Average Error: 15.0 → 1.3
Time: 8.8s
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 r280 = K;
        double r281 = m;
        double r282 = n;
        double r283 = r281 + r282;
        double r284 = r280 * r283;
        double r285 = 2.0;
        double r286 = r284 / r285;
        double r287 = M;
        double r288 = r286 - r287;
        double r289 = cos(r288);
        double r290 = r283 / r285;
        double r291 = r290 - r287;
        double r292 = pow(r291, r285);
        double r293 = -r292;
        double r294 = l;
        double r295 = r281 - r282;
        double r296 = fabs(r295);
        double r297 = r294 - r296;
        double r298 = r293 - r297;
        double r299 = exp(r298);
        double r300 = r289 * r299;
        return r300;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r301 = 1.0;
        double r302 = m;
        double r303 = n;
        double r304 = r302 + r303;
        double r305 = 2.0;
        double r306 = r304 / r305;
        double r307 = M;
        double r308 = r306 - r307;
        double r309 = pow(r308, r305);
        double r310 = l;
        double r311 = r302 - r303;
        double r312 = fabs(r311);
        double r313 = r310 - r312;
        double r314 = r309 + r313;
        double r315 = exp(r314);
        double r316 = r301 / r315;
        return r316;
}

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 15.0

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

  2. Simplified15.1

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

  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 2020025 
(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)))))))