Average Error: 14.6 → 1.4
Time: 22.2s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{\left(\ell - \left|m - n\right|\right) + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)}}\]
\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(\ell - \left|m - n\right|\right) + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)}}
double f(double K, double m, double n, double M, double l) {
        double r2828533 = K;
        double r2828534 = m;
        double r2828535 = n;
        double r2828536 = r2828534 + r2828535;
        double r2828537 = r2828533 * r2828536;
        double r2828538 = 2.0;
        double r2828539 = r2828537 / r2828538;
        double r2828540 = M;
        double r2828541 = r2828539 - r2828540;
        double r2828542 = cos(r2828541);
        double r2828543 = r2828536 / r2828538;
        double r2828544 = r2828543 - r2828540;
        double r2828545 = pow(r2828544, r2828538);
        double r2828546 = -r2828545;
        double r2828547 = l;
        double r2828548 = r2828534 - r2828535;
        double r2828549 = fabs(r2828548);
        double r2828550 = r2828547 - r2828549;
        double r2828551 = r2828546 - r2828550;
        double r2828552 = exp(r2828551);
        double r2828553 = r2828542 * r2828552;
        return r2828553;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r2828554 = 1.0;
        double r2828555 = l;
        double r2828556 = m;
        double r2828557 = n;
        double r2828558 = r2828556 - r2828557;
        double r2828559 = fabs(r2828558);
        double r2828560 = r2828555 - r2828559;
        double r2828561 = r2828556 + r2828557;
        double r2828562 = 2.0;
        double r2828563 = r2828561 / r2828562;
        double r2828564 = M;
        double r2828565 = r2828563 - r2828564;
        double r2828566 = r2828565 * r2828565;
        double r2828567 = r2828560 + r2828566;
        double r2828568 = exp(r2828567);
        double r2828569 = r2828554 / r2828568;
        return r2828569;
}

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 14.6

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

  2. Simplified14.6

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019152 
(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)))))))