Average Error: 0.4 → 0.3
Time: 1.4s
Precision: 64
\[\left(x \cdot 27\right) \cdot y\]
↓
\[27 \cdot \left(x \cdot y\right)\]
\left(x \cdot 27\right) \cdot y
↓
27 \cdot \left(x \cdot y\right)
double f(double x, double y) {
        double r203389 = x;
        double r203390 = 27.0;
        double r203391 = r203389 * r203390;
        double r203392 = y;
        double r203393 = r203391 * r203392;
        return r203393;
}
↓
double f(double x, double y) {
        double r203394 = 27.0;
        double r203395 = x;
        double r203396 = y;
        double r203397 = r203395 * r203396;
        double r203398 = r203394 * r203397;
        return r203398;
}

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 0.4

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

  2. Taylor expanded around 0 0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2020034 
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, F"
  :precision binary64
  (* (* x 27) y))