Average Error: 15.9 → 1.4
Time: 10.0s
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 r118782 = K;
        double r118783 = m;
        double r118784 = n;
        double r118785 = r118783 + r118784;
        double r118786 = r118782 * r118785;
        double r118787 = 2.0;
        double r118788 = r118786 / r118787;
        double r118789 = M;
        double r118790 = r118788 - r118789;
        double r118791 = cos(r118790);
        double r118792 = r118785 / r118787;
        double r118793 = r118792 - r118789;
        double r118794 = pow(r118793, r118787);
        double r118795 = -r118794;
        double r118796 = l;
        double r118797 = r118783 - r118784;
        double r118798 = fabs(r118797);
        double r118799 = r118796 - r118798;
        double r118800 = r118795 - r118799;
        double r118801 = exp(r118800);
        double r118802 = r118791 * r118801;
        return r118802;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r118803 = m;
        double r118804 = n;
        double r118805 = r118803 + r118804;
        double r118806 = 2.0;
        double r118807 = r118805 / r118806;
        double r118808 = M;
        double r118809 = r118807 - r118808;
        double r118810 = pow(r118809, r118806);
        double r118811 = -r118810;
        double r118812 = l;
        double r118813 = r118803 - r118804;
        double r118814 = fabs(r118813);
        double r118815 = r118812 - r118814;
        double r118816 = r118811 - r118815;
        double r118817 = exp(r118816);
        return r118817;
}

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 15.9

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

  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 2020034 +o rules:numerics
(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)))))))