Average Error: 15.2 → 1.3
Time: 22.6s
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 r112495 = K;
        double r112496 = m;
        double r112497 = n;
        double r112498 = r112496 + r112497;
        double r112499 = r112495 * r112498;
        double r112500 = 2.0;
        double r112501 = r112499 / r112500;
        double r112502 = M;
        double r112503 = r112501 - r112502;
        double r112504 = cos(r112503);
        double r112505 = r112498 / r112500;
        double r112506 = r112505 - r112502;
        double r112507 = pow(r112506, r112500);
        double r112508 = -r112507;
        double r112509 = l;
        double r112510 = r112496 - r112497;
        double r112511 = fabs(r112510);
        double r112512 = r112509 - r112511;
        double r112513 = r112508 - r112512;
        double r112514 = exp(r112513);
        double r112515 = r112504 * r112514;
        return r112515;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r112516 = m;
        double r112517 = n;
        double r112518 = r112516 + r112517;
        double r112519 = 2.0;
        double r112520 = r112518 / r112519;
        double r112521 = M;
        double r112522 = r112520 - r112521;
        double r112523 = pow(r112522, r112519);
        double r112524 = -r112523;
        double r112525 = l;
        double r112526 = r112516 - r112517;
        double r112527 = fabs(r112526);
        double r112528 = r112525 - r112527;
        double r112529 = r112524 - r112528;
        double r112530 = exp(r112529);
        return r112530;
}

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 15.2

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

  2. Taylor expanded around 0 1.3

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

  3. Final simplification1.3

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

Reproduce

herbie shell --seed 2019347 
(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)))))))