Average Error: 15.2 → 1.4
Time: 4.8m
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 r39958416 = K;
        double r39958417 = m;
        double r39958418 = n;
        double r39958419 = r39958417 + r39958418;
        double r39958420 = r39958416 * r39958419;
        double r39958421 = 2.0;
        double r39958422 = r39958420 / r39958421;
        double r39958423 = M;
        double r39958424 = r39958422 - r39958423;
        double r39958425 = cos(r39958424);
        double r39958426 = r39958419 / r39958421;
        double r39958427 = r39958426 - r39958423;
        double r39958428 = pow(r39958427, r39958421);
        double r39958429 = -r39958428;
        double r39958430 = l;
        double r39958431 = r39958417 - r39958418;
        double r39958432 = fabs(r39958431);
        double r39958433 = r39958430 - r39958432;
        double r39958434 = r39958429 - r39958433;
        double r39958435 = exp(r39958434);
        double r39958436 = r39958425 * r39958435;
        return r39958436;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r39958437 = m;
        double r39958438 = n;
        double r39958439 = r39958437 + r39958438;
        double r39958440 = 2.0;
        double r39958441 = r39958439 / r39958440;
        double r39958442 = M;
        double r39958443 = r39958441 - r39958442;
        double r39958444 = pow(r39958443, r39958440);
        double r39958445 = -r39958444;
        double r39958446 = l;
        double r39958447 = r39958437 - r39958438;
        double r39958448 = fabs(r39958447);
        double r39958449 = r39958446 - r39958448;
        double r39958450 = r39958445 - r39958449;
        double r39958451 = exp(r39958450);
        return r39958451;
}

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 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))