Average Error: 0.4 → 0.3
Time: 15.1s
Precision: 64
\[0.0 \le u1 \le 1 \land 0.0 \le u2 \le 1\]
\[\left(\frac{1}{6} \cdot {\left(-2 \cdot \log u1\right)}^{0.5}\right) \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
↓
\[\frac{1 \cdot {\left(-2 \cdot \log u1\right)}^{0.5}}{6} \cdot \cos \left(\left(2 \cdot \pi\right) \cdot u2\right) + 0.5\]
\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 r73628 = 1.0;
        double r73629 = 6.0;
        double r73630 = r73628 / r73629;
        double r73631 = -2.0;
        double r73632 = u1;
        double r73633 = log(r73632);
        double r73634 = r73631 * r73633;
        double r73635 = 0.5;
        double r73636 = pow(r73634, r73635);
        double r73637 = r73630 * r73636;
        double r73638 = 2.0;
        double r73639 = atan2(1.0, 0.0);
        double r73640 = r73638 * r73639;
        double r73641 = u2;
        double r73642 = r73640 * r73641;
        double r73643 = cos(r73642);
        double r73644 = r73637 * r73643;
        double r73645 = r73644 + r73635;
        return r73645;
}
↓
double f(double u1, double u2) {
        double r73646 = 1.0;
        double r73647 = -2.0;
        double r73648 = u1;
        double r73649 = log(r73648);
        double r73650 = r73647 * r73649;
        double r73651 = 0.5;
        double r73652 = pow(r73650, r73651);
        double r73653 = r73646 * r73652;
        double r73654 = 6.0;
        double r73655 = r73653 / r73654;
        double r73656 = 2.0;
        double r73657 = atan2(1.0, 0.0);
        double r73658 = r73656 * r73657;
        double r73659 = u2;
        double r73660 = r73658 * r73659;
        double r73661 = cos(r73660);
        double r73662 = r73655 * r73661;
        double r73663 = r73662 + r73651;
        return r73663;
}

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 2020046 
(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))