Average Error: 15.6 → 1.2
Time: 7.9s
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 r149628 = K;
        double r149629 = m;
        double r149630 = n;
        double r149631 = r149629 + r149630;
        double r149632 = r149628 * r149631;
        double r149633 = 2.0;
        double r149634 = r149632 / r149633;
        double r149635 = M;
        double r149636 = r149634 - r149635;
        double r149637 = cos(r149636);
        double r149638 = r149631 / r149633;
        double r149639 = r149638 - r149635;
        double r149640 = pow(r149639, r149633);
        double r149641 = -r149640;
        double r149642 = l;
        double r149643 = r149629 - r149630;
        double r149644 = fabs(r149643);
        double r149645 = r149642 - r149644;
        double r149646 = r149641 - r149645;
        double r149647 = exp(r149646);
        double r149648 = r149637 * r149647;
        return r149648;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r149649 = m;
        double r149650 = n;
        double r149651 = r149649 + r149650;
        double r149652 = 2.0;
        double r149653 = r149651 / r149652;
        double r149654 = M;
        double r149655 = r149653 - r149654;
        double r149656 = pow(r149655, r149652);
        double r149657 = cbrt(r149656);
        double r149658 = r149657 * r149657;
        double r149659 = cbrt(r149658);
        double r149660 = r149659 * r149659;
        double r149661 = r149660 * r149659;
        double r149662 = cbrt(r149655);
        double r149663 = r149662 * r149662;
        double r149664 = pow(r149663, r149652);
        double r149665 = cbrt(r149664);
        double r149666 = pow(r149662, r149652);
        double r149667 = cbrt(r149666);
        double r149668 = r149665 * r149667;
        double r149669 = r149661 * r149668;
        double r149670 = -r149669;
        double r149671 = l;
        double r149672 = r149649 - r149650;
        double r149673 = fabs(r149672);
        double r149674 = r149671 - r149673;
        double r149675 = r149670 - r149674;
        double r149676 = exp(r149675);
        return r149676;
}

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)))))))