Average Error: 15.3 → 1.6
Time: 5.8s
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 r109676 = K;
        double r109677 = m;
        double r109678 = n;
        double r109679 = r109677 + r109678;
        double r109680 = r109676 * r109679;
        double r109681 = 2.0;
        double r109682 = r109680 / r109681;
        double r109683 = M;
        double r109684 = r109682 - r109683;
        double r109685 = cos(r109684);
        double r109686 = r109679 / r109681;
        double r109687 = r109686 - r109683;
        double r109688 = pow(r109687, r109681);
        double r109689 = -r109688;
        double r109690 = l;
        double r109691 = r109677 - r109678;
        double r109692 = fabs(r109691);
        double r109693 = r109690 - r109692;
        double r109694 = r109689 - r109693;
        double r109695 = exp(r109694);
        double r109696 = r109685 * r109695;
        return r109696;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r109697 = m;
        double r109698 = n;
        double r109699 = r109697 + r109698;
        double r109700 = 2.0;
        double r109701 = r109699 / r109700;
        double r109702 = M;
        double r109703 = r109701 - r109702;
        double r109704 = pow(r109703, r109700);
        double r109705 = -r109704;
        double r109706 = l;
        double r109707 = r109697 - r109698;
        double r109708 = fabs(r109707);
        double r109709 = r109706 - r109708;
        double r109710 = r109705 - r109709;
        double r109711 = exp(r109710);
        return r109711;
}

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 15.3

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

  2. Taylor expanded around 0 1.6

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

  3. Final simplification1.6

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

Reproduce

herbie shell --seed 2020062 
(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)))))))