Average Error: 14.7 → 1.4
Time: 3.8m
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 r17411300 = K;
        double r17411301 = m;
        double r17411302 = n;
        double r17411303 = r17411301 + r17411302;
        double r17411304 = r17411300 * r17411303;
        double r17411305 = 2.0;
        double r17411306 = r17411304 / r17411305;
        double r17411307 = M;
        double r17411308 = r17411306 - r17411307;
        double r17411309 = cos(r17411308);
        double r17411310 = r17411303 / r17411305;
        double r17411311 = r17411310 - r17411307;
        double r17411312 = pow(r17411311, r17411305);
        double r17411313 = -r17411312;
        double r17411314 = l;
        double r17411315 = r17411301 - r17411302;
        double r17411316 = fabs(r17411315);
        double r17411317 = r17411314 - r17411316;
        double r17411318 = r17411313 - r17411317;
        double r17411319 = exp(r17411318);
        double r17411320 = r17411309 * r17411319;
        return r17411320;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r17411321 = m;
        double r17411322 = n;
        double r17411323 = r17411321 + r17411322;
        double r17411324 = 2.0;
        double r17411325 = r17411323 / r17411324;
        double r17411326 = M;
        double r17411327 = r17411325 - r17411326;
        double r17411328 = pow(r17411327, r17411324);
        double r17411329 = -r17411328;
        double r17411330 = l;
        double r17411331 = r17411321 - r17411322;
        double r17411332 = fabs(r17411331);
        double r17411333 = r17411330 - r17411332;
        double r17411334 = r17411329 - r17411333;
        double r17411335 = exp(r17411334);
        return r17411335;
}

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 14.7

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

  2. Taylor expanded around 0 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))