Average Error: 14.6 → 1.4
Time: 33.6s
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 r1788539 = K;
        double r1788540 = m;
        double r1788541 = n;
        double r1788542 = r1788540 + r1788541;
        double r1788543 = r1788539 * r1788542;
        double r1788544 = 2.0;
        double r1788545 = r1788543 / r1788544;
        double r1788546 = M;
        double r1788547 = r1788545 - r1788546;
        double r1788548 = cos(r1788547);
        double r1788549 = r1788542 / r1788544;
        double r1788550 = r1788549 - r1788546;
        double r1788551 = pow(r1788550, r1788544);
        double r1788552 = -r1788551;
        double r1788553 = l;
        double r1788554 = r1788540 - r1788541;
        double r1788555 = fabs(r1788554);
        double r1788556 = r1788553 - r1788555;
        double r1788557 = r1788552 - r1788556;
        double r1788558 = exp(r1788557);
        double r1788559 = r1788548 * r1788558;
        return r1788559;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r1788560 = m;
        double r1788561 = n;
        double r1788562 = r1788560 + r1788561;
        double r1788563 = 2.0;
        double r1788564 = r1788562 / r1788563;
        double r1788565 = M;
        double r1788566 = r1788564 - r1788565;
        double r1788567 = pow(r1788566, r1788563);
        double r1788568 = -r1788567;
        double r1788569 = l;
        double r1788570 = r1788560 - r1788561;
        double r1788571 = fabs(r1788570);
        double r1788572 = r1788569 - r1788571;
        double r1788573 = r1788568 - r1788572;
        double r1788574 = exp(r1788573);
        return r1788574;
}

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 14.6

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

  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. 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 2019152 +o rules:numerics
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  (* (cos (- (/ (* K (+ m n)) 2) M)) (exp (- (- (pow (- (/ (+ m n) 2) M) 2)) (- l (fabs (- m n)))))))