Average Error: 15.8 → 1.4
Time: 13.0s
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 r140266 = K;
        double r140267 = m;
        double r140268 = n;
        double r140269 = r140267 + r140268;
        double r140270 = r140266 * r140269;
        double r140271 = 2.0;
        double r140272 = r140270 / r140271;
        double r140273 = M;
        double r140274 = r140272 - r140273;
        double r140275 = cos(r140274);
        double r140276 = r140269 / r140271;
        double r140277 = r140276 - r140273;
        double r140278 = pow(r140277, r140271);
        double r140279 = -r140278;
        double r140280 = l;
        double r140281 = r140267 - r140268;
        double r140282 = fabs(r140281);
        double r140283 = r140280 - r140282;
        double r140284 = r140279 - r140283;
        double r140285 = exp(r140284);
        double r140286 = r140275 * r140285;
        return r140286;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r140287 = m;
        double r140288 = n;
        double r140289 = r140287 + r140288;
        double r140290 = 2.0;
        double r140291 = r140289 / r140290;
        double r140292 = M;
        double r140293 = r140291 - r140292;
        double r140294 = pow(r140293, r140290);
        double r140295 = -r140294;
        double r140296 = l;
        double r140297 = r140287 - r140288;
        double r140298 = fabs(r140297);
        double r140299 = r140296 - r140298;
        double r140300 = r140295 - r140299;
        double r140301 = exp(r140300);
        return r140301;
}

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 15.8

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

  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 2020045 
(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)))))))