Average Error: 15.5 → 1.3
Time: 29.4s
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 r3517052 = K;
        double r3517053 = m;
        double r3517054 = n;
        double r3517055 = r3517053 + r3517054;
        double r3517056 = r3517052 * r3517055;
        double r3517057 = 2.0;
        double r3517058 = r3517056 / r3517057;
        double r3517059 = M;
        double r3517060 = r3517058 - r3517059;
        double r3517061 = cos(r3517060);
        double r3517062 = r3517055 / r3517057;
        double r3517063 = r3517062 - r3517059;
        double r3517064 = pow(r3517063, r3517057);
        double r3517065 = -r3517064;
        double r3517066 = l;
        double r3517067 = r3517053 - r3517054;
        double r3517068 = fabs(r3517067);
        double r3517069 = r3517066 - r3517068;
        double r3517070 = r3517065 - r3517069;
        double r3517071 = exp(r3517070);
        double r3517072 = r3517061 * r3517071;
        return r3517072;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r3517073 = m;
        double r3517074 = n;
        double r3517075 = r3517073 - r3517074;
        double r3517076 = fabs(r3517075);
        double r3517077 = l;
        double r3517078 = r3517076 - r3517077;
        double r3517079 = r3517073 + r3517074;
        double r3517080 = 2.0;
        double r3517081 = r3517079 / r3517080;
        double r3517082 = M;
        double r3517083 = r3517081 - r3517082;
        double r3517084 = pow(r3517083, r3517080);
        double r3517085 = r3517078 - r3517084;
        double r3517086 = exp(r3517085);
        return r3517086;
}

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 15.5

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

  2. Simplified15.5

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

  3. Taylor expanded around 0 1.3

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

  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 2019170 +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)))))))