Average Error: 15.4 → 1.4
Time: 53.5s
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 r4088917 = K;
        double r4088918 = m;
        double r4088919 = n;
        double r4088920 = r4088918 + r4088919;
        double r4088921 = r4088917 * r4088920;
        double r4088922 = 2.0;
        double r4088923 = r4088921 / r4088922;
        double r4088924 = M;
        double r4088925 = r4088923 - r4088924;
        double r4088926 = cos(r4088925);
        double r4088927 = r4088920 / r4088922;
        double r4088928 = r4088927 - r4088924;
        double r4088929 = pow(r4088928, r4088922);
        double r4088930 = -r4088929;
        double r4088931 = l;
        double r4088932 = r4088918 - r4088919;
        double r4088933 = fabs(r4088932);
        double r4088934 = r4088931 - r4088933;
        double r4088935 = r4088930 - r4088934;
        double r4088936 = exp(r4088935);
        double r4088937 = r4088926 * r4088936;
        return r4088937;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r4088938 = m;
        double r4088939 = n;
        double r4088940 = r4088938 - r4088939;
        double r4088941 = fabs(r4088940);
        double r4088942 = l;
        double r4088943 = r4088941 - r4088942;
        double r4088944 = r4088938 + r4088939;
        double r4088945 = 2.0;
        double r4088946 = r4088944 / r4088945;
        double r4088947 = M;
        double r4088948 = r4088946 - r4088947;
        double r4088949 = pow(r4088948, r4088945);
        double r4088950 = r4088943 - r4088949;
        double r4088951 = exp(r4088950);
        return r4088951;
}

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 15.4

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

  2. Simplified15.4

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019168 +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)))))))