Average Error: 0.0 → 0.0
Time: 9.2s
Precision: 64
\[\left(x + y\right) \cdot z\]
↓
\[x \cdot z + z \cdot y\]
\left(x + y\right) \cdot z
↓
x \cdot z + z \cdot y
double f(double x, double y, double z) {
        double r10574 = x;
        double r10575 = y;
        double r10576 = r10574 + r10575;
        double r10577 = z;
        double r10578 = r10576 * r10577;
        return r10578;
}
↓
double f(double x, double y, double z) {
        double r10579 = x;
        double r10580 = z;
        double r10581 = r10579 * r10580;
        double r10582 = y;
        double r10583 = r10580 * r10582;
        double r10584 = r10581 + r10583;
        return r10584;
}

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

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

  3. Applied add-sqr-sqrt32.2

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

  4. Applied associate-*r*32.2

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

  5. Simplified32.2

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

  6. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{x \cdot z + z \cdot y}\]

  7. Final simplification0.0

    \[\leadsto x \cdot z + z \cdot y\]

Reproduce

herbie shell --seed 2019209 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  :precision binary64
  (* (+ x y) z))