Average Error: 14.1 → 0.1
Time: 4.4s
Precision: binary64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sin x}{x} \cdot \sinh y\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sin x}{x} \cdot \sinh y
double code(double x, double y) {
	return (((double) (((double) sin(x)) * ((double) sinh(y)))) / x);
}
↓
double code(double x, double y) {
	return ((double) ((((double) sin(x)) / x) * ((double) sinh(y))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 14.1

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

  2. Simplified0.2

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

  4. Applied clear-num0.9

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

  6. Applied associate-/r/0.3

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

  7. Applied associate-*r*0.2

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020199 
(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))