Average Error: 15.1 → 1.3
Time: 28.6s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left|m - n\right| - \left(\ell + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)}\]
\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|m - n\right| - \left(\ell + \left(\frac{m + n}{2} - M\right) \cdot \left(\frac{m + n}{2} - M\right)\right)}
double f(double K, double m, double n, double M, double l) {
        double r3813085 = K;
        double r3813086 = m;
        double r3813087 = n;
        double r3813088 = r3813086 + r3813087;
        double r3813089 = r3813085 * r3813088;
        double r3813090 = 2.0;
        double r3813091 = r3813089 / r3813090;
        double r3813092 = M;
        double r3813093 = r3813091 - r3813092;
        double r3813094 = cos(r3813093);
        double r3813095 = r3813088 / r3813090;
        double r3813096 = r3813095 - r3813092;
        double r3813097 = pow(r3813096, r3813090);
        double r3813098 = -r3813097;
        double r3813099 = l;
        double r3813100 = r3813086 - r3813087;
        double r3813101 = fabs(r3813100);
        double r3813102 = r3813099 - r3813101;
        double r3813103 = r3813098 - r3813102;
        double r3813104 = exp(r3813103);
        double r3813105 = r3813094 * r3813104;
        return r3813105;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r3813106 = m;
        double r3813107 = n;
        double r3813108 = r3813106 - r3813107;
        double r3813109 = fabs(r3813108);
        double r3813110 = l;
        double r3813111 = r3813106 + r3813107;
        double r3813112 = 2.0;
        double r3813113 = r3813111 / r3813112;
        double r3813114 = M;
        double r3813115 = r3813113 - r3813114;
        double r3813116 = r3813115 * r3813115;
        double r3813117 = r3813110 + r3813116;
        double r3813118 = r3813109 - r3813117;
        double r3813119 = exp(r3813118);
        return r3813119;
}

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. Simplified15.1

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019141 
(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)))))))