Average Error: 0.0 → 0.1
Time: 5.6s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \frac{\frac{1}{y}}{\frac{1}{\sinh y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \frac{\frac{1}{y}}{\frac{1}{\sinh y}}
double code(double x, double y) {
	return (cos(x) * (sinh(y) / y));
}
↓
double code(double x, double y) {
	return (cos(x) * ((1.0 / y) / (1.0 / 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 0.0

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

  3. Applied clear-num0.0

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

  5. Applied div-inv0.2

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

    \[\leadsto \cos x \cdot \frac{\frac{1}{y}}{\frac{1}{\sinh y}}\]

Reproduce

herbie shell --seed 2020105 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))