Average Error: 15.3 → 1.2
Time: 4.7s
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 r110178 = K;
        double r110179 = m;
        double r110180 = n;
        double r110181 = r110179 + r110180;
        double r110182 = r110178 * r110181;
        double r110183 = 2.0;
        double r110184 = r110182 / r110183;
        double r110185 = M;
        double r110186 = r110184 - r110185;
        double r110187 = cos(r110186);
        double r110188 = r110181 / r110183;
        double r110189 = r110188 - r110185;
        double r110190 = pow(r110189, r110183);
        double r110191 = -r110190;
        double r110192 = l;
        double r110193 = r110179 - r110180;
        double r110194 = fabs(r110193);
        double r110195 = r110192 - r110194;
        double r110196 = r110191 - r110195;
        double r110197 = exp(r110196);
        double r110198 = r110187 * r110197;
        return r110198;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r110199 = m;
        double r110200 = n;
        double r110201 = r110199 + r110200;
        double r110202 = 2.0;
        double r110203 = r110201 / r110202;
        double r110204 = M;
        double r110205 = r110203 - r110204;
        double r110206 = pow(r110205, r110202);
        double r110207 = -r110206;
        double r110208 = l;
        double r110209 = r110199 - r110200;
        double r110210 = fabs(r110209);
        double r110211 = r110208 - r110210;
        double r110212 = r110207 - r110211;
        double r110213 = exp(r110212);
        return r110213;
}

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 1.2

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

  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 2020024 +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)))))))