Average Error: 0.4 → 0.4
Time: 28.3s
Precision: 64
\[0.0 \le u1 \le 1 \land 0.0 \le u2 \le 1\]
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
↓
\[0.5 + \left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(u2 \cdot \left(2 \cdot \pi\right)\right)\]
\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 + \left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(u2 \cdot \left(2 \cdot \pi\right)\right)
double f(double u1, double u2) {
        double r78398 = 1.0;
        double r78399 = 6.0;
        double r78400 = r78398 / r78399;
        double r78401 = -2.0;
        double r78402 = u1;
        double r78403 = log(r78402);
        double r78404 = r78401 * r78403;
        double r78405 = 0.5;
        double r78406 = pow(r78404, r78405);
        double r78407 = r78400 * r78406;
        double r78408 = 2.0;
        double r78409 = atan2(1.0, 0.0);
        double r78410 = r78408 * r78409;
        double r78411 = u2;
        double r78412 = r78410 * r78411;
        double r78413 = cos(r78412);
        double r78414 = r78407 * r78413;
        double r78415 = r78414 + r78405;
        return r78415;
}
↓
double f(double u1, double u2) {
        double r78416 = 0.5;
        double r78417 = 1.0;
        double r78418 = 6.0;
        double r78419 = r78417 / r78418;
        double r78420 = -2.0;
        double r78421 = u1;
        double r78422 = log(r78421);
        double r78423 = r78420 * r78422;
        double r78424 = pow(r78423, r78416);
        double r78425 = r78419 * r78424;
        double r78426 = u2;
        double r78427 = 2.0;
        double r78428 = atan2(1.0, 0.0);
        double r78429 = r78427 * r78428;
        double r78430 = r78426 * r78429;
        double r78431 = cos(r78430);
        double r78432 = r78425 * r78431;
        double r78433 = r78416 + r78432;
        return r78433;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019179 
(FPCore (u1 u2)
  :name "normal distribution"
  :pre (and (<= 0.0 u1 1.0) (<= 0.0 u2 1.0))
  (+ (* (* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5)) (cos (* (* 2.0 PI) u2))) 0.5))