Average Error: 15.3 → 1.6
Time: 6.0s
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 r110639 = K;
        double r110640 = m;
        double r110641 = n;
        double r110642 = r110640 + r110641;
        double r110643 = r110639 * r110642;
        double r110644 = 2.0;
        double r110645 = r110643 / r110644;
        double r110646 = M;
        double r110647 = r110645 - r110646;
        double r110648 = cos(r110647);
        double r110649 = r110642 / r110644;
        double r110650 = r110649 - r110646;
        double r110651 = pow(r110650, r110644);
        double r110652 = -r110651;
        double r110653 = l;
        double r110654 = r110640 - r110641;
        double r110655 = fabs(r110654);
        double r110656 = r110653 - r110655;
        double r110657 = r110652 - r110656;
        double r110658 = exp(r110657);
        double r110659 = r110648 * r110658;
        return r110659;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r110660 = m;
        double r110661 = n;
        double r110662 = r110660 + r110661;
        double r110663 = 2.0;
        double r110664 = r110662 / r110663;
        double r110665 = M;
        double r110666 = r110664 - r110665;
        double r110667 = pow(r110666, r110663);
        double r110668 = -r110667;
        double r110669 = l;
        double r110670 = r110660 - r110661;
        double r110671 = fabs(r110670);
        double r110672 = r110669 - r110671;
        double r110673 = r110668 - r110672;
        double r110674 = exp(r110673);
        return r110674;
}

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 15.3

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

  2. Taylor expanded around 0 1.6

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

  3. Final simplification1.6

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

Reproduce

herbie shell --seed 2020062 
(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)))))))