Average Error: 15.3 → 1.3
Time: 4.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r149013 = K;
        double r149014 = m;
        double r149015 = n;
        double r149016 = r149014 + r149015;
        double r149017 = r149013 * r149016;
        double r149018 = 2.0;
        double r149019 = r149017 / r149018;
        double r149020 = M;
        double r149021 = r149019 - r149020;
        double r149022 = cos(r149021);
        double r149023 = r149016 / r149018;
        double r149024 = r149023 - r149020;
        double r149025 = pow(r149024, r149018);
        double r149026 = -r149025;
        double r149027 = l;
        double r149028 = r149014 - r149015;
        double r149029 = fabs(r149028);
        double r149030 = r149027 - r149029;
        double r149031 = r149026 - r149030;
        double r149032 = exp(r149031);
        double r149033 = r149022 * r149032;
        return r149033;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r149034 = 1.0;
        double r149035 = m;
        double r149036 = n;
        double r149037 = r149035 + r149036;
        double r149038 = 2.0;
        double r149039 = r149037 / r149038;
        double r149040 = M;
        double r149041 = r149039 - r149040;
        double r149042 = pow(r149041, r149038);
        double r149043 = l;
        double r149044 = r149035 - r149036;
        double r149045 = fabs(r149044);
        double r149046 = r149043 - r149045;
        double r149047 = r149042 + r149046;
        double r149048 = exp(r149047);
        double r149049 = r149034 / r149048;
        return r149049;
}

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 15.3

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

  2. Simplified15.3

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

  3. Taylor expanded around 0 1.3

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

  4. Final simplification1.3

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

Reproduce

herbie shell --seed 2020039 +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)))))))