Average Error: 15.7 → 1.5
Time: 27.3s
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 r4104166 = K;
        double r4104167 = m;
        double r4104168 = n;
        double r4104169 = r4104167 + r4104168;
        double r4104170 = r4104166 * r4104169;
        double r4104171 = 2.0;
        double r4104172 = r4104170 / r4104171;
        double r4104173 = M;
        double r4104174 = r4104172 - r4104173;
        double r4104175 = cos(r4104174);
        double r4104176 = r4104169 / r4104171;
        double r4104177 = r4104176 - r4104173;
        double r4104178 = pow(r4104177, r4104171);
        double r4104179 = -r4104178;
        double r4104180 = l;
        double r4104181 = r4104167 - r4104168;
        double r4104182 = fabs(r4104181);
        double r4104183 = r4104180 - r4104182;
        double r4104184 = r4104179 - r4104183;
        double r4104185 = exp(r4104184);
        double r4104186 = r4104175 * r4104185;
        return r4104186;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r4104187 = m;
        double r4104188 = n;
        double r4104189 = r4104187 + r4104188;
        double r4104190 = 2.0;
        double r4104191 = r4104189 / r4104190;
        double r4104192 = M;
        double r4104193 = r4104191 - r4104192;
        double r4104194 = pow(r4104193, r4104190);
        double r4104195 = -r4104194;
        double r4104196 = l;
        double r4104197 = r4104187 - r4104188;
        double r4104198 = fabs(r4104197);
        double r4104199 = r4104196 - r4104198;
        double r4104200 = r4104195 - r4104199;
        double r4104201 = exp(r4104200);
        return r4104201;
}

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 15.7

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

  2. Taylor expanded around 0 1.5

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

  3. Final simplification1.5

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

Reproduce

herbie shell --seed 2019162 
(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)))))))