Average Error: 0.0 → 0.0
Time: 2.1s
Precision: 64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[z \cdot \left(x + y\right) + 1 \cdot \left(x + y\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
z \cdot \left(x + y\right) + 1 \cdot \left(x + y\right)
double f(double x, double y, double z) {
        double r43626 = x;
        double r43627 = y;
        double r43628 = r43626 + r43627;
        double r43629 = z;
        double r43630 = 1.0;
        double r43631 = r43629 + r43630;
        double r43632 = r43628 * r43631;
        return r43632;
}
↓
double f(double x, double y, double z) {
        double r43633 = z;
        double r43634 = x;
        double r43635 = y;
        double r43636 = r43634 + r43635;
        double r43637 = r43633 * r43636;
        double r43638 = 1.0;
        double r43639 = r43638 * r43636;
        double r43640 = r43637 + r43639;
        return r43640;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) \cdot \left(z + 1\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

    \[\leadsto z \cdot \left(x + y\right) + 1 \cdot \left(x + y\right)\]

Reproduce

herbie shell --seed 2020089 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1)))