Average Error: 14.9 → 1.3
Time: 54.3s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}\]
\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|m - n\right| - \left({\left(\frac{m + n}{2} - M\right)}^{2} + \ell\right)}
double f(double K, double m, double n, double M, double l) {
        double r132028 = K;
        double r132029 = m;
        double r132030 = n;
        double r132031 = r132029 + r132030;
        double r132032 = r132028 * r132031;
        double r132033 = 2.0;
        double r132034 = r132032 / r132033;
        double r132035 = M;
        double r132036 = r132034 - r132035;
        double r132037 = cos(r132036);
        double r132038 = r132031 / r132033;
        double r132039 = r132038 - r132035;
        double r132040 = pow(r132039, r132033);
        double r132041 = -r132040;
        double r132042 = l;
        double r132043 = r132029 - r132030;
        double r132044 = fabs(r132043);
        double r132045 = r132042 - r132044;
        double r132046 = r132041 - r132045;
        double r132047 = exp(r132046);
        double r132048 = r132037 * r132047;
        return r132048;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r132049 = m;
        double r132050 = n;
        double r132051 = r132049 - r132050;
        double r132052 = fabs(r132051);
        double r132053 = r132049 + r132050;
        double r132054 = 2.0;
        double r132055 = r132053 / r132054;
        double r132056 = M;
        double r132057 = r132055 - r132056;
        double r132058 = pow(r132057, r132054);
        double r132059 = l;
        double r132060 = r132058 + r132059;
        double r132061 = r132052 - r132060;
        double r132062 = exp(r132061);
        return r132062;
}

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 14.9

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

  2. Simplified14.9

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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)))))))