Average Error: 15.7 → 1.2
Time: 22.4s
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 r108283 = K;
        double r108284 = m;
        double r108285 = n;
        double r108286 = r108284 + r108285;
        double r108287 = r108283 * r108286;
        double r108288 = 2.0;
        double r108289 = r108287 / r108288;
        double r108290 = M;
        double r108291 = r108289 - r108290;
        double r108292 = cos(r108291);
        double r108293 = r108286 / r108288;
        double r108294 = r108293 - r108290;
        double r108295 = pow(r108294, r108288);
        double r108296 = -r108295;
        double r108297 = l;
        double r108298 = r108284 - r108285;
        double r108299 = fabs(r108298);
        double r108300 = r108297 - r108299;
        double r108301 = r108296 - r108300;
        double r108302 = exp(r108301);
        double r108303 = r108292 * r108302;
        return r108303;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r108304 = m;
        double r108305 = n;
        double r108306 = r108304 + r108305;
        double r108307 = 2.0;
        double r108308 = r108306 / r108307;
        double r108309 = M;
        double r108310 = r108308 - r108309;
        double r108311 = pow(r108310, r108307);
        double r108312 = -r108311;
        double r108313 = l;
        double r108314 = r108304 - r108305;
        double r108315 = fabs(r108314);
        double r108316 = r108313 - r108315;
        double r108317 = r108312 - r108316;
        double r108318 = exp(r108317);
        return r108318;
}

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 2019208 +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)))))))