Average Error: 14.7 → 1.2
Time: 18.8s
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 r115082 = K;
        double r115083 = m;
        double r115084 = n;
        double r115085 = r115083 + r115084;
        double r115086 = r115082 * r115085;
        double r115087 = 2.0;
        double r115088 = r115086 / r115087;
        double r115089 = M;
        double r115090 = r115088 - r115089;
        double r115091 = cos(r115090);
        double r115092 = r115085 / r115087;
        double r115093 = r115092 - r115089;
        double r115094 = pow(r115093, r115087);
        double r115095 = -r115094;
        double r115096 = l;
        double r115097 = r115083 - r115084;
        double r115098 = fabs(r115097);
        double r115099 = r115096 - r115098;
        double r115100 = r115095 - r115099;
        double r115101 = exp(r115100);
        double r115102 = r115091 * r115101;
        return r115102;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r115103 = m;
        double r115104 = n;
        double r115105 = r115103 + r115104;
        double r115106 = 2.0;
        double r115107 = r115105 / r115106;
        double r115108 = M;
        double r115109 = r115107 - r115108;
        double r115110 = pow(r115109, r115106);
        double r115111 = -r115110;
        double r115112 = l;
        double r115113 = r115103 - r115104;
        double r115114 = fabs(r115113);
        double r115115 = r115112 - r115114;
        double r115116 = r115111 - r115115;
        double r115117 = exp(r115116);
        return r115117;
}

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 1.2

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

  3. Final simplification1.2

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

Reproduce

herbie shell --seed 2019194 
(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)))))))