Average Error: 7.0 → 0.1
Time: 2.7s
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

Enter valid numbers for all inputs

Target

Original7.0
Target0.1
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x} \]

Derivation

  1. Initial program 7.0

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

  2. Taylor expanded in x around inf 22.1

    \[\leadsto \color{blue}{\frac{0.5 \cdot \left(\sin x \cdot e^{y}\right) - 0.5 \cdot \frac{\sin x}{e^{y}}}{x}} \]

  3. Simplified0.1

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

  4. Applied div-inv_binary640.2

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

  5. Applied associate-*l*_binary640.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2022067 
(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))