Average Error: 0.1 → 0.1
Time: 8.2s
Precision: binary64
\[x \cdot \frac{\sin y}{y} \]
↓
\[x \cdot \frac{\sin y}{y} \]
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

Derivation

  1. Initial program 0.1

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

  2. Applied add-cube-cbrt_binary640.6

    \[\leadsto x \cdot \color{blue}{\left(\left(\sqrt[3]{\frac{\sin y}{y}} \cdot \sqrt[3]{\frac{\sin y}{y}}\right) \cdot \sqrt[3]{\frac{\sin y}{y}}\right)} \]

  3. Applied pow1/3_binary6417.0

    \[\leadsto x \cdot \left(\left(\sqrt[3]{\frac{\sin y}{y}} \cdot \sqrt[3]{\frac{\sin y}{y}}\right) \cdot \color{blue}{{\left(\frac{\sin y}{y}\right)}^{0.3333333333333333}}\right) \]

  4. Applied pow1/3_binary6417.1

    \[\leadsto x \cdot \left(\left(\sqrt[3]{\frac{\sin y}{y}} \cdot \color{blue}{{\left(\frac{\sin y}{y}\right)}^{0.3333333333333333}}\right) \cdot {\left(\frac{\sin y}{y}\right)}^{0.3333333333333333}\right) \]

  5. Applied pow1/3_binary6417.2

    \[\leadsto x \cdot \left(\left(\color{blue}{{\left(\frac{\sin y}{y}\right)}^{0.3333333333333333}} \cdot {\left(\frac{\sin y}{y}\right)}^{0.3333333333333333}\right) \cdot {\left(\frac{\sin y}{y}\right)}^{0.3333333333333333}\right) \]

  6. Applied pow-prod-up_binary6417.2

    \[\leadsto x \cdot \left(\color{blue}{{\left(\frac{\sin y}{y}\right)}^{\left(0.3333333333333333 + 0.3333333333333333\right)}} \cdot {\left(\frac{\sin y}{y}\right)}^{0.3333333333333333}\right) \]

  7. Applied pow-prod-up_binary640.1

    \[\leadsto x \cdot \color{blue}{{\left(\frac{\sin y}{y}\right)}^{\left(\left(0.3333333333333333 + 0.3333333333333333\right) + 0.3333333333333333\right)}} \]

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2022068 
(FPCore (x y)
  :name "Linear.Quaternion:$cexp from linear-1.19.1.3"
  :precision binary64
  (* x (/ (sin y) y)))