Average Error: 0.1 → 0.1
Time: 3.2s
Precision: binary64
\[\cosh x \cdot \frac{\sin y}{y} \]
↓
\[\frac{\sin y \cdot \cosh x}{y} \]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\sin y \cdot \cosh x}{y}

(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
↓
(FPCore (x y) :precision binary64 (/ (* (sin y) (cosh x)) y))
double code(double x, double y) {
	return cosh(x) * (sin(y) / y);
}
↓
double code(double x, double y) {
	return (sin(y) * cosh(x)) / y;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.1

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

  2. Applied associate-*r/_binary640.1

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

  3. Applied *-commutative_binary640.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2022088 
(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)))