Average Error: 14.0 → 0.1
Time: 5.8s
Precision: binary64
\[\frac{\sin x \cdot \sinh y}{x} \]
↓
\[\sinh y \cdot \frac{\sin x}{x} \]
\frac{\sin x \cdot \sinh y}{x}
↓
\sinh y \cdot \frac{\sin x}{x}

(FPCore (x y) :precision binary64 (/ (* (sin x) (sinh y)) x))
↓
(FPCore (x y) :precision binary64 (* (sinh y) (/ (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

Original14.0
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x} \]

Derivation

  1. Initial program 14.0

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

  2. Applied associate-/l*_binary640.9

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

  3. Applied *-un-lft-identity_binary640.9

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

  4. Applied *-un-lft-identity_binary640.9

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

  5. Applied times-frac_binary640.9

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

  6. Applied *-un-lft-identity_binary640.9

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

  7. Applied times-frac_binary640.9

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

  8. Simplified0.9

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2021340 
(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))