Average Error: 0.1 → 0.2
Time: 7.7s
Precision: binary64
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}
(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))
↓
(FPCore (x y) :precision binary64 (* x (/ (/ 1.0 y) (/ 1.0 (sin y)))))
double code(double x, double y) {
	return x * (sin(y) / y);
}
↓
double code(double x, double y) {
	return x * ((1.0 / y) / (1.0 / 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 *-un-lft-identity_binary64_18580.1

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

  4. Applied associate-/l*_binary64_19220.2

    \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\]
  5. Using strategy rm

  6. Applied div-inv_binary64_18590.3

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

  7. Applied associate-/r*_binary64_19210.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2020231 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))