Average Error: 0.2 → 0.2
Time: 5.1s
Precision: binary64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{1}{\frac{y}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{1}{\frac{y}{\sin y}}
double code(double x, double y) {
	return ((double) (((double) cosh(x)) * ((double) (((double) sin(y)) / y))));
}
↓
double code(double x, double y) {
	return ((double) (((double) cosh(x)) * ((double) (1.0 / ((double) (y / ((double) sin(y))))))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.2

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

  3. Applied clear-num0.2

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

  4. Final simplification0.2

    \[\leadsto \cosh x \cdot \frac{1}{\frac{y}{\sin y}}\]

Reproduce

herbie shell --seed 2020150 
(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)))