Average Error: 0.1 → 0.1
Time: 5.3s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sin x}{\sqrt{\frac{y}{\sinh y}} \cdot \sqrt{\frac{y}{\sinh y}}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{\sqrt{\frac{y}{\sinh y}} \cdot \sqrt{\frac{y}{\sinh y}}}
double code(double x, double y) {
	return ((double) (((double) sin(x)) * ((double) (((double) sinh(y)) / y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) sin(x)) / ((double) (((double) sqrt(((double) (y / ((double) sinh(y)))))) * ((double) sqrt(((double) (y / ((double) sinh(y))))))))));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied clear-num0.1

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

  4. Applied un-div-inv0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020114 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))