Average Error: 0.0 → 0.0
Time: 4.6s
Precision: 64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[x \cdot z + \left(y \cdot z + 1 \cdot \left(x + y\right)\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
x \cdot z + \left(y \cdot z + 1 \cdot \left(x + y\right)\right)
double f(double x, double y, double z) {
        double r49607 = x;
        double r49608 = y;
        double r49609 = r49607 + r49608;
        double r49610 = z;
        double r49611 = 1.0;
        double r49612 = r49610 + r49611;
        double r49613 = r49609 * r49612;
        return r49613;
}
↓
double f(double x, double y, double z) {
        double r49614 = x;
        double r49615 = z;
        double r49616 = r49614 * r49615;
        double r49617 = y;
        double r49618 = r49617 * r49615;
        double r49619 = 1.0;
        double r49620 = r49614 + r49617;
        double r49621 = r49619 * r49620;
        double r49622 = r49618 + r49621;
        double r49623 = r49616 + r49622;
        return r49623;
}

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. Using strategy rm

  7. Applied distribute-rgt-in0.0

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

  8. Applied associate-+l+0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1)))