Average Error: 15.5 → 1.4
Time: 29.4s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r155122 = K;
        double r155123 = m;
        double r155124 = n;
        double r155125 = r155123 + r155124;
        double r155126 = r155122 * r155125;
        double r155127 = 2.0;
        double r155128 = r155126 / r155127;
        double r155129 = M;
        double r155130 = r155128 - r155129;
        double r155131 = cos(r155130);
        double r155132 = r155125 / r155127;
        double r155133 = r155132 - r155129;
        double r155134 = pow(r155133, r155127);
        double r155135 = -r155134;
        double r155136 = l;
        double r155137 = r155123 - r155124;
        double r155138 = fabs(r155137);
        double r155139 = r155136 - r155138;
        double r155140 = r155135 - r155139;
        double r155141 = exp(r155140);
        double r155142 = r155131 * r155141;
        return r155142;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r155143 = 1.0;
        double r155144 = m;
        double r155145 = n;
        double r155146 = r155144 + r155145;
        double r155147 = 2.0;
        double r155148 = r155146 / r155147;
        double r155149 = M;
        double r155150 = r155148 - r155149;
        double r155151 = pow(r155150, r155147);
        double r155152 = l;
        double r155153 = r155144 - r155145;
        double r155154 = fabs(r155153);
        double r155155 = r155152 - r155154;
        double r155156 = r155151 + r155155;
        double r155157 = exp(r155156);
        double r155158 = r155143 / r155157;
        return r155158;
}

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 15.5

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

  2. Simplified15.5

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(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)))))))