Average Error: 15.3 → 1.3
Time: 7.1s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r175408 = K;
        double r175409 = m;
        double r175410 = n;
        double r175411 = r175409 + r175410;
        double r175412 = r175408 * r175411;
        double r175413 = 2.0;
        double r175414 = r175412 / r175413;
        double r175415 = M;
        double r175416 = r175414 - r175415;
        double r175417 = cos(r175416);
        double r175418 = r175411 / r175413;
        double r175419 = r175418 - r175415;
        double r175420 = pow(r175419, r175413);
        double r175421 = -r175420;
        double r175422 = l;
        double r175423 = r175409 - r175410;
        double r175424 = fabs(r175423);
        double r175425 = r175422 - r175424;
        double r175426 = r175421 - r175425;
        double r175427 = exp(r175426);
        double r175428 = r175417 * r175427;
        return r175428;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r175429 = 1.0;
        double r175430 = m;
        double r175431 = n;
        double r175432 = r175430 + r175431;
        double r175433 = 2.0;
        double r175434 = r175432 / r175433;
        double r175435 = M;
        double r175436 = r175434 - r175435;
        double r175437 = pow(r175436, r175433);
        double r175438 = l;
        double r175439 = r175430 - r175431;
        double r175440 = fabs(r175439);
        double r175441 = r175438 - r175440;
        double r175442 = r175437 + r175441;
        double r175443 = exp(r175442);
        double r175444 = r175429 / r175443;
        return r175444;
}

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 15.3

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

  2. Simplified15.3

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(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)))))))