Average Error: 15.6 → 1.4
Time: 7.6s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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)}
↓
e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
double f(double K, double m, double n, double M, double l) {
        double r155667 = K;
        double r155668 = m;
        double r155669 = n;
        double r155670 = r155668 + r155669;
        double r155671 = r155667 * r155670;
        double r155672 = 2.0;
        double r155673 = r155671 / r155672;
        double r155674 = M;
        double r155675 = r155673 - r155674;
        double r155676 = cos(r155675);
        double r155677 = r155670 / r155672;
        double r155678 = r155677 - r155674;
        double r155679 = pow(r155678, r155672);
        double r155680 = -r155679;
        double r155681 = l;
        double r155682 = r155668 - r155669;
        double r155683 = fabs(r155682);
        double r155684 = r155681 - r155683;
        double r155685 = r155680 - r155684;
        double r155686 = exp(r155685);
        double r155687 = r155676 * r155686;
        return r155687;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r155688 = m;
        double r155689 = n;
        double r155690 = r155688 + r155689;
        double r155691 = 2.0;
        double r155692 = r155690 / r155691;
        double r155693 = M;
        double r155694 = r155692 - r155693;
        double r155695 = pow(r155694, r155691);
        double r155696 = -r155695;
        double r155697 = l;
        double r155698 = r155688 - r155689;
        double r155699 = fabs(r155698);
        double r155700 = r155697 - r155699;
        double r155701 = r155696 - r155700;
        double r155702 = exp(r155701);
        return r155702;
}

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. Taylor expanded around 0 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2020081 
(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)))))))