Average Error: 15.8 → 1.3
Time: 7.1s
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 r119399 = K;
        double r119400 = m;
        double r119401 = n;
        double r119402 = r119400 + r119401;
        double r119403 = r119399 * r119402;
        double r119404 = 2.0;
        double r119405 = r119403 / r119404;
        double r119406 = M;
        double r119407 = r119405 - r119406;
        double r119408 = cos(r119407);
        double r119409 = r119402 / r119404;
        double r119410 = r119409 - r119406;
        double r119411 = pow(r119410, r119404);
        double r119412 = -r119411;
        double r119413 = l;
        double r119414 = r119400 - r119401;
        double r119415 = fabs(r119414);
        double r119416 = r119413 - r119415;
        double r119417 = r119412 - r119416;
        double r119418 = exp(r119417);
        double r119419 = r119408 * r119418;
        return r119419;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r119420 = m;
        double r119421 = n;
        double r119422 = r119420 + r119421;
        double r119423 = 2.0;
        double r119424 = r119422 / r119423;
        double r119425 = M;
        double r119426 = r119424 - r119425;
        double r119427 = pow(r119426, r119423);
        double r119428 = -r119427;
        double r119429 = l;
        double r119430 = r119420 - r119421;
        double r119431 = fabs(r119430);
        double r119432 = r119429 - r119431;
        double r119433 = r119428 - r119432;
        double r119434 = exp(r119433);
        return r119434;
}

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 15.8

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

  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 2019344 +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)))))))