Average Error: 14.8 → 1.3
Time: 23.1s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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)}
↓
e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}
double f(double K, double m, double n, double M, double l) {
        double r6253013 = K;
        double r6253014 = m;
        double r6253015 = n;
        double r6253016 = r6253014 + r6253015;
        double r6253017 = r6253013 * r6253016;
        double r6253018 = 2.0;
        double r6253019 = r6253017 / r6253018;
        double r6253020 = M;
        double r6253021 = r6253019 - r6253020;
        double r6253022 = cos(r6253021);
        double r6253023 = r6253016 / r6253018;
        double r6253024 = r6253023 - r6253020;
        double r6253025 = pow(r6253024, r6253018);
        double r6253026 = -r6253025;
        double r6253027 = l;
        double r6253028 = r6253014 - r6253015;
        double r6253029 = fabs(r6253028);
        double r6253030 = r6253027 - r6253029;
        double r6253031 = r6253026 - r6253030;
        double r6253032 = exp(r6253031);
        double r6253033 = r6253022 * r6253032;
        return r6253033;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r6253034 = m;
        double r6253035 = n;
        double r6253036 = r6253034 + r6253035;
        double r6253037 = 2.0;
        double r6253038 = r6253036 / r6253037;
        double r6253039 = M;
        double r6253040 = r6253038 - r6253039;
        double r6253041 = pow(r6253040, r6253037);
        double r6253042 = -r6253041;
        double r6253043 = l;
        double r6253044 = r6253034 - r6253035;
        double r6253045 = fabs(r6253044);
        double r6253046 = r6253043 - r6253045;
        double r6253047 = r6253042 - r6253046;
        double r6253048 = exp(r6253047);
        return r6253048;
}

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 14.8

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

  2. Taylor expanded around 0 1.3

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

  3. Final simplification1.3

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

Reproduce

herbie shell --seed 2019164 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))