Average Error: 14.2 → 0.1
Time: 4.6s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sin x}{-x} \cdot \left(-\sinh y\right)\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sin x}{-x} \cdot \left(-\sinh y\right)
double code(double x, double y) {
	return ((double) (((double) (((double) sin(x)) * ((double) sinh(y)))) / x));
}
↓
double code(double x, double y) {
	return ((double) (((double) (((double) sin(x)) / ((double) -(x)))) * ((double) -(((double) sinh(y))))));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

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Target

Original14.2
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.2

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

  3. Applied *-un-lft-identity14.2

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

  4. Applied times-frac0.2

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

  5. Simplified0.2

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

  7. Applied clear-num0.9

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

  8. Applied un-div-inv0.8

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

  10. Applied frac-2neg0.8

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

  11. Applied associate-/r/0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(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))