Average Error: 14.9 → 1.4
Time: 20.6s
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 r111639 = K;
        double r111640 = m;
        double r111641 = n;
        double r111642 = r111640 + r111641;
        double r111643 = r111639 * r111642;
        double r111644 = 2.0;
        double r111645 = r111643 / r111644;
        double r111646 = M;
        double r111647 = r111645 - r111646;
        double r111648 = cos(r111647);
        double r111649 = r111642 / r111644;
        double r111650 = r111649 - r111646;
        double r111651 = pow(r111650, r111644);
        double r111652 = -r111651;
        double r111653 = l;
        double r111654 = r111640 - r111641;
        double r111655 = fabs(r111654);
        double r111656 = r111653 - r111655;
        double r111657 = r111652 - r111656;
        double r111658 = exp(r111657);
        double r111659 = r111648 * r111658;
        return r111659;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r111660 = m;
        double r111661 = n;
        double r111662 = r111660 + r111661;
        double r111663 = 2.0;
        double r111664 = r111662 / r111663;
        double r111665 = M;
        double r111666 = r111664 - r111665;
        double r111667 = pow(r111666, r111663);
        double r111668 = -r111667;
        double r111669 = l;
        double r111670 = r111660 - r111661;
        double r111671 = fabs(r111670);
        double r111672 = r111669 - r111671;
        double r111673 = r111668 - r111672;
        double r111674 = exp(r111673);
        return r111674;
}

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 14.9

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

  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 2019179 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))