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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. Initial simplification0.3

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

4. Applied clear-num0.3

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

5. Taylor expanded around -inf 62.0

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

6. Simplified0.4

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

7. Final simplification0.4

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

Runtime

Time bar (total: 54.6s)Debug logProfile

herbie shell --seed 2018242 
(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))