Average Error: 0.0 → 0.0
Time: 3.7s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt{\frac{\sinh y}{y}} \cdot \left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\sqrt{\frac{\sinh y}{y}} \cdot \left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right)
(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
↓
(FPCore (x y)
 :precision binary64
 (* (sqrt (/ (sinh y) y)) (* (cos x) (sqrt (/ (sinh y) y)))))
double code(double x, double y) {
	return ((double) (((double) cos(x)) * (((double) sinh(y)) / y)));
}
↓
double code(double x, double y) {
	return ((double) (((double) sqrt((((double) sinh(y)) / y))) * ((double) (((double) cos(x)) * ((double) sqrt((((double) 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 Error: 0.0 bits

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

  3. Applied add-sqr-sqrtError: 0.0 bits

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

  4. Applied associate-*r*Error: 0.0 bits

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

  5. Final simplificationError: 0.0 bits

    \[\leadsto \sqrt{\frac{\sinh y}{y}} \cdot \left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right)\]

Reproduce

herbie shell --seed 2020203 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))