Average Error: 15.7 → 1.3
Time: 30.3s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r76195 = K;
        double r76196 = m;
        double r76197 = n;
        double r76198 = r76196 + r76197;
        double r76199 = r76195 * r76198;
        double r76200 = 2.0;
        double r76201 = r76199 / r76200;
        double r76202 = M;
        double r76203 = r76201 - r76202;
        double r76204 = cos(r76203);
        double r76205 = r76198 / r76200;
        double r76206 = r76205 - r76202;
        double r76207 = pow(r76206, r76200);
        double r76208 = -r76207;
        double r76209 = l;
        double r76210 = r76196 - r76197;
        double r76211 = fabs(r76210);
        double r76212 = r76209 - r76211;
        double r76213 = r76208 - r76212;
        double r76214 = exp(r76213);
        double r76215 = r76204 * r76214;
        return r76215;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r76216 = 1.0;
        double r76217 = m;
        double r76218 = n;
        double r76219 = r76217 + r76218;
        double r76220 = 2.0;
        double r76221 = r76219 / r76220;
        double r76222 = M;
        double r76223 = r76221 - r76222;
        double r76224 = pow(r76223, r76220);
        double r76225 = l;
        double r76226 = r76217 - r76218;
        double r76227 = fabs(r76226);
        double r76228 = r76225 - r76227;
        double r76229 = r76224 + r76228;
        double r76230 = exp(r76229);
        double r76231 = r76216 / r76230;
        return r76231;
}

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 15.7

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

  2. Simplified15.7

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019322 +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)))))))