Average Error: 0.0 → 0.0
Time: 1.5s
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 r43412 = x;
        double r43413 = y;
        double r43414 = r43412 + r43413;
        double r43415 = z;
        double r43416 = 1.0;
        double r43417 = r43415 + r43416;
        double r43418 = r43414 * r43417;
        return r43418;
}
↓
double f(double x, double y, double z) {
        double r43419 = z;
        double r43420 = x;
        double r43421 = y;
        double r43422 = r43420 + r43421;
        double r43423 = r43419 * r43422;
        double r43424 = 1.0;
        double r43425 = r43424 * r43422;
        double r43426 = r43423 + r43425;
        return r43426;
}

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 2019352 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1)))