Average Error: 0.0 → 0.0
Time: 14.9s
Precision: 64
\[\left(x + y\right) \cdot z\]
↓
\[z \cdot y + x \cdot z\]
\left(x + y\right) \cdot z
↓
z \cdot y + x \cdot z
double f(double x, double y, double z) {
        double r912554 = x;
        double r912555 = y;
        double r912556 = r912554 + r912555;
        double r912557 = z;
        double r912558 = r912556 * r912557;
        return r912558;
}
↓
double f(double x, double y, double z) {
        double r912559 = z;
        double r912560 = y;
        double r912561 = r912559 * r912560;
        double r912562 = x;
        double r912563 = r912562 * r912559;
        double r912564 = r912561 + r912563;
        return r912564;
}

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-sqrt31.5

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

  4. Applied associate-*r*31.5

    \[\leadsto \color{blue}{\left(\left(x + y\right) \cdot \sqrt{z}\right) \cdot \sqrt{z}}\]
  5. Using strategy rm

  6. Applied add-sqr-sqrt31.5

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

  7. Applied sqrt-prod31.6

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

  8. Applied associate-*r*31.6

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

  9. Taylor expanded around inf 0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Text.Parsec.Token:makeTokenParser from parsec-3.1.9, B"
  (* (+ x y) z))