Average Error: 15.4 → 1.3
Time: 15.1s
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 r126633 = K;
        double r126634 = m;
        double r126635 = n;
        double r126636 = r126634 + r126635;
        double r126637 = r126633 * r126636;
        double r126638 = 2.0;
        double r126639 = r126637 / r126638;
        double r126640 = M;
        double r126641 = r126639 - r126640;
        double r126642 = cos(r126641);
        double r126643 = r126636 / r126638;
        double r126644 = r126643 - r126640;
        double r126645 = pow(r126644, r126638);
        double r126646 = -r126645;
        double r126647 = l;
        double r126648 = r126634 - r126635;
        double r126649 = fabs(r126648);
        double r126650 = r126647 - r126649;
        double r126651 = r126646 - r126650;
        double r126652 = exp(r126651);
        double r126653 = r126642 * r126652;
        return r126653;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r126654 = m;
        double r126655 = n;
        double r126656 = r126654 + r126655;
        double r126657 = 2.0;
        double r126658 = r126656 / r126657;
        double r126659 = M;
        double r126660 = r126658 - r126659;
        double r126661 = pow(r126660, r126657);
        double r126662 = -r126661;
        double r126663 = l;
        double r126664 = r126654 - r126655;
        double r126665 = fabs(r126664);
        double r126666 = r126663 - r126665;
        double r126667 = r126662 - r126666;
        double r126668 = exp(r126667);
        return r126668;
}

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 15.4

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

  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 2020042 
(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)))))))