Average Error: 15.4 → 1.4
Time: 21.1s
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 r3194618 = K;
        double r3194619 = m;
        double r3194620 = n;
        double r3194621 = r3194619 + r3194620;
        double r3194622 = r3194618 * r3194621;
        double r3194623 = 2.0;
        double r3194624 = r3194622 / r3194623;
        double r3194625 = M;
        double r3194626 = r3194624 - r3194625;
        double r3194627 = cos(r3194626);
        double r3194628 = r3194621 / r3194623;
        double r3194629 = r3194628 - r3194625;
        double r3194630 = pow(r3194629, r3194623);
        double r3194631 = -r3194630;
        double r3194632 = l;
        double r3194633 = r3194619 - r3194620;
        double r3194634 = fabs(r3194633);
        double r3194635 = r3194632 - r3194634;
        double r3194636 = r3194631 - r3194635;
        double r3194637 = exp(r3194636);
        double r3194638 = r3194627 * r3194637;
        return r3194638;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r3194639 = m;
        double r3194640 = n;
        double r3194641 = r3194639 + r3194640;
        double r3194642 = 2.0;
        double r3194643 = r3194641 / r3194642;
        double r3194644 = M;
        double r3194645 = r3194643 - r3194644;
        double r3194646 = pow(r3194645, r3194642);
        double r3194647 = -r3194646;
        double r3194648 = l;
        double r3194649 = r3194639 - r3194640;
        double r3194650 = fabs(r3194649);
        double r3194651 = r3194648 - r3194650;
        double r3194652 = r3194647 - r3194651;
        double r3194653 = exp(r3194652);
        return r3194653;
}

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 1.4

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

  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 2019144 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))