Average Error: 0.0 → 0.0
Time: 14.0s
Precision: binary64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[0.5 \cdot \frac{\cos x}{\frac{\frac{y}{\sinh y}}{2}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
0.5 \cdot \frac{\cos x}{\frac{\frac{y}{\sinh y}}{2}}
(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
↓
(FPCore (x y) :precision binary64 (* 0.5 (/ (cos x) (/ (/ y (sinh y)) 2.0))))
double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return 0.5 * (cos(x) / ((y / sinh(y)) / 2.0));
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  2. Taylor expanded around inf 59.4

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

  3. Simplified0.0

    \[\leadsto \color{blue}{0.5 \cdot \frac{\cos x}{\frac{\frac{y}{\sinh y}}{2}}}\]

  4. Final simplification0.0

    \[\leadsto 0.5 \cdot \frac{\cos x}{\frac{\frac{y}{\sinh y}}{2}}\]

Reproduce

herbie shell --seed 2021176 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))