Average Error: 15.7 → 1.2
Time: 21.4s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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 r122322 = K;
        double r122323 = m;
        double r122324 = n;
        double r122325 = r122323 + r122324;
        double r122326 = r122322 * r122325;
        double r122327 = 2.0;
        double r122328 = r122326 / r122327;
        double r122329 = M;
        double r122330 = r122328 - r122329;
        double r122331 = cos(r122330);
        double r122332 = r122325 / r122327;
        double r122333 = r122332 - r122329;
        double r122334 = pow(r122333, r122327);
        double r122335 = -r122334;
        double r122336 = l;
        double r122337 = r122323 - r122324;
        double r122338 = fabs(r122337);
        double r122339 = r122336 - r122338;
        double r122340 = r122335 - r122339;
        double r122341 = exp(r122340);
        double r122342 = r122331 * r122341;
        return r122342;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r122343 = 1.0;
        double r122344 = m;
        double r122345 = n;
        double r122346 = r122344 + r122345;
        double r122347 = 2.0;
        double r122348 = r122346 / r122347;
        double r122349 = M;
        double r122350 = r122348 - r122349;
        double r122351 = pow(r122350, r122347);
        double r122352 = l;
        double r122353 = r122344 - r122345;
        double r122354 = fabs(r122353);
        double r122355 = r122352 - r122354;
        double r122356 = r122351 + r122355;
        double r122357 = exp(r122356);
        double r122358 = r122343 / r122357;
        return r122358;
}

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. Simplified15.7

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

  3. Taylor expanded around 0 1.2

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

  4. Final simplification1.2

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

Reproduce

herbie shell --seed 2019297 
(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)))))))