Average Error: 14.9 → 1.3
Time: 25.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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 r128603 = K;
        double r128604 = m;
        double r128605 = n;
        double r128606 = r128604 + r128605;
        double r128607 = r128603 * r128606;
        double r128608 = 2.0;
        double r128609 = r128607 / r128608;
        double r128610 = M;
        double r128611 = r128609 - r128610;
        double r128612 = cos(r128611);
        double r128613 = r128606 / r128608;
        double r128614 = r128613 - r128610;
        double r128615 = pow(r128614, r128608);
        double r128616 = -r128615;
        double r128617 = l;
        double r128618 = r128604 - r128605;
        double r128619 = fabs(r128618);
        double r128620 = r128617 - r128619;
        double r128621 = r128616 - r128620;
        double r128622 = exp(r128621);
        double r128623 = r128612 * r128622;
        return r128623;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r128624 = m;
        double r128625 = n;
        double r128626 = r128624 - r128625;
        double r128627 = fabs(r128626);
        double r128628 = l;
        double r128629 = r128627 - r128628;
        double r128630 = r128624 + r128625;
        double r128631 = 2.0;
        double r128632 = r128630 / r128631;
        double r128633 = M;
        double r128634 = r128632 - r128633;
        double r128635 = pow(r128634, r128631);
        double r128636 = r128629 - r128635;
        double r128637 = exp(r128636);
        return r128637;
}

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 14.9

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

  2. Simplified14.9

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019323 
(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)))))))