Average Error: 0.1 → 0.3
Time: 4.7s
Precision: binary64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\cosh x}{y} \cdot \sin y\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\cosh x}{y} \cdot \sin y
(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
↓
(FPCore (x y) :precision binary64 (* (/ (cosh x) y) (sin y)))
double code(double x, double y) {
	return ((double) (((double) cosh(x)) * (((double) sin(y)) / y)));
}
↓
double code(double x, double y) {
	return ((double) ((((double) cosh(x)) / y) * ((double) sin(y))));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original0.1
Target0.1
Herbie0.3
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

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

  3. Applied clear-num_binary640.2

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

  5. Applied associate-/r/_binary640.3

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

  6. Applied associate-*r*_binary640.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

    \[\leadsto \frac{\cosh x}{y} \cdot \sin y\]

Reproduce

herbie shell --seed 2020210 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

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

  (* (cosh x) (/ (sin y) y)))