Average Error: 0.0 → 0.0
Time: 6.7s
Precision: binary64
\[\sin x \cdot \frac{\sinh y}{y} \]
↓
\[\frac{\sin x}{\frac{y}{\sinh y}} \]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{\frac{y}{\sinh y}}

(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) y)))
↓
(FPCore (x y) :precision binary64 (/ (sin x) (/ y (sinh y))))
double code(double x, double y) {
	return sin(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return sin(x) / (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. Applied add-cube-cbrt_binary641.6

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

  3. Applied *-un-lft-identity_binary641.6

    \[\leadsto \sin x \cdot \frac{\color{blue}{1 \cdot \sinh y}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \]

  4. Applied times-frac_binary641.6

    \[\leadsto \sin x \cdot \color{blue}{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{\sinh y}{\sqrt[3]{y}}\right)} \]

  5. Applied associate-*r*_binary641.6

    \[\leadsto \color{blue}{\left(\sin x \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sinh y}{\sqrt[3]{y}}} \]

  6. Applied pow1_binary641.6

    \[\leadsto \left(\sin x \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \color{blue}{{\left(\frac{\sinh y}{\sqrt[3]{y}}\right)}^{1}} \]

  7. Applied pow1_binary641.6

    \[\leadsto \left(\sin x \cdot \color{blue}{{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)}^{1}}\right) \cdot {\left(\frac{\sinh y}{\sqrt[3]{y}}\right)}^{1} \]

  8. Applied pow1_binary641.6

    \[\leadsto \left(\color{blue}{{\sin x}^{1}} \cdot {\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)}^{1}\right) \cdot {\left(\frac{\sinh y}{\sqrt[3]{y}}\right)}^{1} \]

  9. Applied pow-prod-down_binary641.6

    \[\leadsto \color{blue}{{\left(\sin x \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right)}^{1}} \cdot {\left(\frac{\sinh y}{\sqrt[3]{y}}\right)}^{1} \]

  10. Applied pow-prod-down_binary641.6

    \[\leadsto \color{blue}{{\left(\left(\sin x \cdot \frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sinh y}{\sqrt[3]{y}}\right)}^{1}} \]

  11. Simplified0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2022077 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))