Average Error: 15.7 → 1.2
Time: 5.6s
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 r145228 = K;
        double r145229 = m;
        double r145230 = n;
        double r145231 = r145229 + r145230;
        double r145232 = r145228 * r145231;
        double r145233 = 2.0;
        double r145234 = r145232 / r145233;
        double r145235 = M;
        double r145236 = r145234 - r145235;
        double r145237 = cos(r145236);
        double r145238 = r145231 / r145233;
        double r145239 = r145238 - r145235;
        double r145240 = pow(r145239, r145233);
        double r145241 = -r145240;
        double r145242 = l;
        double r145243 = r145229 - r145230;
        double r145244 = fabs(r145243);
        double r145245 = r145242 - r145244;
        double r145246 = r145241 - r145245;
        double r145247 = exp(r145246);
        double r145248 = r145237 * r145247;
        return r145248;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r145249 = m;
        double r145250 = n;
        double r145251 = r145249 + r145250;
        double r145252 = 2.0;
        double r145253 = r145251 / r145252;
        double r145254 = M;
        double r145255 = r145253 - r145254;
        double r145256 = pow(r145255, r145252);
        double r145257 = -r145256;
        double r145258 = l;
        double r145259 = r145249 - r145250;
        double r145260 = fabs(r145259);
        double r145261 = r145258 - r145260;
        double r145262 = r145257 - r145261;
        double r145263 = exp(r145262);
        return r145263;
}

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. 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 2019353 +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)))))))