Average Error: 0.4 → 0.3
Time: 42.3s
Precision: 64
Internal Precision: 576
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
↓
\[\frac{1}{\frac{\frac{6}{\cos \left(\left(2 \cdot u2\right) \cdot \pi\right)}}{{\left(\log u1 \cdot -2\right)}^{0.5}}} + 0.5\]

Error

Bits error versus u1

Bits error versus u2

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Final simplification0.3

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

Runtime

Time bar (total: 42.3s)Debug logProfile

herbie shell --seed 2018221 
(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))