Average Error: 14.7 → 1.3
Time: 17.3s
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 r1715058 = K;
        double r1715059 = m;
        double r1715060 = n;
        double r1715061 = r1715059 + r1715060;
        double r1715062 = r1715058 * r1715061;
        double r1715063 = 2.0;
        double r1715064 = r1715062 / r1715063;
        double r1715065 = M;
        double r1715066 = r1715064 - r1715065;
        double r1715067 = cos(r1715066);
        double r1715068 = r1715061 / r1715063;
        double r1715069 = r1715068 - r1715065;
        double r1715070 = pow(r1715069, r1715063);
        double r1715071 = -r1715070;
        double r1715072 = l;
        double r1715073 = r1715059 - r1715060;
        double r1715074 = fabs(r1715073);
        double r1715075 = r1715072 - r1715074;
        double r1715076 = r1715071 - r1715075;
        double r1715077 = exp(r1715076);
        double r1715078 = r1715067 * r1715077;
        return r1715078;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r1715079 = m;
        double r1715080 = n;
        double r1715081 = r1715079 + r1715080;
        double r1715082 = 2.0;
        double r1715083 = r1715081 / r1715082;
        double r1715084 = M;
        double r1715085 = r1715083 - r1715084;
        double r1715086 = pow(r1715085, r1715082);
        double r1715087 = -r1715086;
        double r1715088 = l;
        double r1715089 = r1715079 - r1715080;
        double r1715090 = fabs(r1715089);
        double r1715091 = r1715088 - r1715090;
        double r1715092 = r1715087 - r1715091;
        double r1715093 = exp(r1715092);
        return r1715093;
}

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 14.7

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

  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 2019155 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))