Average Error: 15.3 → 1.3
Time: 5.5s
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 r108987 = K;
        double r108988 = m;
        double r108989 = n;
        double r108990 = r108988 + r108989;
        double r108991 = r108987 * r108990;
        double r108992 = 2.0;
        double r108993 = r108991 / r108992;
        double r108994 = M;
        double r108995 = r108993 - r108994;
        double r108996 = cos(r108995);
        double r108997 = r108990 / r108992;
        double r108998 = r108997 - r108994;
        double r108999 = pow(r108998, r108992);
        double r109000 = -r108999;
        double r109001 = l;
        double r109002 = r108988 - r108989;
        double r109003 = fabs(r109002);
        double r109004 = r109001 - r109003;
        double r109005 = r109000 - r109004;
        double r109006 = exp(r109005);
        double r109007 = r108996 * r109006;
        return r109007;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r109008 = m;
        double r109009 = n;
        double r109010 = r109008 + r109009;
        double r109011 = 2.0;
        double r109012 = r109010 / r109011;
        double r109013 = M;
        double r109014 = r109012 - r109013;
        double r109015 = pow(r109014, r109011);
        double r109016 = -r109015;
        double r109017 = l;
        double r109018 = r109008 - r109009;
        double r109019 = fabs(r109018);
        double r109020 = r109017 - r109019;
        double r109021 = r109016 - r109020;
        double r109022 = exp(r109021);
        return r109022;
}

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. Taylor expanded around 0 1.3

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

  3. Final simplification1.3

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

Reproduce

herbie shell --seed 2020065 
(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)))))))