Average Error: 0.0 → 0.0
Time: 2.8s
Precision: binary64
\[\sin x \cdot \frac{\sinh y}{y} \]
↓
\[\begin{array}{l} t_0 := \sqrt{\frac{\sinh y}{y}}\\ t_0 \cdot \left(\sin x \cdot t_0\right) \end{array} \]
\sin x \cdot \frac{\sinh y}{y}
↓
\begin{array}{l}
t_0 := \sqrt{\frac{\sinh y}{y}}\\
t_0 \cdot \left(\sin x \cdot t_0\right)
\end{array}

(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) y)))
↓
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (sqrt (/ (sinh y) y)))) (* t_0 (* (sin x) t_0))))
double code(double x, double y) {
	return sin(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	double t_0 = sqrt(sinh(y) / y);
	return t_0 * (sin(x) * t_0);
}

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. Applied add-sqr-sqrt_binary640.0

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

  3. Applied associate-*r*_binary640.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2022067 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))