Average Error: 15.5 → 1.5
Time: 6.7s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r199452 = K;
        double r199453 = m;
        double r199454 = n;
        double r199455 = r199453 + r199454;
        double r199456 = r199452 * r199455;
        double r199457 = 2.0;
        double r199458 = r199456 / r199457;
        double r199459 = M;
        double r199460 = r199458 - r199459;
        double r199461 = cos(r199460);
        double r199462 = r199455 / r199457;
        double r199463 = r199462 - r199459;
        double r199464 = pow(r199463, r199457);
        double r199465 = -r199464;
        double r199466 = l;
        double r199467 = r199453 - r199454;
        double r199468 = fabs(r199467);
        double r199469 = r199466 - r199468;
        double r199470 = r199465 - r199469;
        double r199471 = exp(r199470);
        double r199472 = r199461 * r199471;
        return r199472;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r199473 = 1.0;
        double r199474 = m;
        double r199475 = n;
        double r199476 = r199474 + r199475;
        double r199477 = 2.0;
        double r199478 = r199476 / r199477;
        double r199479 = M;
        double r199480 = r199478 - r199479;
        double r199481 = pow(r199480, r199477);
        double r199482 = l;
        double r199483 = r199474 - r199475;
        double r199484 = fabs(r199483);
        double r199485 = r199482 - r199484;
        double r199486 = r199481 + r199485;
        double r199487 = exp(r199486);
        double r199488 = r199473 / r199487;
        return r199488;
}

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 15.5

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

  2. Simplified15.5

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

  3. Taylor expanded around 0 1.5

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

  4. Final simplification1.5

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

Reproduce

herbie shell --seed 2020020 +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)))))))