Average Error: 13.9 → 0.2
Time: 4.1s
Precision: binary64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sinh y \cdot \frac{1}{x \cdot \frac{1}{\sin x}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sinh y \cdot \frac{1}{x \cdot \frac{1}{\sin x}}
(FPCore (x y) :precision binary64 (/ (* (sin x) (sinh y)) x))
↓
(FPCore (x y) :precision binary64 (* (sinh y) (/ 1.0 (* x (/ 1.0 (sin x))))))
double code(double x, double y) {
	return (((double) (((double) sin(x)) * ((double) sinh(y)))) / x);
}
↓
double code(double x, double y) {
	return ((double) (((double) sinh(y)) * (1.0 / ((double) (x * (1.0 / ((double) sin(x))))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original13.9
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program Error: 13.9 bits

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

  2. SimplifiedError: 0.2 bits

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

  4. Applied div-invError: 0.3 bits

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

  5. Taylor expanded around inf Error: 43.3 bits

    \[\leadsto \color{blue}{\frac{0.5 \cdot \left(\sin x \cdot e^{y}\right) - 0.5 \cdot \left(e^{-y} \cdot \sin x\right)}{x}}\]

  6. SimplifiedError: 0.1 bits

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

  8. Applied clear-numError: 0.1 bits

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

  10. Applied div-invError: 0.2 bits

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

  11. Final simplificationError: 0.2 bits

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

Reproduce

herbie shell --seed 2020203 
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))