Average Error: 15.0 → 1.4
Time: 30.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left|m - n\right| - \left(\ell + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)}\]
\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
↓
e^{\left|m - n\right| - \left(\ell + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)}
double f(double K, double m, double n, double M, double l) {
        double r4846572 = K;
        double r4846573 = m;
        double r4846574 = n;
        double r4846575 = r4846573 + r4846574;
        double r4846576 = r4846572 * r4846575;
        double r4846577 = 2.0;
        double r4846578 = r4846576 / r4846577;
        double r4846579 = M;
        double r4846580 = r4846578 - r4846579;
        double r4846581 = cos(r4846580);
        double r4846582 = r4846575 / r4846577;
        double r4846583 = r4846582 - r4846579;
        double r4846584 = pow(r4846583, r4846577);
        double r4846585 = -r4846584;
        double r4846586 = l;
        double r4846587 = r4846573 - r4846574;
        double r4846588 = fabs(r4846587);
        double r4846589 = r4846586 - r4846588;
        double r4846590 = r4846585 - r4846589;
        double r4846591 = exp(r4846590);
        double r4846592 = r4846581 * r4846591;
        return r4846592;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r4846593 = m;
        double r4846594 = n;
        double r4846595 = r4846593 - r4846594;
        double r4846596 = fabs(r4846595);
        double r4846597 = l;
        double r4846598 = r4846593 + r4846594;
        double r4846599 = 2.0;
        double r4846600 = r4846598 / r4846599;
        double r4846601 = M;
        double r4846602 = r4846600 - r4846601;
        double r4846603 = r4846602 * r4846602;
        double r4846604 = r4846597 + r4846603;
        double r4846605 = r4846596 - r4846604;
        double r4846606 = exp(r4846605);
        return r4846606;
}

Error

Bits error versus K

Bits error versus m

Bits error versus n

Bits error versus M

Bits error versus l

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.0

    \[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]

  2. Simplified15.0

    \[\leadsto \color{blue}{\cos \left(\frac{\left(m + n\right) \cdot K}{2} - M\right) \cdot e^{\left|m - n\right| - \left(\ell + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)}}\]

  3. Taylor expanded around 0 1.4

    \[\leadsto \color{blue}{1} \cdot e^{\left|m - n\right| - \left(\ell + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)}\]

  4. Final simplification1.4

    \[\leadsto e^{\left|m - n\right| - \left(\ell + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)}\]

Reproduce

herbie shell --seed 2019139 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))