Average Error: 15.5 → 1.4
Time: 20.1s
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 r143645 = K;
        double r143646 = m;
        double r143647 = n;
        double r143648 = r143646 + r143647;
        double r143649 = r143645 * r143648;
        double r143650 = 2.0;
        double r143651 = r143649 / r143650;
        double r143652 = M;
        double r143653 = r143651 - r143652;
        double r143654 = cos(r143653);
        double r143655 = r143648 / r143650;
        double r143656 = r143655 - r143652;
        double r143657 = pow(r143656, r143650);
        double r143658 = -r143657;
        double r143659 = l;
        double r143660 = r143646 - r143647;
        double r143661 = fabs(r143660);
        double r143662 = r143659 - r143661;
        double r143663 = r143658 - r143662;
        double r143664 = exp(r143663);
        double r143665 = r143654 * r143664;
        return r143665;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r143666 = m;
        double r143667 = n;
        double r143668 = r143666 + r143667;
        double r143669 = 2.0;
        double r143670 = r143668 / r143669;
        double r143671 = M;
        double r143672 = r143670 - r143671;
        double r143673 = pow(r143672, r143669);
        double r143674 = -r143673;
        double r143675 = l;
        double r143676 = r143666 - r143667;
        double r143677 = fabs(r143676);
        double r143678 = r143675 - r143677;
        double r143679 = r143674 - r143678;
        double r143680 = exp(r143679);
        return r143680;
}

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 15.5

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

  2. Taylor expanded around 0 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2020043 
(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)))))))