Average Error: 15.5 → 1.4
Time: 29.3s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}\]
\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)}
↓
\frac{1}{e^{{\left(\frac{m + n}{2} - M\right)}^{2} + \left(\ell - \left|m - n\right|\right)}}
double f(double K, double m, double n, double M, double l) {
        double r88391 = K;
        double r88392 = m;
        double r88393 = n;
        double r88394 = r88392 + r88393;
        double r88395 = r88391 * r88394;
        double r88396 = 2.0;
        double r88397 = r88395 / r88396;
        double r88398 = M;
        double r88399 = r88397 - r88398;
        double r88400 = cos(r88399);
        double r88401 = r88394 / r88396;
        double r88402 = r88401 - r88398;
        double r88403 = pow(r88402, r88396);
        double r88404 = -r88403;
        double r88405 = l;
        double r88406 = r88392 - r88393;
        double r88407 = fabs(r88406);
        double r88408 = r88405 - r88407;
        double r88409 = r88404 - r88408;
        double r88410 = exp(r88409);
        double r88411 = r88400 * r88410;
        return r88411;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r88412 = 1.0;
        double r88413 = m;
        double r88414 = n;
        double r88415 = r88413 + r88414;
        double r88416 = 2.0;
        double r88417 = r88415 / r88416;
        double r88418 = M;
        double r88419 = r88417 - r88418;
        double r88420 = pow(r88419, r88416);
        double r88421 = l;
        double r88422 = r88413 - r88414;
        double r88423 = fabs(r88422);
        double r88424 = r88421 - r88423;
        double r88425 = r88420 + r88424;
        double r88426 = exp(r88425);
        double r88427 = r88412 / r88426;
        return r88427;
}

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 15.5

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

  2. Simplified15.5

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

  3. Taylor expanded around 0 1.4

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

  4. Final simplification1.4

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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)))))))