Average Error: 15.0 → 1.3
Time: 22.5s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\]
\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)}
↓
e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}
double f(double K, double m, double n, double M, double l) {
        double r5723051 = K;
        double r5723052 = m;
        double r5723053 = n;
        double r5723054 = r5723052 + r5723053;
        double r5723055 = r5723051 * r5723054;
        double r5723056 = 2.0;
        double r5723057 = r5723055 / r5723056;
        double r5723058 = M;
        double r5723059 = r5723057 - r5723058;
        double r5723060 = cos(r5723059);
        double r5723061 = r5723054 / r5723056;
        double r5723062 = r5723061 - r5723058;
        double r5723063 = pow(r5723062, r5723056);
        double r5723064 = -r5723063;
        double r5723065 = l;
        double r5723066 = r5723052 - r5723053;
        double r5723067 = fabs(r5723066);
        double r5723068 = r5723065 - r5723067;
        double r5723069 = r5723064 - r5723068;
        double r5723070 = exp(r5723069);
        double r5723071 = r5723060 * r5723070;
        return r5723071;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r5723072 = m;
        double r5723073 = n;
        double r5723074 = r5723072 - r5723073;
        double r5723075 = fabs(r5723074);
        double r5723076 = l;
        double r5723077 = r5723075 - r5723076;
        double r5723078 = r5723072 + r5723073;
        double r5723079 = 2.0;
        double r5723080 = r5723078 / r5723079;
        double r5723081 = M;
        double r5723082 = r5723080 - r5723081;
        double r5723083 = pow(r5723082, r5723079);
        double r5723084 = r5723077 - r5723083;
        double r5723085 = exp(r5723084);
        return r5723085;
}

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 15.0

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

  2. Simplified15.0

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019171 
(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)))))))