Average Error: 0.4 → 0.3
Time: 11.9s
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 r74386 = 1.0;
        double r74387 = 6.0;
        double r74388 = r74386 / r74387;
        double r74389 = -2.0;
        double r74390 = u1;
        double r74391 = log(r74390);
        double r74392 = r74389 * r74391;
        double r74393 = 0.5;
        double r74394 = pow(r74392, r74393);
        double r74395 = r74388 * r74394;
        double r74396 = 2.0;
        double r74397 = atan2(1.0, 0.0);
        double r74398 = r74396 * r74397;
        double r74399 = u2;
        double r74400 = r74398 * r74399;
        double r74401 = cos(r74400);
        double r74402 = r74395 * r74401;
        double r74403 = r74402 + r74393;
        return r74403;
}
↓
double f(double u1, double u2) {
        double r74404 = 1.0;
        double r74405 = -2.0;
        double r74406 = u1;
        double r74407 = log(r74406);
        double r74408 = r74405 * r74407;
        double r74409 = 0.5;
        double r74410 = pow(r74408, r74409);
        double r74411 = r74404 * r74410;
        double r74412 = 6.0;
        double r74413 = r74411 / r74412;
        double r74414 = 2.0;
        double r74415 = atan2(1.0, 0.0);
        double r74416 = r74414 * r74415;
        double r74417 = u2;
        double r74418 = r74416 * r74417;
        double r74419 = cos(r74418);
        double r74420 = r74413 * r74419;
        double r74421 = r74420 + r74409;
        return r74421;
}

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 2020056 
(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))