Average Error: 15.2 → 1.4
Time: 37.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
\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(-{\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 r133267 = K;
        double r133268 = m;
        double r133269 = n;
        double r133270 = r133268 + r133269;
        double r133271 = r133267 * r133270;
        double r133272 = 2.0;
        double r133273 = r133271 / r133272;
        double r133274 = M;
        double r133275 = r133273 - r133274;
        double r133276 = cos(r133275);
        double r133277 = r133270 / r133272;
        double r133278 = r133277 - r133274;
        double r133279 = pow(r133278, r133272);
        double r133280 = -r133279;
        double r133281 = l;
        double r133282 = r133268 - r133269;
        double r133283 = fabs(r133282);
        double r133284 = r133281 - r133283;
        double r133285 = r133280 - r133284;
        double r133286 = exp(r133285);
        double r133287 = r133276 * r133286;
        return r133287;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r133288 = m;
        double r133289 = n;
        double r133290 = r133288 + r133289;
        double r133291 = 2.0;
        double r133292 = r133290 / r133291;
        double r133293 = M;
        double r133294 = r133292 - r133293;
        double r133295 = pow(r133294, r133291);
        double r133296 = -r133295;
        double r133297 = l;
        double r133298 = r133288 - r133289;
        double r133299 = fabs(r133298);
        double r133300 = r133297 - r133299;
        double r133301 = r133296 - r133300;
        double r133302 = exp(r133301);
        return r133302;
}

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 1.4

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

  3. Final simplification1.4

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

Reproduce

herbie shell --seed 2019235 +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)))))))