Average Error: 15.3 → 1.4
Time: 34.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}\]
\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(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}
double f(double K, double m, double n, double M, double l) {
        double r91356 = K;
        double r91357 = m;
        double r91358 = n;
        double r91359 = r91357 + r91358;
        double r91360 = r91356 * r91359;
        double r91361 = 2.0;
        double r91362 = r91360 / r91361;
        double r91363 = M;
        double r91364 = r91362 - r91363;
        double r91365 = cos(r91364);
        double r91366 = r91359 / r91361;
        double r91367 = r91366 - r91363;
        double r91368 = pow(r91367, r91361);
        double r91369 = -r91368;
        double r91370 = l;
        double r91371 = r91357 - r91358;
        double r91372 = fabs(r91371);
        double r91373 = r91370 - r91372;
        double r91374 = r91369 - r91373;
        double r91375 = exp(r91374);
        double r91376 = r91365 * r91375;
        return r91376;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r91377 = exp(1.0);
        double r91378 = m;
        double r91379 = n;
        double r91380 = r91378 + r91379;
        double r91381 = 2.0;
        double r91382 = r91380 / r91381;
        double r91383 = M;
        double r91384 = r91382 - r91383;
        double r91385 = pow(r91384, r91381);
        double r91386 = -r91385;
        double r91387 = l;
        double r91388 = r91378 - r91379;
        double r91389 = fabs(r91388);
        double r91390 = r91387 - r91389;
        double r91391 = r91386 - r91390;
        double r91392 = pow(r91377, r91391);
        return r91392;
}

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 1.4

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

  4. Applied *-un-lft-identity1.4

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

  5. Applied exp-prod1.4

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

  6. Simplified1.4

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

  7. Final simplification1.4

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

Reproduce

herbie shell --seed 2019325 
(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)))))))