Average Error: 17.6 → 0.1
Time: 22.4s
Precision: binary64
Cost: 1088
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
↓
\[\left(J \cdot \left(2 \cdot \left(\left(2 \cdot \sinh \ell\right) \cdot 0.5\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]
\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U
↓
\left(J \cdot \left(2 \cdot \left(\left(2 \cdot \sinh \ell\right) \cdot 0.5\right)\right)\right) \cdot \cos \left(\frac{K}{2}\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 (* (* 2.0 (sinh l)) 0.5))) (cos (/ K 2.0))) U))
double code(double J, double l, double K, double U) {
	return ((J * (exp(l) - exp(-l))) * cos(K / 2.0)) + U;
}
↓
double code(double J, double l, double K, double U) {
	return ((J * (2.0 * ((2.0 * sinh(l)) * 0.5))) * 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
Alternative 1
Accuracy17.6
Cost960
\[\left(J \cdot \left(e^{\ell} - e^{-\ell}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

Derivation

  1. Initial program 17.6

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

  3. Applied sinh-undef_binary64_9530.1

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

  4. Taylor expanded around inf 17.6

    \[\leadsto \left(J \cdot \left(2 \cdot \color{blue}{\left(0.5 \cdot \left(e^{\ell} - e^{-\ell}\right)\right)}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  5. Simplified0.1

    \[\leadsto \left(J \cdot \left(2 \cdot \color{blue}{\left(\left(2 \cdot \sinh \ell\right) \cdot 0.5\right)}\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

  6. Final simplification0.1

    \[\leadsto \left(J \cdot \left(2 \cdot \left(\left(2 \cdot \sinh \ell\right) \cdot 0.5\right)\right)\right) \cdot \cos \left(\frac{K}{2}\right) + U\]

Reproduce

herbie shell --seed 2020322 
(FPCore (J l K U)
  :name "Maksimov and Kolovsky, Equation (4)"
  :precision binary64
  (+ (* (* J (- (exp l) (exp (- l)))) (cos (/ K 2.0))) U))