Average Error: 14.8 → 1.5
Time: 3.3m
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 r20755636 = K;
        double r20755637 = m;
        double r20755638 = n;
        double r20755639 = r20755637 + r20755638;
        double r20755640 = r20755636 * r20755639;
        double r20755641 = 2.0;
        double r20755642 = r20755640 / r20755641;
        double r20755643 = M;
        double r20755644 = r20755642 - r20755643;
        double r20755645 = cos(r20755644);
        double r20755646 = r20755639 / r20755641;
        double r20755647 = r20755646 - r20755643;
        double r20755648 = pow(r20755647, r20755641);
        double r20755649 = -r20755648;
        double r20755650 = l;
        double r20755651 = r20755637 - r20755638;
        double r20755652 = fabs(r20755651);
        double r20755653 = r20755650 - r20755652;
        double r20755654 = r20755649 - r20755653;
        double r20755655 = exp(r20755654);
        double r20755656 = r20755645 * r20755655;
        return r20755656;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r20755657 = m;
        double r20755658 = n;
        double r20755659 = r20755657 + r20755658;
        double r20755660 = 2.0;
        double r20755661 = r20755659 / r20755660;
        double r20755662 = M;
        double r20755663 = r20755661 - r20755662;
        double r20755664 = pow(r20755663, r20755660);
        double r20755665 = -r20755664;
        double r20755666 = l;
        double r20755667 = r20755657 - r20755658;
        double r20755668 = fabs(r20755667);
        double r20755669 = r20755666 - r20755668;
        double r20755670 = r20755665 - r20755669;
        double r20755671 = exp(r20755670);
        return r20755671;
}

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 14.8

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

  2. Taylor expanded around 0 1.5

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

  3. Final simplification1.5

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

Reproduce

herbie shell --seed 2019107 +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)))))))