Average Error: 15.5 → 1.4
Time: 30.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r100537 = K;
        double r100538 = m;
        double r100539 = n;
        double r100540 = r100538 + r100539;
        double r100541 = r100537 * r100540;
        double r100542 = 2.0;
        double r100543 = r100541 / r100542;
        double r100544 = M;
        double r100545 = r100543 - r100544;
        double r100546 = cos(r100545);
        double r100547 = r100540 / r100542;
        double r100548 = r100547 - r100544;
        double r100549 = pow(r100548, r100542);
        double r100550 = -r100549;
        double r100551 = l;
        double r100552 = r100538 - r100539;
        double r100553 = fabs(r100552);
        double r100554 = r100551 - r100553;
        double r100555 = r100550 - r100554;
        double r100556 = exp(r100555);
        double r100557 = r100546 * r100556;
        return r100557;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r100558 = 1.0;
        double r100559 = m;
        double r100560 = n;
        double r100561 = r100559 + r100560;
        double r100562 = 2.0;
        double r100563 = r100561 / r100562;
        double r100564 = M;
        double r100565 = r100563 - r100564;
        double r100566 = pow(r100565, r100562);
        double r100567 = l;
        double r100568 = r100559 - r100560;
        double r100569 = fabs(r100568);
        double r100570 = r100567 - r100569;
        double r100571 = r100566 + r100570;
        double r100572 = exp(r100571);
        double r100573 = r100558 / r100572;
        return r100573;
}

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 15.5

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

  2. Simplified15.5

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019326 +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)))))))