Average Error: 17.6 → 0.1
Time: 6.5s
Precision: binary64
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[J \cdot \left(\left(2 \cdot \sinh \ell\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
J \cdot \left(\left(2 \cdot \sinh \ell\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U
(FPCore (J l K U)
 :precision binary64
 (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))
↓
(FPCore (J l K U)
 :precision binary64
 (+ (* J (* (* 2.0 (sinh l)) (cos (/ K 2.0)))) U))
double code(double J, double l, double K, double U) {
	return ((double) (((double) (((double) (J * ((double) (((double) exp(l)) - ((double) exp(((double) -(l)))))))) * ((double) cos((K / 2.0))))) + U));
}
↓
double code(double J, double l, double K, double U) {
	return ((double) (((double) (J * ((double) (((double) (2.0 * ((double) sinh(l)))) * ((double) cos((K / 2.0))))))) + U));
}

Error

Bits error versus J

Bits error versus l

Bits error versus K

Bits error versus U

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program Error: 17.6 bits

    \[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  2. SimplifiedError: 17.6 bits

    \[\leadsto \color{blue}{J \cdot \left(\left(e^{\ell} - e^{-\ell}\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U}\]
  3. Using strategy rm

  4. Applied sinh-undefError: 0.1 bits

    \[\leadsto J \cdot \left(\color{blue}{\left(2 \cdot \sinh \ell\right)} \cdot \cos \left(\frac{K}{2}\right)\right) + U\]

  5. Final simplificationError: 0.1 bits

    \[\leadsto J \cdot \left(\left(2 \cdot \sinh \ell\right) \cdot \cos \left(\frac{K}{2}\right)\right) + U\]

Reproduce

herbie shell --seed 2020203 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))