Average Error: 0.3 → 0.4
Time: 1.8s
Precision: binary64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[\sqrt{27} \cdot \left(\sqrt{27} \cdot \left(x \cdot y\right)\right)\]
\left(x \cdot 27\right) \cdot y
↓
\sqrt{27} \cdot \left(\sqrt{27} \cdot \left(x \cdot y\right)\right)
double code(double x, double y) {
	return ((double) (((double) (x * 27.0)) * y));
}
↓
double code(double x, double y) {
	return ((double) (((double) sqrt(27.0)) * ((double) (((double) sqrt(27.0)) * ((double) (x * y))))));
}

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. Taylor expanded around 0 0.3

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

  4. Applied add-sqr-sqrt0.3

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

  5. Applied associate-*l*0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2020162 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27.0) y))