Average Error: 15.3 → 1.6
Time: 6.7s
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 r127283 = K;
        double r127284 = m;
        double r127285 = n;
        double r127286 = r127284 + r127285;
        double r127287 = r127283 * r127286;
        double r127288 = 2.0;
        double r127289 = r127287 / r127288;
        double r127290 = M;
        double r127291 = r127289 - r127290;
        double r127292 = cos(r127291);
        double r127293 = r127286 / r127288;
        double r127294 = r127293 - r127290;
        double r127295 = pow(r127294, r127288);
        double r127296 = -r127295;
        double r127297 = l;
        double r127298 = r127284 - r127285;
        double r127299 = fabs(r127298);
        double r127300 = r127297 - r127299;
        double r127301 = r127296 - r127300;
        double r127302 = exp(r127301);
        double r127303 = r127292 * r127302;
        return r127303;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r127304 = m;
        double r127305 = n;
        double r127306 = r127304 + r127305;
        double r127307 = 2.0;
        double r127308 = r127306 / r127307;
        double r127309 = M;
        double r127310 = r127308 - r127309;
        double r127311 = pow(r127310, r127307);
        double r127312 = -r127311;
        double r127313 = l;
        double r127314 = r127304 - r127305;
        double r127315 = fabs(r127314);
        double r127316 = r127313 - r127315;
        double r127317 = r127312 - r127316;
        double r127318 = exp(r127317);
        return r127318;
}

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 1.6

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

  3. Final simplification1.6

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

Reproduce

herbie shell --seed 2020062 +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)))))))