Average Error: 14.1 → 0.2
Time: 4.5s
Precision: binary64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\sinh y}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \frac{\sinh y}{x}
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) sin(x)) * ((double) (((double) sinh(y)) / x))));
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

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. Final simplification0.2

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

Reproduce

herbie shell --seed 2020184 
(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))