Average Error: 0.4 → 0.4
Time: 11.2s
Precision: 64
Internal precision: 384
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
⬇
\[0.5 + \frac{1}{\frac{\frac{6}{\cos \left(u2 \cdot \left(\pi + \pi\right)\right)}}{{\left(-2 \cdot \log u1\right)}^{0.5}}}\]

Error

Bits error versus u1

Bits error versus u2

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 simplify 0.3

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

  4. Applied clear-num 0.4

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

Runtime

Time bar (total: 11.2s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1064524629 4159152179 2999149171 575749698 4006532819 692958815)'
(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))