Average Error: 14.9 → 1.3
Time: 27.3s
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 r93540 = K;
        double r93541 = m;
        double r93542 = n;
        double r93543 = r93541 + r93542;
        double r93544 = r93540 * r93543;
        double r93545 = 2.0;
        double r93546 = r93544 / r93545;
        double r93547 = M;
        double r93548 = r93546 - r93547;
        double r93549 = cos(r93548);
        double r93550 = r93543 / r93545;
        double r93551 = r93550 - r93547;
        double r93552 = pow(r93551, r93545);
        double r93553 = -r93552;
        double r93554 = l;
        double r93555 = r93541 - r93542;
        double r93556 = fabs(r93555);
        double r93557 = r93554 - r93556;
        double r93558 = r93553 - r93557;
        double r93559 = exp(r93558);
        double r93560 = r93549 * r93559;
        return r93560;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r93561 = m;
        double r93562 = n;
        double r93563 = r93561 + r93562;
        double r93564 = 2.0;
        double r93565 = r93563 / r93564;
        double r93566 = M;
        double r93567 = r93565 - r93566;
        double r93568 = pow(r93567, r93564);
        double r93569 = -r93568;
        double r93570 = l;
        double r93571 = r93561 - r93562;
        double r93572 = fabs(r93571);
        double r93573 = r93570 - r93572;
        double r93574 = r93569 - r93573;
        double r93575 = exp(r93574);
        return r93575;
}

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 14.9

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

  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 2019323 
(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)))))))