Average Error: 0.4 → 0.3
Time: 11.2s
Precision: 64
\[0.0 \le u1 \le 1 \land 0.0 \le u2 \le 1\]
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
↓
\[\frac{1 \cdot {\left(-2 \cdot \log u1\right)}^{0.5}}{6} \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
\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
↓
\frac{1 \cdot {\left(-2 \cdot \log u1\right)}^{0.5}}{6} \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5
double f(double u1, double u2) {
        double r68875 = 1.0;
        double r68876 = 6.0;
        double r68877 = r68875 / r68876;
        double r68878 = -2.0;
        double r68879 = u1;
        double r68880 = log(r68879);
        double r68881 = r68878 * r68880;
        double r68882 = 0.5;
        double r68883 = pow(r68881, r68882);
        double r68884 = r68877 * r68883;
        double r68885 = 2.0;
        double r68886 = atan2(1.0, 0.0);
        double r68887 = r68885 * r68886;
        double r68888 = u2;
        double r68889 = r68887 * r68888;
        double r68890 = cos(r68889);
        double r68891 = r68884 * r68890;
        double r68892 = r68891 + r68882;
        return r68892;
}
↓
double f(double u1, double u2) {
        double r68893 = 1.0;
        double r68894 = -2.0;
        double r68895 = u1;
        double r68896 = log(r68895);
        double r68897 = r68894 * r68896;
        double r68898 = 0.5;
        double r68899 = pow(r68897, r68898);
        double r68900 = r68893 * r68899;
        double r68901 = 6.0;
        double r68902 = r68900 / r68901;
        double r68903 = 2.0;
        double r68904 = atan2(1.0, 0.0);
        double r68905 = r68903 * r68904;
        double r68906 = u2;
        double r68907 = r68905 * r68906;
        double r68908 = cos(r68907);
        double r68909 = r68902 * r68908;
        double r68910 = r68909 + r68898;
        return r68910;
}

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 associate-*l/0.3

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

  4. Final simplification0.3

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

Reproduce

herbie shell --seed 2020049 
(FPCore (u1 u2)
  :name "normal distribution"
  :precision binary64
  :pre (and (<= 0.0 u1 1) (<= 0.0 u2 1))
  (+ (* (* (/ 1 6) (pow (* -2 (log u1)) 0.5)) (cos (* (* 2 PI) u2))) 0.5))