Average Error: 0.1 → 0.1
Time: 1.4min
Precision: binary64
Cost: 6720
\[x \cdot \frac{\sin y}{y}\]
↓
\[x \cdot \frac{\sin y}{y}\]
x \cdot \frac{\sin y}{y}
↓
x \cdot \frac{\sin y}{y}
(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))
↓
(FPCore (x y) :precision binary64 (* x (/ (sin y) y)))
double code(double x, double y) {
	return x * (sin(y) / y);
}
↓
double code(double x, double y) {
	return x * (sin(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

Alternatives

Alternative 1
Error23.3
Cost1218
\[\begin{array}{l} \mathbf{if}\;y \leq -225398903361574.72:\\ \;\;\;\;0\\ \mathbf{elif}\;y \leq 1007490.0096188163:\\ \;\;\;\;x - x \cdot \left(\left(y \cdot y\right) \cdot 0.16666666666666666\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 2
Error23.7
Cost706
\[\begin{array}{l} \mathbf{if}\;y \leq -1.1082785621089667 \cdot 10^{+83}:\\ \;\;\;\;0\\ \mathbf{elif}\;y \leq 3.0233011228189676 \cdot 10^{+44}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
Alternative 3
Error31.1
Cost64
\[x\]

Error

Time

Derivation

  1. Initial program 0.1

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

  3. Applied pow1_binary64_25260.1

    \[\leadsto x \cdot \color{blue}{{\left(\frac{\sin y}{y}\right)}^{1}}\]
  4. Using strategy rm

  5. Applied pow1_binary64_25260.1

    \[\leadsto \color{blue}{{\left(x \cdot {\left(\frac{\sin y}{y}\right)}^{1}\right)}^{1}}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity_binary64_24650.1

    \[\leadsto {\left(x \cdot {\left(\frac{\sin y}{\color{blue}{1 \cdot y}}\right)}^{1}\right)}^{1}\]

  8. Applied *-un-lft-identity_binary64_24650.1

    \[\leadsto {\left(x \cdot {\left(\frac{\color{blue}{1 \cdot \sin y}}{1 \cdot y}\right)}^{1}\right)}^{1}\]

  9. Applied times-frac_binary64_24710.1

    \[\leadsto {\left(x \cdot {\color{blue}{\left(\frac{1}{1} \cdot \frac{\sin y}{y}\right)}}^{1}\right)}^{1}\]

  10. Simplified0.1

    \[\leadsto {\left(x \cdot {\left(\color{blue}{1} \cdot \frac{\sin y}{y}\right)}^{1}\right)}^{1}\]

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2021040 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))