Average Error: 15.6 → 1.4
Time: 8.3s
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 r159607 = K;
        double r159608 = m;
        double r159609 = n;
        double r159610 = r159608 + r159609;
        double r159611 = r159607 * r159610;
        double r159612 = 2.0;
        double r159613 = r159611 / r159612;
        double r159614 = M;
        double r159615 = r159613 - r159614;
        double r159616 = cos(r159615);
        double r159617 = r159610 / r159612;
        double r159618 = r159617 - r159614;
        double r159619 = pow(r159618, r159612);
        double r159620 = -r159619;
        double r159621 = l;
        double r159622 = r159608 - r159609;
        double r159623 = fabs(r159622);
        double r159624 = r159621 - r159623;
        double r159625 = r159620 - r159624;
        double r159626 = exp(r159625);
        double r159627 = r159616 * r159626;
        return r159627;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r159628 = 1.0;
        double r159629 = m;
        double r159630 = n;
        double r159631 = r159629 + r159630;
        double r159632 = 2.0;
        double r159633 = r159631 / r159632;
        double r159634 = M;
        double r159635 = r159633 - r159634;
        double r159636 = pow(r159635, r159632);
        double r159637 = l;
        double r159638 = r159629 - r159630;
        double r159639 = fabs(r159638);
        double r159640 = r159637 - r159639;
        double r159641 = r159636 + r159640;
        double r159642 = exp(r159641);
        double r159643 = r159628 / r159642;
        return r159643;
}

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

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019362 
(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)))))))