Average Error: 0.0 → 0.0
Time: 6.0s
Precision: binary64
Cost: 32576
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\cos x \cdot \sqrt{\frac{\sinh y}{y}}}{\sqrt{\frac{y}{\sinh y}}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\frac{\cos x \cdot \sqrt{\frac{\sinh y}{y}}}{\sqrt{\frac{y}{\sinh y}}}
(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
↓
(FPCore (x y)
 :precision binary64
 (/ (* (cos x) (sqrt (/ (sinh y) y))) (sqrt (/ y (sinh 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(y / sinh(y));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Alternatives

Alternative 1
Error0.0
Cost13120
\[\cos x \cdot \frac{\sinh y}{y}\]
Alternative 2
Error0.8
Cost6976
\[\cos x \cdot \left(1 + \left(y \cdot y\right) \cdot 0.16666666666666666\right)\]
Alternative 3
Error1.1
Cost6464
\[\cos x\]
Alternative 4
Error29.4
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  3. Applied clear-num_binary64_28050.0

    \[\leadsto \cos x \cdot \color{blue}{\frac{1}{\frac{y}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt_binary64_28280.0

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

  6. Applied associate-*r*_binary64_27460.0

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

  7. Simplified0.0

    \[\leadsto \color{blue}{\left(\sqrt{\frac{\sinh y}{y}} \cdot \cos x\right)} \cdot \sqrt{\frac{1}{\frac{y}{\sinh y}}}\]
  8. Using strategy rm

  9. Applied sqrt-div_binary64_28230.0

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

  10. Applied associate-*r/_binary64_27480.0

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

  11. Simplified0.0

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

  12. Simplified0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))