Average Error: 0.4 → 0.3
Time: 10.2s
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 r61387 = 1.0;
        double r61388 = 6.0;
        double r61389 = r61387 / r61388;
        double r61390 = -2.0;
        double r61391 = u1;
        double r61392 = log(r61391);
        double r61393 = r61390 * r61392;
        double r61394 = 0.5;
        double r61395 = pow(r61393, r61394);
        double r61396 = r61389 * r61395;
        double r61397 = 2.0;
        double r61398 = atan2(1.0, 0.0);
        double r61399 = r61397 * r61398;
        double r61400 = u2;
        double r61401 = r61399 * r61400;
        double r61402 = cos(r61401);
        double r61403 = r61396 * r61402;
        double r61404 = r61403 + r61394;
        return r61404;
}
↓
double f(double u1, double u2) {
        double r61405 = 1.0;
        double r61406 = -2.0;
        double r61407 = u1;
        double r61408 = log(r61407);
        double r61409 = r61406 * r61408;
        double r61410 = 0.5;
        double r61411 = pow(r61409, r61410);
        double r61412 = r61405 * r61411;
        double r61413 = 6.0;
        double r61414 = r61412 / r61413;
        double r61415 = 2.0;
        double r61416 = atan2(1.0, 0.0);
        double r61417 = r61415 * r61416;
        double r61418 = u2;
        double r61419 = r61417 * r61418;
        double r61420 = cos(r61419);
        double r61421 = r61414 * r61420;
        double r61422 = r61421 + r61410;
        return r61422;
}

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 2019353 
(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))