Average Error: 15.6 → 1.4
Time: 33.4s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - {\left(\frac{n + m}{2} - M\right)}^{2}\right) - \ell}\]
\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| - {\left(\frac{n + m}{2} - M\right)}^{2}\right) - \ell}
double f(double K, double m, double n, double M, double l) {
        double r6365621 = K;
        double r6365622 = m;
        double r6365623 = n;
        double r6365624 = r6365622 + r6365623;
        double r6365625 = r6365621 * r6365624;
        double r6365626 = 2.0;
        double r6365627 = r6365625 / r6365626;
        double r6365628 = M;
        double r6365629 = r6365627 - r6365628;
        double r6365630 = cos(r6365629);
        double r6365631 = r6365624 / r6365626;
        double r6365632 = r6365631 - r6365628;
        double r6365633 = pow(r6365632, r6365626);
        double r6365634 = -r6365633;
        double r6365635 = l;
        double r6365636 = r6365622 - r6365623;
        double r6365637 = fabs(r6365636);
        double r6365638 = r6365635 - r6365637;
        double r6365639 = r6365634 - r6365638;
        double r6365640 = exp(r6365639);
        double r6365641 = r6365630 * r6365640;
        return r6365641;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r6365642 = m;
        double r6365643 = n;
        double r6365644 = r6365642 - r6365643;
        double r6365645 = fabs(r6365644);
        double r6365646 = r6365643 + r6365642;
        double r6365647 = 2.0;
        double r6365648 = r6365646 / r6365647;
        double r6365649 = M;
        double r6365650 = r6365648 - r6365649;
        double r6365651 = pow(r6365650, r6365647);
        double r6365652 = r6365645 - r6365651;
        double r6365653 = l;
        double r6365654 = r6365652 - r6365653;
        double r6365655 = exp(r6365654);
        return r6365655;
}

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 15.6

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

  2. Simplified15.6

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019174 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))