Average Error: 15.6 → 1.4
Time: 9.2s
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 r167404 = K;
        double r167405 = m;
        double r167406 = n;
        double r167407 = r167405 + r167406;
        double r167408 = r167404 * r167407;
        double r167409 = 2.0;
        double r167410 = r167408 / r167409;
        double r167411 = M;
        double r167412 = r167410 - r167411;
        double r167413 = cos(r167412);
        double r167414 = r167407 / r167409;
        double r167415 = r167414 - r167411;
        double r167416 = pow(r167415, r167409);
        double r167417 = -r167416;
        double r167418 = l;
        double r167419 = r167405 - r167406;
        double r167420 = fabs(r167419);
        double r167421 = r167418 - r167420;
        double r167422 = r167417 - r167421;
        double r167423 = exp(r167422);
        double r167424 = r167413 * r167423;
        return r167424;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r167425 = 1.0;
        double r167426 = m;
        double r167427 = n;
        double r167428 = r167426 + r167427;
        double r167429 = 2.0;
        double r167430 = r167428 / r167429;
        double r167431 = M;
        double r167432 = r167430 - r167431;
        double r167433 = pow(r167432, r167429);
        double r167434 = l;
        double r167435 = r167426 - r167427;
        double r167436 = fabs(r167435);
        double r167437 = r167434 - r167436;
        double r167438 = r167433 + r167437;
        double r167439 = exp(r167438);
        double r167440 = r167425 / r167439;
        return r167440;
}

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. Simplified15.6

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2020021 +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)))))))