Average Error: 15.3 → 1.3
Time: 9.9s
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 r176413 = K;
        double r176414 = m;
        double r176415 = n;
        double r176416 = r176414 + r176415;
        double r176417 = r176413 * r176416;
        double r176418 = 2.0;
        double r176419 = r176417 / r176418;
        double r176420 = M;
        double r176421 = r176419 - r176420;
        double r176422 = cos(r176421);
        double r176423 = r176416 / r176418;
        double r176424 = r176423 - r176420;
        double r176425 = pow(r176424, r176418);
        double r176426 = -r176425;
        double r176427 = l;
        double r176428 = r176414 - r176415;
        double r176429 = fabs(r176428);
        double r176430 = r176427 - r176429;
        double r176431 = r176426 - r176430;
        double r176432 = exp(r176431);
        double r176433 = r176422 * r176432;
        return r176433;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r176434 = m;
        double r176435 = n;
        double r176436 = r176434 + r176435;
        double r176437 = 2.0;
        double r176438 = r176436 / r176437;
        double r176439 = M;
        double r176440 = r176438 - r176439;
        double r176441 = pow(r176440, r176437);
        double r176442 = -r176441;
        double r176443 = l;
        double r176444 = r176434 - r176435;
        double r176445 = fabs(r176444);
        double r176446 = r176443 - r176445;
        double r176447 = r176442 - r176446;
        double r176448 = exp(r176447);
        return r176448;
}

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 15.3

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

  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 2020039 
(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)))))))