Average Error: 14.9 → 1.3
Time: 34.5s
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 r81512 = K;
        double r81513 = m;
        double r81514 = n;
        double r81515 = r81513 + r81514;
        double r81516 = r81512 * r81515;
        double r81517 = 2.0;
        double r81518 = r81516 / r81517;
        double r81519 = M;
        double r81520 = r81518 - r81519;
        double r81521 = cos(r81520);
        double r81522 = r81515 / r81517;
        double r81523 = r81522 - r81519;
        double r81524 = pow(r81523, r81517);
        double r81525 = -r81524;
        double r81526 = l;
        double r81527 = r81513 - r81514;
        double r81528 = fabs(r81527);
        double r81529 = r81526 - r81528;
        double r81530 = r81525 - r81529;
        double r81531 = exp(r81530);
        double r81532 = r81521 * r81531;
        return r81532;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r81533 = m;
        double r81534 = n;
        double r81535 = r81533 + r81534;
        double r81536 = 2.0;
        double r81537 = r81535 / r81536;
        double r81538 = M;
        double r81539 = r81537 - r81538;
        double r81540 = pow(r81539, r81536);
        double r81541 = -r81540;
        double r81542 = l;
        double r81543 = r81533 - r81534;
        double r81544 = fabs(r81543);
        double r81545 = r81542 - r81544;
        double r81546 = r81541 - r81545;
        double r81547 = exp(r81546);
        return r81547;
}

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 14.9

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

  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 2019323 
(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)))))))