Average Error: 15.7 → 1.5
Time: 27.7s
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 r4526237 = K;
        double r4526238 = m;
        double r4526239 = n;
        double r4526240 = r4526238 + r4526239;
        double r4526241 = r4526237 * r4526240;
        double r4526242 = 2.0;
        double r4526243 = r4526241 / r4526242;
        double r4526244 = M;
        double r4526245 = r4526243 - r4526244;
        double r4526246 = cos(r4526245);
        double r4526247 = r4526240 / r4526242;
        double r4526248 = r4526247 - r4526244;
        double r4526249 = pow(r4526248, r4526242);
        double r4526250 = -r4526249;
        double r4526251 = l;
        double r4526252 = r4526238 - r4526239;
        double r4526253 = fabs(r4526252);
        double r4526254 = r4526251 - r4526253;
        double r4526255 = r4526250 - r4526254;
        double r4526256 = exp(r4526255);
        double r4526257 = r4526246 * r4526256;
        return r4526257;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r4526258 = m;
        double r4526259 = n;
        double r4526260 = r4526258 + r4526259;
        double r4526261 = 2.0;
        double r4526262 = r4526260 / r4526261;
        double r4526263 = M;
        double r4526264 = r4526262 - r4526263;
        double r4526265 = pow(r4526264, r4526261);
        double r4526266 = -r4526265;
        double r4526267 = l;
        double r4526268 = r4526258 - r4526259;
        double r4526269 = fabs(r4526268);
        double r4526270 = r4526267 - r4526269;
        double r4526271 = r4526266 - r4526270;
        double r4526272 = exp(r4526271);
        return r4526272;
}

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 +o rules:numerics
(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)))))))