Average Error: 15.4 → 1.3
Time: 17.1s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}\]
\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|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}
double f(double K, double m, double n, double M, double l) {
        double r139307 = K;
        double r139308 = m;
        double r139309 = n;
        double r139310 = r139308 + r139309;
        double r139311 = r139307 * r139310;
        double r139312 = 2.0;
        double r139313 = r139311 / r139312;
        double r139314 = M;
        double r139315 = r139313 - r139314;
        double r139316 = cos(r139315);
        double r139317 = r139310 / r139312;
        double r139318 = r139317 - r139314;
        double r139319 = pow(r139318, r139312);
        double r139320 = -r139319;
        double r139321 = l;
        double r139322 = r139308 - r139309;
        double r139323 = fabs(r139322);
        double r139324 = r139321 - r139323;
        double r139325 = r139320 - r139324;
        double r139326 = exp(r139325);
        double r139327 = r139316 * r139326;
        return r139327;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r139328 = m;
        double r139329 = n;
        double r139330 = r139328 - r139329;
        double r139331 = fabs(r139330);
        double r139332 = r139328 + r139329;
        double r139333 = 2.0;
        double r139334 = r139332 / r139333;
        double r139335 = M;
        double r139336 = r139334 - r139335;
        double r139337 = pow(r139336, r139333);
        double r139338 = l;
        double r139339 = r139337 + r139338;
        double r139340 = r139331 - r139339;
        double r139341 = exp(r139340);
        return r139341;
}

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 15.4

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

  2. Simplified15.4

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020042 +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)))))))