Average Error: 15.2 → 1.4
Time: 9.9s
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 r183001 = K;
        double r183002 = m;
        double r183003 = n;
        double r183004 = r183002 + r183003;
        double r183005 = r183001 * r183004;
        double r183006 = 2.0;
        double r183007 = r183005 / r183006;
        double r183008 = M;
        double r183009 = r183007 - r183008;
        double r183010 = cos(r183009);
        double r183011 = r183004 / r183006;
        double r183012 = r183011 - r183008;
        double r183013 = pow(r183012, r183006);
        double r183014 = -r183013;
        double r183015 = l;
        double r183016 = r183002 - r183003;
        double r183017 = fabs(r183016);
        double r183018 = r183015 - r183017;
        double r183019 = r183014 - r183018;
        double r183020 = exp(r183019);
        double r183021 = r183010 * r183020;
        return r183021;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r183022 = m;
        double r183023 = n;
        double r183024 = r183022 + r183023;
        double r183025 = 2.0;
        double r183026 = r183024 / r183025;
        double r183027 = M;
        double r183028 = r183026 - r183027;
        double r183029 = pow(r183028, r183025);
        double r183030 = -r183029;
        double r183031 = l;
        double r183032 = r183022 - r183023;
        double r183033 = fabs(r183032);
        double r183034 = r183031 - r183033;
        double r183035 = r183030 - r183034;
        double r183036 = exp(r183035);
        return r183036;
}

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 15.2

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

  2. Taylor expanded around 0 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2019352 
(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)))))))