Average Error: 15.7 → 1.4
Time: 16.5s
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 r96434 = K;
        double r96435 = m;
        double r96436 = n;
        double r96437 = r96435 + r96436;
        double r96438 = r96434 * r96437;
        double r96439 = 2.0;
        double r96440 = r96438 / r96439;
        double r96441 = M;
        double r96442 = r96440 - r96441;
        double r96443 = cos(r96442);
        double r96444 = r96437 / r96439;
        double r96445 = r96444 - r96441;
        double r96446 = pow(r96445, r96439);
        double r96447 = -r96446;
        double r96448 = l;
        double r96449 = r96435 - r96436;
        double r96450 = fabs(r96449);
        double r96451 = r96448 - r96450;
        double r96452 = r96447 - r96451;
        double r96453 = exp(r96452);
        double r96454 = r96443 * r96453;
        return r96454;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r96455 = m;
        double r96456 = n;
        double r96457 = r96455 + r96456;
        double r96458 = 2.0;
        double r96459 = r96457 / r96458;
        double r96460 = M;
        double r96461 = r96459 - r96460;
        double r96462 = pow(r96461, r96458);
        double r96463 = -r96462;
        double r96464 = l;
        double r96465 = r96455 - r96456;
        double r96466 = fabs(r96465);
        double r96467 = r96464 - r96466;
        double r96468 = r96463 - r96467;
        double r96469 = exp(r96468);
        return r96469;
}

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 1.4

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

  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 2019294 
(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)))))))