Average Error: 0.1 → 0.1
Time: 8.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot e^{\log \left(\sqrt{\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}}\right) + \log \left(\sqrt{\sqrt[3]{\frac{\sinh y}{y}}}\right)}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot e^{\log \left(\sqrt{\sqrt[3]{\frac{\sinh y}{y}} \cdot \sqrt[3]{\frac{\sinh y}{y}}}\right) + \log \left(\sqrt{\sqrt[3]{\frac{\sinh y}{y}}}\right)}
double code(double x, double y) {
	return (sin(x) * (sinh(y) / y));
}
↓
double code(double x, double y) {
	return ((sin(x) * sqrt((sinh(y) / y))) * exp((log(sqrt((cbrt((sinh(y) / y)) * cbrt((sinh(y) / y))))) + log(sqrt(cbrt((sinh(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

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

  3. Applied add-sqr-sqrt0.1

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

  4. Applied associate-*r*0.1

    \[\leadsto \color{blue}{\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}}\]
  5. Using strategy rm

  6. Applied add-exp-log0.1

    \[\leadsto \left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \color{blue}{e^{\log \left(\sqrt{\frac{\sinh y}{y}}\right)}}\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.1

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

  9. Applied sqrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))