Average Error: 15.4 → 1.4
Time: 6.4s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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 r148051 = K;
        double r148052 = m;
        double r148053 = n;
        double r148054 = r148052 + r148053;
        double r148055 = r148051 * r148054;
        double r148056 = 2.0;
        double r148057 = r148055 / r148056;
        double r148058 = M;
        double r148059 = r148057 - r148058;
        double r148060 = cos(r148059);
        double r148061 = r148054 / r148056;
        double r148062 = r148061 - r148058;
        double r148063 = pow(r148062, r148056);
        double r148064 = -r148063;
        double r148065 = l;
        double r148066 = r148052 - r148053;
        double r148067 = fabs(r148066);
        double r148068 = r148065 - r148067;
        double r148069 = r148064 - r148068;
        double r148070 = exp(r148069);
        double r148071 = r148060 * r148070;
        return r148071;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r148072 = 1.0;
        double r148073 = m;
        double r148074 = n;
        double r148075 = r148073 + r148074;
        double r148076 = 2.0;
        double r148077 = r148075 / r148076;
        double r148078 = M;
        double r148079 = r148077 - r148078;
        double r148080 = pow(r148079, r148076);
        double r148081 = l;
        double r148082 = r148073 - r148074;
        double r148083 = fabs(r148082);
        double r148084 = r148081 - r148083;
        double r148085 = r148080 + r148084;
        double r148086 = exp(r148085);
        double r148087 = r148072 / r148086;
        return r148087;
}

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 15.4

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

  2. Simplified15.4

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2020059 
(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)))))))