Average Error: 0.4 → 0.4
Time: 1.2m
Precision: 64
Internal Precision: 320
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
↓
\[\cos \left(\sqrt{u2 \cdot \left(2 \cdot \pi\right)} \cdot \sqrt{u2 \cdot \left(2 \cdot \pi\right)}\right) \cdot \left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) + 0.5\]

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. Using strategy rm

  3. Applied add-sqr-sqrt0.4

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

  4. Final simplification0.4

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

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed 2018227 
(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))