Average Error: 15.2 → 1.3
Time: 16.6s
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 r270431 = K;
        double r270432 = m;
        double r270433 = n;
        double r270434 = r270432 + r270433;
        double r270435 = r270431 * r270434;
        double r270436 = 2.0;
        double r270437 = r270435 / r270436;
        double r270438 = M;
        double r270439 = r270437 - r270438;
        double r270440 = cos(r270439);
        double r270441 = r270434 / r270436;
        double r270442 = r270441 - r270438;
        double r270443 = pow(r270442, r270436);
        double r270444 = -r270443;
        double r270445 = l;
        double r270446 = r270432 - r270433;
        double r270447 = fabs(r270446);
        double r270448 = r270445 - r270447;
        double r270449 = r270444 - r270448;
        double r270450 = exp(r270449);
        double r270451 = r270440 * r270450;
        return r270451;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r270452 = m;
        double r270453 = n;
        double r270454 = r270452 + r270453;
        double r270455 = 2.0;
        double r270456 = r270454 / r270455;
        double r270457 = M;
        double r270458 = r270456 - r270457;
        double r270459 = pow(r270458, r270455);
        double r270460 = -r270459;
        double r270461 = l;
        double r270462 = r270452 - r270453;
        double r270463 = fabs(r270462);
        double r270464 = r270461 - r270463;
        double r270465 = r270460 - r270464;
        double r270466 = exp(r270465);
        return r270466;
}

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 15.2

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

  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 2020047 +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)))))))