Average Error: 15.6 → 1.5
Time: 10.7s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\sqrt{{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}} \cdot \sqrt{{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}}\]
\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)}
↓
\sqrt{{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}} \cdot \sqrt{{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 r155277 = K;
        double r155278 = m;
        double r155279 = n;
        double r155280 = r155278 + r155279;
        double r155281 = r155277 * r155280;
        double r155282 = 2.0;
        double r155283 = r155281 / r155282;
        double r155284 = M;
        double r155285 = r155283 - r155284;
        double r155286 = cos(r155285);
        double r155287 = r155280 / r155282;
        double r155288 = r155287 - r155284;
        double r155289 = pow(r155288, r155282);
        double r155290 = -r155289;
        double r155291 = l;
        double r155292 = r155278 - r155279;
        double r155293 = fabs(r155292);
        double r155294 = r155291 - r155293;
        double r155295 = r155290 - r155294;
        double r155296 = exp(r155295);
        double r155297 = r155286 * r155296;
        return r155297;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r155298 = exp(1.0);
        double r155299 = m;
        double r155300 = n;
        double r155301 = r155299 + r155300;
        double r155302 = 2.0;
        double r155303 = r155301 / r155302;
        double r155304 = M;
        double r155305 = r155303 - r155304;
        double r155306 = pow(r155305, r155302);
        double r155307 = -r155306;
        double r155308 = l;
        double r155309 = r155299 - r155300;
        double r155310 = fabs(r155309);
        double r155311 = r155308 - r155310;
        double r155312 = r155307 - r155311;
        double r155313 = pow(r155298, r155312);
        double r155314 = sqrt(r155313);
        double r155315 = r155314 * r155314;
        return r155315;
}

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 15.6

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

  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. Using strategy rm

  4. Applied *-un-lft-identity1.5

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

  5. Applied exp-prod1.5

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

  6. Simplified1.5

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

  8. Applied add-sqr-sqrt1.5

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

  9. Final simplification1.5

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

Reproduce

herbie shell --seed 2020033 
(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)))))))