Average Error: 0.0 → 0.1
Time: 4.8s
Precision: binary64
\[\sin x \cdot \frac{\sinh y}{y} \]
↓
\[\sin x \cdot \frac{1}{\frac{y}{\sinh y}} \]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot \frac{1}{\frac{y}{\sinh y}}

(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) y)))
↓
(FPCore (x y) :precision binary64 (* (sin x) (/ 1.0 (/ y (sinh y)))))
double code(double x, double y) {
	return sin(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return sin(x) * (1.0 / (y / sinh(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 clear-num_binary640.1

    \[\leadsto \sin x \cdot \color{blue}{\frac{1}{\frac{y}{\sinh y}}} \]

  4. Final simplification0.1

    \[\leadsto \sin x \cdot \frac{1}{\frac{y}{\sinh y}} \]

Reproduce

herbie shell --seed 2021198 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))