Average Error: 14.8 → 1.4
Time: 30.7s
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 r100240 = K;
        double r100241 = m;
        double r100242 = n;
        double r100243 = r100241 + r100242;
        double r100244 = r100240 * r100243;
        double r100245 = 2.0;
        double r100246 = r100244 / r100245;
        double r100247 = M;
        double r100248 = r100246 - r100247;
        double r100249 = cos(r100248);
        double r100250 = r100243 / r100245;
        double r100251 = r100250 - r100247;
        double r100252 = pow(r100251, r100245);
        double r100253 = -r100252;
        double r100254 = l;
        double r100255 = r100241 - r100242;
        double r100256 = fabs(r100255);
        double r100257 = r100254 - r100256;
        double r100258 = r100253 - r100257;
        double r100259 = exp(r100258);
        double r100260 = r100249 * r100259;
        return r100260;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r100261 = m;
        double r100262 = n;
        double r100263 = r100261 + r100262;
        double r100264 = 2.0;
        double r100265 = r100263 / r100264;
        double r100266 = M;
        double r100267 = r100265 - r100266;
        double r100268 = pow(r100267, r100264);
        double r100269 = -r100268;
        double r100270 = l;
        double r100271 = r100261 - r100262;
        double r100272 = fabs(r100271);
        double r100273 = r100270 - r100272;
        double r100274 = r100269 - r100273;
        double r100275 = exp(r100274);
        return r100275;
}

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 14.8

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

  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 2019306 +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)))))))