Average Error: 15.2 → 1.3
Time: 12.3s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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 r270300 = K;
        double r270301 = m;
        double r270302 = n;
        double r270303 = r270301 + r270302;
        double r270304 = r270300 * r270303;
        double r270305 = 2.0;
        double r270306 = r270304 / r270305;
        double r270307 = M;
        double r270308 = r270306 - r270307;
        double r270309 = cos(r270308);
        double r270310 = r270303 / r270305;
        double r270311 = r270310 - r270307;
        double r270312 = pow(r270311, r270305);
        double r270313 = -r270312;
        double r270314 = l;
        double r270315 = r270301 - r270302;
        double r270316 = fabs(r270315);
        double r270317 = r270314 - r270316;
        double r270318 = r270313 - r270317;
        double r270319 = exp(r270318);
        double r270320 = r270309 * r270319;
        return r270320;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r270321 = m;
        double r270322 = n;
        double r270323 = r270321 + r270322;
        double r270324 = 2.0;
        double r270325 = r270323 / r270324;
        double r270326 = M;
        double r270327 = r270325 - r270326;
        double r270328 = pow(r270327, r270324);
        double r270329 = -r270328;
        double r270330 = l;
        double r270331 = r270321 - r270322;
        double r270332 = fabs(r270331);
        double r270333 = r270330 - r270332;
        double r270334 = r270329 - r270333;
        double r270335 = exp(r270334);
        return r270335;
}

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 15.2

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

  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 2020047 +o rules:numerics
(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)))))))