Average Error: 0.0 → 0.1
Time: 5.5s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \frac{1}{\sqrt[3]{{\left(\frac{y}{\sinh y}\right)}^{3}}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \frac{1}{\sqrt[3]{{\left(\frac{y}{\sinh y}\right)}^{3}}}
double code(double x, double y) {
	return ((double) (((double) cos(x)) * ((double) (((double) sinh(y)) / y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) cos(x)) * ((double) (1.0 / ((double) cbrt(((double) pow(((double) (y / ((double) sinh(y)))), 3.0))))))));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied clear-num0.0

    \[\leadsto \cos x \cdot \color{blue}{\frac{1}{\frac{y}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube40.8

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

  6. Applied add-cbrt-cube41.4

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

  7. Applied cbrt-undiv41.4

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020169 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))