Average Error: 0.1 → 0.2
Time: 4.0s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\sin x}{-y} \cdot \left(-\sinh y\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\frac{\sin x}{-y} \cdot \left(-\sinh y\right)
double code(double x, double y) {
	return (sin(x) * (sinh(y) / y));
}
↓
double code(double x, double y) {
	return ((sin(x) / -y) * -sinh(y));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied clear-num0.1

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

  4. Applied un-div-inv0.1

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{y}{\sinh y}}}\]
  5. Using strategy rm

  6. Applied frac-2neg0.1

    \[\leadsto \frac{\sin x}{\color{blue}{\frac{-y}{-\sinh y}}}\]

  7. Applied associate-/r/0.2

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

  8. Final simplification0.2

    \[\leadsto \frac{\sin x}{-y} \cdot \left(-\sinh y\right)\]

Reproduce

herbie shell --seed 2020078 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))