Average Error: 15.6 → 1.5
Time: 32.8s
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 r111594 = K;
        double r111595 = m;
        double r111596 = n;
        double r111597 = r111595 + r111596;
        double r111598 = r111594 * r111597;
        double r111599 = 2.0;
        double r111600 = r111598 / r111599;
        double r111601 = M;
        double r111602 = r111600 - r111601;
        double r111603 = cos(r111602);
        double r111604 = r111597 / r111599;
        double r111605 = r111604 - r111601;
        double r111606 = pow(r111605, r111599);
        double r111607 = -r111606;
        double r111608 = l;
        double r111609 = r111595 - r111596;
        double r111610 = fabs(r111609);
        double r111611 = r111608 - r111610;
        double r111612 = r111607 - r111611;
        double r111613 = exp(r111612);
        double r111614 = r111603 * r111613;
        return r111614;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r111615 = m;
        double r111616 = n;
        double r111617 = r111615 + r111616;
        double r111618 = 2.0;
        double r111619 = r111617 / r111618;
        double r111620 = M;
        double r111621 = r111619 - r111620;
        double r111622 = pow(r111621, r111618);
        double r111623 = -r111622;
        double r111624 = l;
        double r111625 = r111615 - r111616;
        double r111626 = fabs(r111625);
        double r111627 = r111624 - r111626;
        double r111628 = r111623 - r111627;
        double r111629 = exp(r111628);
        return r111629;
}

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. Taylor expanded around 0 1.5

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

  3. Final simplification1.5

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

Reproduce

herbie shell --seed 2019209 +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)))))))