Average Error: 15.5 → 4.1
Time: 1.8min
Precision: binary64
Cost: 64
\[\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(-{\left(\frac{m + n}{2} - M\right)}^{2}\right) - \left(\ell - \left|m - n\right|\right)}\]
↓
\[0\]
\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)}
↓
0
(FPCore (K m n M l)
 :precision binary64
 (*
  (cos (- (/ (* K (+ m n)) 2.0) M))
  (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))
↓
(FPCore (K m n M l) :precision binary64 0.0)
double code(double K, double m, double n, double M, double l) {
	return cos(((K * (m + n)) / 2.0) - M) * exp(-pow((((m + n) / 2.0) - M), 2.0) - (l - fabs(m - n)));
}
↓
double code(double K, double m, double n, double M, double l) {
	return 0.0;
}

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

Alternatives

Alternative 1
Error4.1
Cost54529
\[\begin{array}{l} \mathbf{if}\;\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}} \leq \mathsf{NaN}:\\ \;\;\;\;\cos \left(\frac{K \cdot \left(m + n\right)}{2} - M\right) \cdot e^{\left(\left|m - n\right| - \ell\right) - {\left(\frac{m + n}{2} - M\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 2
Error59.3
Cost64
\[1\]

Error

Time

Derivation

  1. Initial program 4.1

    \[0\]

  2. Simplified4.1

    \[\leadsto \color{blue}{0}\]

  3. Final simplification4.1

    \[\leadsto 0\]

Reproduce

herbie shell --seed 2021065 
(FPCore (K m n M l)
  :name "Maksimov and Kolovsky, Equation (32)"
  :precision binary64
  (* (cos (- (/ (* K (+ m n)) 2.0) M)) (exp (- (- (pow (- (/ (+ m n) 2.0) M) 2.0)) (- l (fabs (- m n)))))))