Average Error: 15.8 → 1.3
Time: 53.8s
Precision: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2.0} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2.0} - M\right)}^{2.0}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2.0} - M\right)}^{2.0}}\]
\cos \left(\frac{K \cdot \left(m + n\right)}{2.0} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2.0} - M\right)}^{2.0}\right) - \left(\ell - \left|m - n\right|\right)}
↓
e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2.0} - M\right)}^{2.0}}
double f(double K, double m, double n, double M, double l) {
        double r3840130 = K;
        double r3840131 = m;
        double r3840132 = n;
        double r3840133 = r3840131 + r3840132;
        double r3840134 = r3840130 * r3840133;
        double r3840135 = 2.0;
        double r3840136 = r3840134 / r3840135;
        double r3840137 = M;
        double r3840138 = r3840136 - r3840137;
        double r3840139 = cos(r3840138);
        double r3840140 = r3840133 / r3840135;
        double r3840141 = r3840140 - r3840137;
        double r3840142 = pow(r3840141, r3840135);
        double r3840143 = -r3840142;
        double r3840144 = l;
        double r3840145 = r3840131 - r3840132;
        double r3840146 = fabs(r3840145);
        double r3840147 = r3840144 - r3840146;
        double r3840148 = r3840143 - r3840147;
        double r3840149 = exp(r3840148);
        double r3840150 = r3840139 * r3840149;
        return r3840150;
}
↓
double f(double __attribute__((unused)) K, double m, double n, double M, double l) {
        double r3840151 = m;
        double r3840152 = n;
        double r3840153 = r3840151 - r3840152;
        double r3840154 = fabs(r3840153);
        double r3840155 = l;
        double r3840156 = r3840154 - r3840155;
        double r3840157 = r3840151 + r3840152;
        double r3840158 = 2.0;
        double r3840159 = r3840157 / r3840158;
        double r3840160 = M;
        double r3840161 = r3840159 - r3840160;
        double r3840162 = pow(r3840161, r3840158);
        double r3840163 = r3840156 - r3840162;
        double r3840164 = exp(r3840163);
        return r3840164;
}

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 15.8

    \[\cos \left(\frac{K \cdot \left(m + n\right)}{2.0} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2.0} - M\right)}^{2.0}\right) - \left(\ell - \left|m - n\right|\right)}\]

  2. Simplified15.8

    \[\leadsto \color{blue}{\cos \left(\frac{\left(m + n\right) \cdot K}{2.0} - M\right) \cdot e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2.0} - M\right)}^{2.0}}}\]

  3. Taylor expanded around 0 1.3

    \[\leadsto \color{blue}{1} \cdot e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2.0} - M\right)}^{2.0}}\]

  4. Final simplification1.3

    \[\leadsto e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2.0} - M\right)}^{2.0}}\]

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(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)))))))