Average Error: 15.7 → 1.2
Time: 6.2s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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 r139167 = K;
        double r139168 = m;
        double r139169 = n;
        double r139170 = r139168 + r139169;
        double r139171 = r139167 * r139170;
        double r139172 = 2.0;
        double r139173 = r139171 / r139172;
        double r139174 = M;
        double r139175 = r139173 - r139174;
        double r139176 = cos(r139175);
        double r139177 = r139170 / r139172;
        double r139178 = r139177 - r139174;
        double r139179 = pow(r139178, r139172);
        double r139180 = -r139179;
        double r139181 = l;
        double r139182 = r139168 - r139169;
        double r139183 = fabs(r139182);
        double r139184 = r139181 - r139183;
        double r139185 = r139180 - r139184;
        double r139186 = exp(r139185);
        double r139187 = r139176 * r139186;
        return r139187;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r139188 = m;
        double r139189 = n;
        double r139190 = r139188 + r139189;
        double r139191 = 2.0;
        double r139192 = r139190 / r139191;
        double r139193 = M;
        double r139194 = r139192 - r139193;
        double r139195 = pow(r139194, r139191);
        double r139196 = -r139195;
        double r139197 = l;
        double r139198 = r139188 - r139189;
        double r139199 = fabs(r139198);
        double r139200 = r139197 - r139199;
        double r139201 = r139196 - r139200;
        double r139202 = exp(r139201);
        return r139202;
}

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 15.7

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

  2. Taylor expanded around 0 1.2

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

  3. Final simplification1.2

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

Reproduce

herbie shell --seed 2019353 
(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)))))))