Average Error: 15.6 → 1.2
Time: 7.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-\left(\left(\sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \left(\sqrt[3]{{\left(\sqrt[3]{\frac{m + n}{2} - M} \cdot \sqrt[3]{\frac{m + n}{2} - M}\right)}^{2}} \cdot \sqrt[3]{{\left(\sqrt[3]{\frac{m + n}{2} - M}\right)}^{2}}\right)\right) - \left(\ell - \left|m - n\right|\right)}\]
\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(\left(\sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \left(\sqrt[3]{{\left(\sqrt[3]{\frac{m + n}{2} - M} \cdot \sqrt[3]{\frac{m + n}{2} - M}\right)}^{2}} \cdot \sqrt[3]{{\left(\sqrt[3]{\frac{m + n}{2} - M}\right)}^{2}}\right)\right) - \left(\ell - \left|m - n\right|\right)}
double f(double K, double m, double n, double M, double l) {
        double r119623 = K;
        double r119624 = m;
        double r119625 = n;
        double r119626 = r119624 + r119625;
        double r119627 = r119623 * r119626;
        double r119628 = 2.0;
        double r119629 = r119627 / r119628;
        double r119630 = M;
        double r119631 = r119629 - r119630;
        double r119632 = cos(r119631);
        double r119633 = r119626 / r119628;
        double r119634 = r119633 - r119630;
        double r119635 = pow(r119634, r119628);
        double r119636 = -r119635;
        double r119637 = l;
        double r119638 = r119624 - r119625;
        double r119639 = fabs(r119638);
        double r119640 = r119637 - r119639;
        double r119641 = r119636 - r119640;
        double r119642 = exp(r119641);
        double r119643 = r119632 * r119642;
        return r119643;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r119644 = m;
        double r119645 = n;
        double r119646 = r119644 + r119645;
        double r119647 = 2.0;
        double r119648 = r119646 / r119647;
        double r119649 = M;
        double r119650 = r119648 - r119649;
        double r119651 = pow(r119650, r119647);
        double r119652 = cbrt(r119651);
        double r119653 = r119652 * r119652;
        double r119654 = cbrt(r119653);
        double r119655 = r119654 * r119654;
        double r119656 = r119655 * r119654;
        double r119657 = cbrt(r119650);
        double r119658 = r119657 * r119657;
        double r119659 = pow(r119658, r119647);
        double r119660 = cbrt(r119659);
        double r119661 = pow(r119657, r119647);
        double r119662 = cbrt(r119661);
        double r119663 = r119660 * r119662;
        double r119664 = r119656 * r119663;
        double r119665 = -r119664;
        double r119666 = l;
        double r119667 = r119644 - r119645;
        double r119668 = fabs(r119667);
        double r119669 = r119666 - r119668;
        double r119670 = r119665 - r119669;
        double r119671 = exp(r119670);
        return r119671;
}

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 15.6

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

  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. Using strategy rm

  4. Applied add-cube-cbrt1.2

    \[\leadsto 1 \cdot e^{\left(-\color{blue}{\left(\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}\right) \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) - \left(\ell - \left|m - n\right|\right)}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt1.2

    \[\leadsto 1 \cdot e^{\left(-\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right)} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}\right) - \left(\ell - \left|m - n\right|\right)}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt1.2

    \[\leadsto 1 \cdot e^{\left(-\left(\left(\sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \sqrt[3]{{\color{blue}{\left(\left(\sqrt[3]{\frac{m + n}{2} - M} \cdot \sqrt[3]{\frac{m + n}{2} - M}\right) \cdot \sqrt[3]{\frac{m + n}{2} - M}\right)}}^{2}}\right) - \left(\ell - \left|m - n\right|\right)}\]

  9. Applied unpow-prod-down1.2

    \[\leadsto 1 \cdot e^{\left(-\left(\left(\sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \sqrt[3]{\color{blue}{{\left(\sqrt[3]{\frac{m + n}{2} - M} \cdot \sqrt[3]{\frac{m + n}{2} - M}\right)}^{2} \cdot {\left(\sqrt[3]{\frac{m + n}{2} - M}\right)}^{2}}}\right) - \left(\ell - \left|m - n\right|\right)}\]

  10. Applied cbrt-prod1.2

    \[\leadsto 1 \cdot e^{\left(-\left(\left(\sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \color{blue}{\left(\sqrt[3]{{\left(\sqrt[3]{\frac{m + n}{2} - M} \cdot \sqrt[3]{\frac{m + n}{2} - M}\right)}^{2}} \cdot \sqrt[3]{{\left(\sqrt[3]{\frac{m + n}{2} - M}\right)}^{2}}\right)}\right) - \left(\ell - \left|m - n\right|\right)}\]

  11. Final simplification1.2

    \[\leadsto e^{\left(-\left(\left(\sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}} \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \sqrt[3]{\sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}} \cdot \sqrt[3]{{\left(\frac{m + n}{2} - M\right)}^{2}}}\right) \cdot \left(\sqrt[3]{{\left(\sqrt[3]{\frac{m + n}{2} - M} \cdot \sqrt[3]{\frac{m + n}{2} - M}\right)}^{2}} \cdot \sqrt[3]{{\left(\sqrt[3]{\frac{m + n}{2} - M}\right)}^{2}}\right)\right) - \left(\ell - \left|m - n\right|\right)}\]

Reproduce

herbie shell --seed 2020001 
(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)))))))