Average Error: 15.0 → 1.3
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 r149609 = K;
        double r149610 = m;
        double r149611 = n;
        double r149612 = r149610 + r149611;
        double r149613 = r149609 * r149612;
        double r149614 = 2.0;
        double r149615 = r149613 / r149614;
        double r149616 = M;
        double r149617 = r149615 - r149616;
        double r149618 = cos(r149617);
        double r149619 = r149612 / r149614;
        double r149620 = r149619 - r149616;
        double r149621 = pow(r149620, r149614);
        double r149622 = -r149621;
        double r149623 = l;
        double r149624 = r149610 - r149611;
        double r149625 = fabs(r149624);
        double r149626 = r149623 - r149625;
        double r149627 = r149622 - r149626;
        double r149628 = exp(r149627);
        double r149629 = r149618 * r149628;
        return r149629;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r149630 = m;
        double r149631 = n;
        double r149632 = r149630 + r149631;
        double r149633 = 2.0;
        double r149634 = r149632 / r149633;
        double r149635 = M;
        double r149636 = r149634 - r149635;
        double r149637 = pow(r149636, r149633);
        double r149638 = -r149637;
        double r149639 = l;
        double r149640 = r149630 - r149631;
        double r149641 = fabs(r149640);
        double r149642 = r149639 - r149641;
        double r149643 = r149638 - r149642;
        double r149644 = exp(r149643);
        return r149644;
}

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 15.0

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

  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 2019351 
(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)))))))