Average Error: 14.2 → 0.1
Time: 12.0s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sinh y \cdot \frac{\sin x}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sinh y \cdot \frac{\sin x}{x}
double code(double x, double y) {
	return ((sin(x) * sinh(y)) / x);
}
↓
double code(double x, double y) {
	return (sinh(y) * (sin(x) / x));
}

Error

Bits error versus x

Bits error versus y

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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 *-commutative14.2

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

  5. Applied times-frac0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020066 +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))