Average Error: 15.2 → 1.3
Time: 7.2s
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 r186156 = K;
        double r186157 = m;
        double r186158 = n;
        double r186159 = r186157 + r186158;
        double r186160 = r186156 * r186159;
        double r186161 = 2.0;
        double r186162 = r186160 / r186161;
        double r186163 = M;
        double r186164 = r186162 - r186163;
        double r186165 = cos(r186164);
        double r186166 = r186159 / r186161;
        double r186167 = r186166 - r186163;
        double r186168 = pow(r186167, r186161);
        double r186169 = -r186168;
        double r186170 = l;
        double r186171 = r186157 - r186158;
        double r186172 = fabs(r186171);
        double r186173 = r186170 - r186172;
        double r186174 = r186169 - r186173;
        double r186175 = exp(r186174);
        double r186176 = r186165 * r186175;
        return r186176;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r186177 = m;
        double r186178 = n;
        double r186179 = r186177 + r186178;
        double r186180 = 2.0;
        double r186181 = r186179 / r186180;
        double r186182 = M;
        double r186183 = r186181 - r186182;
        double r186184 = pow(r186183, r186180);
        double r186185 = -r186184;
        double r186186 = l;
        double r186187 = r186177 - r186178;
        double r186188 = fabs(r186187);
        double r186189 = r186186 - r186188;
        double r186190 = r186185 - r186189;
        double r186191 = exp(r186190);
        return r186191;
}

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 15.2

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

  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 2020047 
(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)))))))