Average Error: 0.0 → 0.0
Time: 4.8s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y} \]
↓
\[\cos x \cdot \frac{\sinh y}{y} \]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \frac{\sinh y}{y}

(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
↓
(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\cos x \cdot \frac{\sinh y}{y} \]
  2. Using strategy rm

  3. Applied add-log-exp_binary640.7

    \[\leadsto \color{blue}{\log \left(e^{\cos x \cdot \frac{\sinh y}{y}}\right)} \]

  4. Simplified0.7

    \[\leadsto \log \color{blue}{\left({\left(e^{\frac{\sinh y}{y}}\right)}^{\cos x}\right)} \]
  5. Using strategy rm

  6. Applied *-un-lft-identity_binary640.7

    \[\leadsto \log \left({\color{blue}{\left(1 \cdot e^{\frac{\sinh y}{y}}\right)}}^{\cos x}\right) \]

  7. Applied unpow-prod-down_binary640.7

    \[\leadsto \log \color{blue}{\left({1}^{\cos x} \cdot {\left(e^{\frac{\sinh y}{y}}\right)}^{\cos x}\right)} \]

  8. Applied log-prod_binary640.7

    \[\leadsto \color{blue}{\log \left({1}^{\cos x}\right) + \log \left({\left(e^{\frac{\sinh y}{y}}\right)}^{\cos x}\right)} \]

  9. Simplified0.7

    \[\leadsto \color{blue}{0} + \log \left({\left(e^{\frac{\sinh y}{y}}\right)}^{\cos x}\right) \]

  10. Simplified0.0

    \[\leadsto 0 + \color{blue}{\cos x \cdot \frac{\sinh y}{y}} \]

  11. Final simplification0.0

    \[\leadsto \cos x \cdot \frac{\sinh y}{y} \]

Reproduce

herbie shell --seed 2021207 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))