Average Error: 15.5 → 1.4
Time: 24.9s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}
double f(double K, double m, double n, double M, double l) {
        double r84571 = K;
        double r84572 = m;
        double r84573 = n;
        double r84574 = r84572 + r84573;
        double r84575 = r84571 * r84574;
        double r84576 = 2.0;
        double r84577 = r84575 / r84576;
        double r84578 = M;
        double r84579 = r84577 - r84578;
        double r84580 = cos(r84579);
        double r84581 = r84574 / r84576;
        double r84582 = r84581 - r84578;
        double r84583 = pow(r84582, r84576);
        double r84584 = -r84583;
        double r84585 = l;
        double r84586 = r84572 - r84573;
        double r84587 = fabs(r84586);
        double r84588 = r84585 - r84587;
        double r84589 = r84584 - r84588;
        double r84590 = exp(r84589);
        double r84591 = r84580 * r84590;
        return r84591;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r84592 = m;
        double r84593 = n;
        double r84594 = r84592 - r84593;
        double r84595 = fabs(r84594);
        double r84596 = l;
        double r84597 = r84595 - r84596;
        double r84598 = r84592 + r84593;
        double r84599 = 2.0;
        double r84600 = r84598 / r84599;
        double r84601 = M;
        double r84602 = r84600 - r84601;
        double r84603 = pow(r84602, r84599);
        double r84604 = r84597 - r84603;
        double r84605 = exp(r84604);
        return r84605;
}

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 15.5

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

  2. Simplified15.5

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019326 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))