Error

Derivation

1. Initial program 0.4

   \[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]

2. Applied simplify0.3

   \[\leadsto \color{blue}{0.5 + \cos \left(u2 \cdot \left(\pi + \pi\right)\right) \cdot \frac{{\left(-2 \cdot \log u1\right)}^{0.5}}{6}}\]
3. Using strategy rm

4. Applied clear-num0.3

   \[\leadsto 0.5 + \cos \left(u2 \cdot \left(\pi + \pi\right)\right) \cdot \color{blue}{\frac{1}{\frac{6}{{\left(-2 \cdot \log u1\right)}^{0.5}}}}\]

5. Taylor expanded around 0 0.4

   \[\leadsto 0.5 + \cos \left(u2 \cdot \left(\pi + \pi\right)\right) \cdot \frac{1}{\color{blue}{6 \cdot {\left(\frac{1}{{-2}^{1.0} \cdot {\left(\log u1\right)}^{1.0}}\right)}^{0.5}}}\]

6. Applied simplify0.4

   \[\leadsto \color{blue}{0.5 + \frac{\frac{\cos \left(\left(u2 + u2\right) \cdot \pi\right)}{6}}{{\left(\frac{\frac{1}{{-2}^{1.0}}}{{\left(\log u1\right)}^{1.0}}\right)}^{0.5}}}\]
7. Removed slow pow expressions.

Runtime

Time bar (total: 1.5m)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit +o reduce:binary-search
(FPCore (u1 u2)
  :name "normal distribution"
  :pre (and (<= 0 u1 1) (<= 0 u2 1))
  (+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5))