Average Error: 15.3 → 1.4
Time: 34.0s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[{e}^{\left(\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)\right)}\]
\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)}
↓
{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 r91195 = K;
        double r91196 = m;
        double r91197 = n;
        double r91198 = r91196 + r91197;
        double r91199 = r91195 * r91198;
        double r91200 = 2.0;
        double r91201 = r91199 / r91200;
        double r91202 = M;
        double r91203 = r91201 - r91202;
        double r91204 = cos(r91203);
        double r91205 = r91198 / r91200;
        double r91206 = r91205 - r91202;
        double r91207 = pow(r91206, r91200);
        double r91208 = -r91207;
        double r91209 = l;
        double r91210 = r91196 - r91197;
        double r91211 = fabs(r91210);
        double r91212 = r91209 - r91211;
        double r91213 = r91208 - r91212;
        double r91214 = exp(r91213);
        double r91215 = r91204 * r91214;
        return r91215;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r91216 = exp(1.0);
        double r91217 = m;
        double r91218 = n;
        double r91219 = r91217 + r91218;
        double r91220 = 2.0;
        double r91221 = r91219 / r91220;
        double r91222 = M;
        double r91223 = r91221 - r91222;
        double r91224 = pow(r91223, r91220);
        double r91225 = -r91224;
        double r91226 = l;
        double r91227 = r91217 - r91218;
        double r91228 = fabs(r91227);
        double r91229 = r91226 - r91228;
        double r91230 = r91225 - r91229;
        double r91231 = pow(r91216, r91230);
        return r91231;
}

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 15.3

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

  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. Final simplification1.4

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

Reproduce

herbie shell --seed 2019325 
(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)))))))