Average Error: 14.9 → 1.3
Time: 30.9s
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 r116509 = K;
        double r116510 = m;
        double r116511 = n;
        double r116512 = r116510 + r116511;
        double r116513 = r116509 * r116512;
        double r116514 = 2.0;
        double r116515 = r116513 / r116514;
        double r116516 = M;
        double r116517 = r116515 - r116516;
        double r116518 = cos(r116517);
        double r116519 = r116512 / r116514;
        double r116520 = r116519 - r116516;
        double r116521 = pow(r116520, r116514);
        double r116522 = -r116521;
        double r116523 = l;
        double r116524 = r116510 - r116511;
        double r116525 = fabs(r116524);
        double r116526 = r116523 - r116525;
        double r116527 = r116522 - r116526;
        double r116528 = exp(r116527);
        double r116529 = r116518 * r116528;
        return r116529;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r116530 = m;
        double r116531 = n;
        double r116532 = r116530 + r116531;
        double r116533 = 2.0;
        double r116534 = r116532 / r116533;
        double r116535 = M;
        double r116536 = r116534 - r116535;
        double r116537 = pow(r116536, r116533);
        double r116538 = -r116537;
        double r116539 = l;
        double r116540 = r116530 - r116531;
        double r116541 = fabs(r116540);
        double r116542 = r116539 - r116541;
        double r116543 = r116538 - r116542;
        double r116544 = exp(r116543);
        return r116544;
}

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 +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)))))))