Average Error: 15.2 → 1.3
Time: 17.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\sqrt[3]{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)} \cdot \sqrt[3]{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\right) \cdot \sqrt[3]{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}}\]
\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(\sqrt[3]{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)} \cdot \sqrt[3]{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\right) \cdot \sqrt[3]{\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 r164534 = K;
        double r164535 = m;
        double r164536 = n;
        double r164537 = r164535 + r164536;
        double r164538 = r164534 * r164537;
        double r164539 = 2.0;
        double r164540 = r164538 / r164539;
        double r164541 = M;
        double r164542 = r164540 - r164541;
        double r164543 = cos(r164542);
        double r164544 = r164537 / r164539;
        double r164545 = r164544 - r164541;
        double r164546 = pow(r164545, r164539);
        double r164547 = -r164546;
        double r164548 = l;
        double r164549 = r164535 - r164536;
        double r164550 = fabs(r164549);
        double r164551 = r164548 - r164550;
        double r164552 = r164547 - r164551;
        double r164553 = exp(r164552);
        double r164554 = r164543 * r164553;
        return r164554;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r164555 = m;
        double r164556 = n;
        double r164557 = r164555 + r164556;
        double r164558 = 2.0;
        double r164559 = r164557 / r164558;
        double r164560 = M;
        double r164561 = r164559 - r164560;
        double r164562 = pow(r164561, r164558);
        double r164563 = -r164562;
        double r164564 = l;
        double r164565 = r164555 - r164556;
        double r164566 = fabs(r164565);
        double r164567 = r164564 - r164566;
        double r164568 = r164563 - r164567;
        double r164569 = cbrt(r164568);
        double r164570 = r164569 * r164569;
        double r164571 = r164570 * r164569;
        double r164572 = exp(r164571);
        return r164572;
}

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 15.2

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

  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-cbrt1.3

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

  5. Final simplification1.3

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

Reproduce

herbie shell --seed 2019346 
(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)))))))