Average Error: 0.2 → 0.3
Time: 5.6s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\left(\cosh x \cdot \sin y\right) \cdot \frac{1}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\left(\cosh x \cdot \sin y\right) \cdot \frac{1}{y}
double code(double x, double y) {
	return (cosh(x) * (sin(y) / y));
}
↓
double code(double x, double y) {
	return ((cosh(x) * sin(y)) * (1.0 / y));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original0.2
Target0.2
Herbie0.3
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.2

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

  3. Applied div-inv0.3

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

  4. Applied associate-*r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020079 +o rules:numerics
(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)))