Average Error: 0.4 → 0.3
Time: 33.1s
Precision: 64
\[0.0 \le u1 \le 1 \land 0.0 \le u2 \le 1\]
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
↓
\[\frac{1 \cdot {\left(\log u1 \cdot -2\right)}^{0.5}}{6} \cdot \cos \left(u2 \cdot \left(2 \cdot \pi\right)\right) + 0.5\]
\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(\log u1 \cdot -2\right)}^{0.5}}{6} \cdot \cos \left(u2 \cdot \left(2 \cdot \pi\right)\right) + 0.5
double f(double u1, double u2) {
        double r2069470 = 1.0;
        double r2069471 = 6.0;
        double r2069472 = r2069470 / r2069471;
        double r2069473 = -2.0;
        double r2069474 = u1;
        double r2069475 = log(r2069474);
        double r2069476 = r2069473 * r2069475;
        double r2069477 = 0.5;
        double r2069478 = pow(r2069476, r2069477);
        double r2069479 = r2069472 * r2069478;
        double r2069480 = 2.0;
        double r2069481 = atan2(1.0, 0.0);
        double r2069482 = r2069480 * r2069481;
        double r2069483 = u2;
        double r2069484 = r2069482 * r2069483;
        double r2069485 = cos(r2069484);
        double r2069486 = r2069479 * r2069485;
        double r2069487 = r2069486 + r2069477;
        return r2069487;
}
↓
double f(double u1, double u2) {
        double r2069488 = 1.0;
        double r2069489 = u1;
        double r2069490 = log(r2069489);
        double r2069491 = -2.0;
        double r2069492 = r2069490 * r2069491;
        double r2069493 = 0.5;
        double r2069494 = pow(r2069492, r2069493);
        double r2069495 = r2069488 * r2069494;
        double r2069496 = 6.0;
        double r2069497 = r2069495 / r2069496;
        double r2069498 = u2;
        double r2069499 = 2.0;
        double r2069500 = atan2(1.0, 0.0);
        double r2069501 = r2069499 * r2069500;
        double r2069502 = r2069498 * r2069501;
        double r2069503 = cos(r2069502);
        double r2069504 = r2069497 * r2069503;
        double r2069505 = r2069504 + r2069493;
        return r2069505;
}

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

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

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))