Average Error: 15.3 → 1.3
Time: 15.9s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{\left(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right) - \left|m - n\right|}}\]
\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(\left(\frac{n + m}{2} - M\right) \cdot \left(\frac{n + m}{2} - M\right) + \ell\right) - \left|m - n\right|}}
double f(double K, double m, double n, double M, double l) {
        double r2292669 = K;
        double r2292670 = m;
        double r2292671 = n;
        double r2292672 = r2292670 + r2292671;
        double r2292673 = r2292669 * r2292672;
        double r2292674 = 2.0;
        double r2292675 = r2292673 / r2292674;
        double r2292676 = M;
        double r2292677 = r2292675 - r2292676;
        double r2292678 = cos(r2292677);
        double r2292679 = r2292672 / r2292674;
        double r2292680 = r2292679 - r2292676;
        double r2292681 = pow(r2292680, r2292674);
        double r2292682 = -r2292681;
        double r2292683 = l;
        double r2292684 = r2292670 - r2292671;
        double r2292685 = fabs(r2292684);
        double r2292686 = r2292683 - r2292685;
        double r2292687 = r2292682 - r2292686;
        double r2292688 = exp(r2292687);
        double r2292689 = r2292678 * r2292688;
        return r2292689;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r2292690 = 1.0;
        double r2292691 = n;
        double r2292692 = m;
        double r2292693 = r2292691 + r2292692;
        double r2292694 = 2.0;
        double r2292695 = r2292693 / r2292694;
        double r2292696 = M;
        double r2292697 = r2292695 - r2292696;
        double r2292698 = r2292697 * r2292697;
        double r2292699 = l;
        double r2292700 = r2292698 + r2292699;
        double r2292701 = r2292692 - r2292691;
        double r2292702 = fabs(r2292701);
        double r2292703 = r2292700 - r2292702;
        double r2292704 = exp(r2292703);
        double r2292705 = r2292690 / r2292704;
        return r2292705;
}

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

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019156 
(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)))))))