Average Error: 15.6 → 1.5
Time: 25.7s
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 r103244 = K;
        double r103245 = m;
        double r103246 = n;
        double r103247 = r103245 + r103246;
        double r103248 = r103244 * r103247;
        double r103249 = 2.0;
        double r103250 = r103248 / r103249;
        double r103251 = M;
        double r103252 = r103250 - r103251;
        double r103253 = cos(r103252);
        double r103254 = r103247 / r103249;
        double r103255 = r103254 - r103251;
        double r103256 = pow(r103255, r103249);
        double r103257 = -r103256;
        double r103258 = l;
        double r103259 = r103245 - r103246;
        double r103260 = fabs(r103259);
        double r103261 = r103258 - r103260;
        double r103262 = r103257 - r103261;
        double r103263 = exp(r103262);
        double r103264 = r103253 * r103263;
        return r103264;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r103265 = m;
        double r103266 = n;
        double r103267 = r103265 + r103266;
        double r103268 = 2.0;
        double r103269 = r103267 / r103268;
        double r103270 = M;
        double r103271 = r103269 - r103270;
        double r103272 = pow(r103271, r103268);
        double r103273 = -r103272;
        double r103274 = l;
        double r103275 = r103265 - r103266;
        double r103276 = fabs(r103275);
        double r103277 = r103274 - r103276;
        double r103278 = r103273 - r103277;
        double r103279 = exp(r103278);
        return r103279;
}

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 15.6

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

  2. Taylor expanded around 0 1.5

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

  3. Final simplification1.5

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

Reproduce

herbie shell --seed 2019209 
(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)))))))