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 simplify0.4

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

4. Applied div-inv0.4

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

5. Applied associate-*l*0.4

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

6. Applied simplify0.3

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

Runtime

Time bar (total: 47.1s)Debug logProfile

herbie shell --seed '#(1071979731 1496239409 439705970 2863295848 982327776 189749553)' 
(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))