Average Error: 15.1 → 1.3
Time: 24.7s
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 r151006 = K;
        double r151007 = m;
        double r151008 = n;
        double r151009 = r151007 + r151008;
        double r151010 = r151006 * r151009;
        double r151011 = 2.0;
        double r151012 = r151010 / r151011;
        double r151013 = M;
        double r151014 = r151012 - r151013;
        double r151015 = cos(r151014);
        double r151016 = r151009 / r151011;
        double r151017 = r151016 - r151013;
        double r151018 = pow(r151017, r151011);
        double r151019 = -r151018;
        double r151020 = l;
        double r151021 = r151007 - r151008;
        double r151022 = fabs(r151021);
        double r151023 = r151020 - r151022;
        double r151024 = r151019 - r151023;
        double r151025 = exp(r151024);
        double r151026 = r151015 * r151025;
        return r151026;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r151027 = m;
        double r151028 = n;
        double r151029 = r151027 + r151028;
        double r151030 = 2.0;
        double r151031 = r151029 / r151030;
        double r151032 = M;
        double r151033 = r151031 - r151032;
        double r151034 = pow(r151033, r151030);
        double r151035 = -r151034;
        double r151036 = l;
        double r151037 = r151027 - r151028;
        double r151038 = fabs(r151037);
        double r151039 = r151036 - r151038;
        double r151040 = r151035 - r151039;
        double r151041 = exp(r151040);
        return r151041;
}

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 15.1

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

  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 2020046 
(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)))))))