Average Error: 0.3 → 0.3
Time: 1.6s
Precision: binary64
\[[x, y]=\mathsf{sort}([x, y])\]
\[\left(x \cdot 27\right) \cdot y \]
↓
\[\left(27 \cdot y\right) \cdot x \]
\left(x \cdot 27\right) \cdot y
↓
\left(27 \cdot y\right) \cdot x

(FPCore (x y) :precision binary64 (* (* x 27.0) y))
↓
(FPCore (x y) :precision binary64 (* (* 27.0 y) x))
double code(double x, double y) {
	return (x * 27.0) * y;
}
↓
double code(double x, double y) {
	return (27.0 * y) * x;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

    \[\left(x \cdot 27\right) \cdot y \]
  2. Using strategy rm

  3. Applied pow1_binary640.3

    \[\leadsto \left(x \cdot 27\right) \cdot \color{blue}{{y}^{1}} \]

  4. Applied pow1_binary640.3

    \[\leadsto \left(x \cdot \color{blue}{{27}^{1}}\right) \cdot {y}^{1} \]

  5. Applied pow1_binary640.3

    \[\leadsto \left(\color{blue}{{x}^{1}} \cdot {27}^{1}\right) \cdot {y}^{1} \]

  6. Applied pow-prod-down_binary640.3

    \[\leadsto \color{blue}{{\left(x \cdot 27\right)}^{1}} \cdot {y}^{1} \]

  7. Applied pow-prod-down_binary640.3

    \[\leadsto \color{blue}{{\left(\left(x \cdot 27\right) \cdot y\right)}^{1}} \]

  8. Simplified0.3

    \[\leadsto {\color{blue}{\left(27 \cdot \left(y \cdot x\right)\right)}}^{1} \]
  9. Using strategy rm

  10. Applied associate-*r*_binary640.3

    \[\leadsto {\color{blue}{\left(\left(27 \cdot y\right) \cdot x\right)}}^{1} \]

  11. Final simplification0.3

    \[\leadsto \left(27 \cdot y\right) \cdot x \]

Reproduce

herbie shell --seed 2021204 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27.0) y))