Average Error: 0.0 → 0.0
Time: 1.7min
Precision: binary64
Cost: 13120
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\frac{\cos x}{\frac{y}{\sinh y}}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\frac{\cos x}{\frac{y}{\sinh y}}
(FPCore (x y) :precision binary64 (* (cos x) (/ (sinh y) y)))
↓
(FPCore (x y) :precision binary64 (/ (cos x) (/ y (sinh y))))
double code(double x, double y) {
	return cos(x) * (sinh(y) / y);
}
↓
double code(double x, double y) {
	return cos(x) / (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
\[\cos x \cdot \left(y \cdot \left(y \cdot 0.16666666666666666\right) + 1\right)\]
Alternative 3
Error1.1
Cost6464
\[\cos x\]
Alternative 4
Error29.4
Cost64
\[1\]
Alternative 5
Error59.9
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_34870.0

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

  5. Applied un-div-inv_binary64_34860.0

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

  7. Applied *-un-lft-identity_binary64_34880.0

    \[\leadsto \frac{\cos x}{\frac{y}{\color{blue}{1 \cdot \sinh y}}}\]

  8. Applied *-un-lft-identity_binary64_34880.0

    \[\leadsto \frac{\cos x}{\frac{\color{blue}{1 \cdot y}}{1 \cdot \sinh y}}\]

  9. Applied times-frac_binary64_34940.0

    \[\leadsto \frac{\cos x}{\color{blue}{\frac{1}{1} \cdot \frac{y}{\sinh y}}}\]

  10. Simplified0.0

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

  12. Applied pow1_binary64_35490.0

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

  13. Simplified0.0

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

  14. Final simplification0.0

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

Reproduce

herbie shell --seed 2021014 
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))