Average Error: 15.0 → 1.3
Time: 27.9s
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 r4115454 = K;
        double r4115455 = m;
        double r4115456 = n;
        double r4115457 = r4115455 + r4115456;
        double r4115458 = r4115454 * r4115457;
        double r4115459 = 2.0;
        double r4115460 = r4115458 / r4115459;
        double r4115461 = M;
        double r4115462 = r4115460 - r4115461;
        double r4115463 = cos(r4115462);
        double r4115464 = r4115457 / r4115459;
        double r4115465 = r4115464 - r4115461;
        double r4115466 = pow(r4115465, r4115459);
        double r4115467 = -r4115466;
        double r4115468 = l;
        double r4115469 = r4115455 - r4115456;
        double r4115470 = fabs(r4115469);
        double r4115471 = r4115468 - r4115470;
        double r4115472 = r4115467 - r4115471;
        double r4115473 = exp(r4115472);
        double r4115474 = r4115463 * r4115473;
        return r4115474;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r4115475 = m;
        double r4115476 = n;
        double r4115477 = r4115475 + r4115476;
        double r4115478 = 2.0;
        double r4115479 = r4115477 / r4115478;
        double r4115480 = M;
        double r4115481 = r4115479 - r4115480;
        double r4115482 = pow(r4115481, r4115478);
        double r4115483 = -r4115482;
        double r4115484 = l;
        double r4115485 = r4115475 - r4115476;
        double r4115486 = fabs(r4115485);
        double r4115487 = r4115484 - r4115486;
        double r4115488 = r4115483 - r4115487;
        double r4115489 = exp(r4115488);
        return r4115489;
}

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 15.0

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

  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 2019171 +o rules:numerics
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))