Average Error: 15.4 → 1.1
Time: 17.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\log \left({\left(e^{e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}}\right)}^{\left(\cos \left(\frac{\left(\sqrt[3]{K} \cdot \sqrt[3]{K}\right) \cdot \left(\sqrt[3]{K} \cdot \left(m + n\right)\right)}{2} - M\right)\right)}\right)\]
\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)}
↓
\log \left({\left(e^{e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}}\right)}^{\left(\cos \left(\frac{\left(\sqrt[3]{K} \cdot \sqrt[3]{K}\right) \cdot \left(\sqrt[3]{K} \cdot \left(m + n\right)\right)}{2} - M\right)\right)}\right)
double f(double K, double m, double n, double M, double l) {
        double r126914 = K;
        double r126915 = m;
        double r126916 = n;
        double r126917 = r126915 + r126916;
        double r126918 = r126914 * r126917;
        double r126919 = 2.0;
        double r126920 = r126918 / r126919;
        double r126921 = M;
        double r126922 = r126920 - r126921;
        double r126923 = cos(r126922);
        double r126924 = r126917 / r126919;
        double r126925 = r126924 - r126921;
        double r126926 = pow(r126925, r126919);
        double r126927 = -r126926;
        double r126928 = l;
        double r126929 = r126915 - r126916;
        double r126930 = fabs(r126929);
        double r126931 = r126928 - r126930;
        double r126932 = r126927 - r126931;
        double r126933 = exp(r126932);
        double r126934 = r126923 * r126933;
        return r126934;
}
↓
double f(double K, double m, double n, double M, double l) {
        double r126935 = m;
        double r126936 = n;
        double r126937 = r126935 - r126936;
        double r126938 = fabs(r126937);
        double r126939 = r126935 + r126936;
        double r126940 = 2.0;
        double r126941 = r126939 / r126940;
        double r126942 = M;
        double r126943 = r126941 - r126942;
        double r126944 = pow(r126943, r126940);
        double r126945 = l;
        double r126946 = r126944 + r126945;
        double r126947 = r126938 - r126946;
        double r126948 = exp(r126947);
        double r126949 = exp(r126948);
        double r126950 = K;
        double r126951 = cbrt(r126950);
        double r126952 = r126951 * r126951;
        double r126953 = r126951 * r126939;
        double r126954 = r126952 * r126953;
        double r126955 = r126954 / r126940;
        double r126956 = r126955 - r126942;
        double r126957 = cos(r126956);
        double r126958 = pow(r126949, r126957);
        double r126959 = log(r126958);
        return r126959;
}

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. Using strategy rm

  3. Applied add-log-exp15.5

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

  4. Simplified1.1

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

  6. Applied add-cube-cbrt1.1

    \[\leadsto \log \left({\left(e^{e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}}\right)}^{\left(\cos \left(\frac{\color{blue}{\left(\left(\sqrt[3]{K} \cdot \sqrt[3]{K}\right) \cdot \sqrt[3]{K}\right)} \cdot \left(m + n\right)}{2} - M\right)\right)}\right)\]

  7. Applied associate-*l*1.1

    \[\leadsto \log \left({\left(e^{e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}}\right)}^{\left(\cos \left(\frac{\color{blue}{\left(\sqrt[3]{K} \cdot \sqrt[3]{K}\right) \cdot \left(\sqrt[3]{K} \cdot \left(m + n\right)\right)}}{2} - M\right)\right)}\right)\]

  8. Final simplification1.1

    \[\leadsto \log \left({\left(e^{e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}}\right)}^{\left(\cos \left(\frac{\left(\sqrt[3]{K} \cdot \sqrt[3]{K}\right) \cdot \left(\sqrt[3]{K} \cdot \left(m + n\right)\right)}{2} - M\right)\right)}\right)\]

Reproduce

herbie shell --seed 2020046 
(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)))))))