Average Error: 0.1 → 0.2
Time: 4.2s
Precision: binary64
\[x \cdot \frac{\sin y}{y}\]
↓
\[\frac{x}{\frac{y}{\sin y}}\]
x \cdot \frac{\sin y}{y}
↓
\frac{x}{\frac{y}{\sin y}}
(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))
↓
(FPCore (x y) :precision binary64 (/ x (/ y (sin y))))
double code(double x, double y) {
	return x * (sin(y) / y);
}
↓
double code(double x, double y) {
	return x / (y / sin(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 0.1

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

  3. Applied associate-*r/_binary64_20667.3

    \[\leadsto \color{blue}{\frac{x \cdot \sin y}{y}}\]
  4. Using strategy rm

  5. Applied associate-/l*_binary64_20690.2

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

  6. Final simplification0.2

    \[\leadsto \frac{x}{\frac{y}{\sin y}}\]

Reproduce

herbie shell --seed 2020354 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))