Average Error: 0.0 → 0.1
Time: 6.1s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \frac{\sqrt[3]{\sinh y} \cdot \sqrt[3]{\sinh y}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{\sinh y}}{\sqrt[3]{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \frac{\sqrt[3]{\sinh y} \cdot \sqrt[3]{\sinh y}}{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot \frac{\sqrt[3]{\sinh y}}{\sqrt[3]{y}}
double code(double x, double y) {
	return (sin(x) * (sinh(y) / y));
}
↓
double code(double x, double y) {
	return ((sin(x) * ((cbrt(sinh(y)) * cbrt(sinh(y))) / (cbrt(y) * cbrt(y)))) * (cbrt(sinh(y)) / cbrt(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. Using strategy rm

  3. Applied add-cube-cbrt1.6

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

  4. Applied add-cube-cbrt0.1

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

  5. Applied times-frac0.1

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

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020075 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))