Average Error: 15.6 → 1.4
Time: 37.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\left(\sqrt[3]{{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}} \cdot \sqrt[3]{{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}}\right) \cdot \sqrt[3]{{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}}\]
\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)}
↓
\left(\sqrt[3]{{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}} \cdot \sqrt[3]{{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}}\right) \cdot \sqrt[3]{{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}}
double f(double K, double m, double n, double M, double l) {
        double r9165510 = K;
        double r9165511 = m;
        double r9165512 = n;
        double r9165513 = r9165511 + r9165512;
        double r9165514 = r9165510 * r9165513;
        double r9165515 = 2.0;
        double r9165516 = r9165514 / r9165515;
        double r9165517 = M;
        double r9165518 = r9165516 - r9165517;
        double r9165519 = cos(r9165518);
        double r9165520 = r9165513 / r9165515;
        double r9165521 = r9165520 - r9165517;
        double r9165522 = pow(r9165521, r9165515);
        double r9165523 = -r9165522;
        double r9165524 = l;
        double r9165525 = r9165511 - r9165512;
        double r9165526 = fabs(r9165525);
        double r9165527 = r9165524 - r9165526;
        double r9165528 = r9165523 - r9165527;
        double r9165529 = exp(r9165528);
        double r9165530 = r9165519 * r9165529;
        return r9165530;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r9165531 = exp(1.0);
        double r9165532 = m;
        double r9165533 = n;
        double r9165534 = r9165532 + r9165533;
        double r9165535 = 2.0;
        double r9165536 = r9165534 / r9165535;
        double r9165537 = M;
        double r9165538 = r9165536 - r9165537;
        double r9165539 = pow(r9165538, r9165535);
        double r9165540 = -r9165539;
        double r9165541 = l;
        double r9165542 = r9165532 - r9165533;
        double r9165543 = fabs(r9165542);
        double r9165544 = r9165541 - r9165543;
        double r9165545 = r9165540 - r9165544;
        double r9165546 = pow(r9165531, r9165545);
        double r9165547 = cbrt(r9165546);
        double r9165548 = r9165547 * r9165547;
        double r9165549 = r9165548 * r9165547;
        return r9165549;
}

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 1.4

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

  4. Applied *-un-lft-identity1.4

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

  5. Applied exp-prod1.4

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

  6. Simplified1.4

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

  8. Applied add-cube-cbrt1.4

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

  9. Final simplification1.4

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

Reproduce

herbie shell --seed 2019174 
(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)))))))