Average Error: 15.7 → 1.2
Time: 5.7s
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 r139570 = K;
        double r139571 = m;
        double r139572 = n;
        double r139573 = r139571 + r139572;
        double r139574 = r139570 * r139573;
        double r139575 = 2.0;
        double r139576 = r139574 / r139575;
        double r139577 = M;
        double r139578 = r139576 - r139577;
        double r139579 = cos(r139578);
        double r139580 = r139573 / r139575;
        double r139581 = r139580 - r139577;
        double r139582 = pow(r139581, r139575);
        double r139583 = -r139582;
        double r139584 = l;
        double r139585 = r139571 - r139572;
        double r139586 = fabs(r139585);
        double r139587 = r139584 - r139586;
        double r139588 = r139583 - r139587;
        double r139589 = exp(r139588);
        double r139590 = r139579 * r139589;
        return r139590;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r139591 = m;
        double r139592 = n;
        double r139593 = r139591 + r139592;
        double r139594 = 2.0;
        double r139595 = r139593 / r139594;
        double r139596 = M;
        double r139597 = r139595 - r139596;
        double r139598 = pow(r139597, r139594);
        double r139599 = -r139598;
        double r139600 = l;
        double r139601 = r139591 - r139592;
        double r139602 = fabs(r139601);
        double r139603 = r139600 - r139602;
        double r139604 = r139599 - r139603;
        double r139605 = exp(r139604);
        return r139605;
}

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 15.7

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

  2. Taylor expanded around 0 1.2

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

  3. Final simplification1.2

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

Reproduce

herbie shell --seed 2019353 
(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)))))))