Average Error: 0.1 → 0.3
Time: 5.3s
Precision: binary64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\frac{1}{y}}{\frac{1}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\frac{1}{y}}{\frac{1}{\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) (((double) (1.0 / y)) / ((double) (1.0 / ((double) sin(y))))))));
}

Error

Bits error versus x

Bits error versus y

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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-num0.2

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

  5. Applied div-inv0.3

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

  6. Applied associate-/r*0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2020161 
(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)))