Average Error: 0.0 → 0.0
Time: 7.8s
Precision: binary64
\[\sin x \cdot \frac{\sinh y}{y} \]
↓
\[\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{1}{\frac{y}{\sinh y}}} \]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{1}{\frac{y}{\sinh y}}}

(FPCore (x y) :precision binary64 (* (sin x) (/ (sinh y) y)))
↓
(FPCore (x y)
 :precision binary64
 (* (* (sin x) (sqrt (/ (sinh y) y))) (sqrt (/ 1.0 (/ y (sinh y))))))
double code(double x, double y) {
	return sin(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return (sin(x) * sqrt(sinh(y) / y)) * sqrt(1.0 / (y / sinh(y)));
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  2. Applied add-sqr-sqrt_binary640.1

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

  3. Applied associate-*r*_binary640.0

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

  4. Applied clear-num_binary640.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2022088 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))