Average Error: 15.0 → 1.3
Time: 33.5s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[{e}^{\left(\left(\left|m - n\right| - {\left(\frac{m + n}{2} - M\right)}^{2}\right) - \ell\right)}\]
\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(\left(\left|m - n\right| - {\left(\frac{m + n}{2} - M\right)}^{2}\right) - \ell\right)}
double f(double K, double m, double n, double M, double l) {
        double r6430079 = K;
        double r6430080 = m;
        double r6430081 = n;
        double r6430082 = r6430080 + r6430081;
        double r6430083 = r6430079 * r6430082;
        double r6430084 = 2.0;
        double r6430085 = r6430083 / r6430084;
        double r6430086 = M;
        double r6430087 = r6430085 - r6430086;
        double r6430088 = cos(r6430087);
        double r6430089 = r6430082 / r6430084;
        double r6430090 = r6430089 - r6430086;
        double r6430091 = pow(r6430090, r6430084);
        double r6430092 = -r6430091;
        double r6430093 = l;
        double r6430094 = r6430080 - r6430081;
        double r6430095 = fabs(r6430094);
        double r6430096 = r6430093 - r6430095;
        double r6430097 = r6430092 - r6430096;
        double r6430098 = exp(r6430097);
        double r6430099 = r6430088 * r6430098;
        return r6430099;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r6430100 = exp(1.0);
        double r6430101 = m;
        double r6430102 = n;
        double r6430103 = r6430101 - r6430102;
        double r6430104 = fabs(r6430103);
        double r6430105 = r6430101 + r6430102;
        double r6430106 = 2.0;
        double r6430107 = r6430105 / r6430106;
        double r6430108 = M;
        double r6430109 = r6430107 - r6430108;
        double r6430110 = pow(r6430109, r6430106);
        double r6430111 = r6430104 - r6430110;
        double r6430112 = l;
        double r6430113 = r6430111 - r6430112;
        double r6430114 = pow(r6430100, r6430113);
        return r6430114;
}

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

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

  3. Taylor expanded around 0 1.3

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

  5. Applied *-un-lft-identity1.3

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

  6. Applied exp-prod1.3

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

  7. Simplified1.3

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

  8. Final simplification1.3

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

Reproduce

herbie shell --seed 2019192 
(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)))))))