Average Error: 0.0 → 0.0
Time: 5.0s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\left(\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt{\sqrt{\frac{\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(sqrt((sinh(y) / y)))) * sqrt(sqrt((sinh(y) / y))));
}

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. Using strategy rm

  3. Applied add-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\cos x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt0.0

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

  7. Applied sqrt-prod0.0

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

  8. Applied associate-*r*0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020053 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))