Average Error: 14.9 → 1.4
Time: 22.5s
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 r104569 = K;
        double r104570 = m;
        double r104571 = n;
        double r104572 = r104570 + r104571;
        double r104573 = r104569 * r104572;
        double r104574 = 2.0;
        double r104575 = r104573 / r104574;
        double r104576 = M;
        double r104577 = r104575 - r104576;
        double r104578 = cos(r104577);
        double r104579 = r104572 / r104574;
        double r104580 = r104579 - r104576;
        double r104581 = pow(r104580, r104574);
        double r104582 = -r104581;
        double r104583 = l;
        double r104584 = r104570 - r104571;
        double r104585 = fabs(r104584);
        double r104586 = r104583 - r104585;
        double r104587 = r104582 - r104586;
        double r104588 = exp(r104587);
        double r104589 = r104578 * r104588;
        return r104589;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r104590 = m;
        double r104591 = n;
        double r104592 = r104590 + r104591;
        double r104593 = 2.0;
        double r104594 = r104592 / r104593;
        double r104595 = M;
        double r104596 = r104594 - r104595;
        double r104597 = pow(r104596, r104593);
        double r104598 = -r104597;
        double r104599 = l;
        double r104600 = r104590 - r104591;
        double r104601 = fabs(r104600);
        double r104602 = r104599 - r104601;
        double r104603 = r104598 - r104602;
        double r104604 = exp(r104603);
        return r104604;
}

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 1.4

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

  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 2019179 +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)))))))