Average Error: 0.0 → 0.1
Time: 8.5s
Precision: binary64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sqrt{\frac{\sinh y}{y}} \cdot \left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sqrt{\frac{\sinh y}{y}} \cdot \left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right)
(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) y)))
↓
(FPCore (x y)
 :precision binary64
 (* (sqrt (/ (sinh y) y)) (* (sin x) (sqrt (/ (sinh y) y)))))
double code(double x, double y) {
	return sin(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return sqrt(sinh(y) / y) * (sin(x) * sqrt(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

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

  3. Applied add-sqr-sqrt_binary64_28280.1

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

  4. Applied associate-*r*_binary64_27460.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020342 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))