Average Error: 0.0 → 0.0
Time: 46.0s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot \left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right)
(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
↓
(FPCore (x y)
 :precision binary64
 (* (cos x) (* (sqrt (/ (sinh y) y)) (sqrt (/ (sinh y) y)))))
double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return cos(x) * (sqrt(sinh(y) / y) * sqrt(sinh(y) / y));
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\cos x \cdot \frac{\sinh y}{y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary64_35100.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2021090 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))