Average Error: 0.1 → 0.1
Time: 5.3s
Precision: binary64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{\sin y}{y}\right)\]
\cosh x \cdot \frac{\sin y}{y}
↓
\sqrt{\cosh x} \cdot \left(\sqrt{\cosh x} \cdot \frac{\sin y}{y}\right)
(FPCore (x y) :precision binary64 (* (cosh x) (/ (sin y) y)))
↓
(FPCore (x y)
 :precision binary64
 (* (sqrt (cosh x)) (* (sqrt (cosh x)) (/ (sin y) y))))
double code(double x, double y) {
	return cosh(x) * (sin(y) / y);
}
↓
double code(double x, double y) {
	return sqrt(cosh(x)) * (sqrt(cosh(x)) * (sin(y) / 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. Using strategy rm

  3. Applied add-sqr-sqrt_binary640.1

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

  4. Applied associate-*l*_binary640.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020260 
(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)))