Average Error: 15.2 → 1.3
Time: 16.2s
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 r178071 = K;
        double r178072 = m;
        double r178073 = n;
        double r178074 = r178072 + r178073;
        double r178075 = r178071 * r178074;
        double r178076 = 2.0;
        double r178077 = r178075 / r178076;
        double r178078 = M;
        double r178079 = r178077 - r178078;
        double r178080 = cos(r178079);
        double r178081 = r178074 / r178076;
        double r178082 = r178081 - r178078;
        double r178083 = pow(r178082, r178076);
        double r178084 = -r178083;
        double r178085 = l;
        double r178086 = r178072 - r178073;
        double r178087 = fabs(r178086);
        double r178088 = r178085 - r178087;
        double r178089 = r178084 - r178088;
        double r178090 = exp(r178089);
        double r178091 = r178080 * r178090;
        return r178091;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r178092 = m;
        double r178093 = n;
        double r178094 = r178092 + r178093;
        double r178095 = 2.0;
        double r178096 = r178094 / r178095;
        double r178097 = M;
        double r178098 = r178096 - r178097;
        double r178099 = pow(r178098, r178095);
        double r178100 = -r178099;
        double r178101 = l;
        double r178102 = r178092 - r178093;
        double r178103 = fabs(r178102);
        double r178104 = r178101 - r178103;
        double r178105 = r178100 - r178104;
        double r178106 = exp(r178105);
        return r178106;
}

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 1.3

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

  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 2020047 +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)))))))