Average Error: 13.8 → 1.2
Time: 5.0s
Precision: binary64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \left(\left(\sqrt[3]{\sinh y} \cdot \sqrt[3]{\sinh y}\right) \cdot \frac{\sqrt[3]{\sinh y}}{x}\right)\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \left(\left(\sqrt[3]{\sinh y} \cdot \sqrt[3]{\sinh y}\right) \cdot \frac{\sqrt[3]{\sinh y}}{x}\right)
double code(double x, double y) {
	return ((double) (((double) (((double) sin(x)) * ((double) sinh(y)))) / x));
}
↓
double code(double x, double y) {
	return ((double) (((double) sin(x)) * ((double) (((double) (((double) cbrt(((double) sinh(y)))) * ((double) cbrt(((double) sinh(y)))))) * ((double) (((double) cbrt(((double) sinh(y)))) / x))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original13.8
Target0.3
Herbie1.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.8

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

  2. Simplified0.3

    \[\leadsto \color{blue}{\sin x \cdot \frac{\sinh y}{x}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.3

    \[\leadsto \sin x \cdot \frac{\sinh y}{\color{blue}{1 \cdot x}}\]

  5. Applied add-cube-cbrt1.2

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

  6. Applied times-frac1.2

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

  7. Simplified1.2

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

  8. Final simplification1.2

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

Reproduce

herbie shell --seed 2020184 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))