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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. Using strategy rm

3. Applied flip-+0.4

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

4. Final simplification0.4

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

Runtime

Time bar (total: 50.8s)Debug logProfile

herbie shell --seed 2018339 +o rules:numerics
(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))