.0 3.0)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1.0 3.0))))) rand))))