Average Error: 0.0 → 0.0
Time: 5.9s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[x + \left(y \cdot z + x \cdot y\right)\]
x + y \cdot \left(z + x\right)
↓
x + \left(y \cdot z + x \cdot y\right)
double f(double x, double y, double z) {
        double r128013 = x;
        double r128014 = y;
        double r128015 = z;
        double r128016 = r128015 + r128013;
        double r128017 = r128014 * r128016;
        double r128018 = r128013 + r128017;
        return r128018;
}
↓
double f(double x, double y, double z) {
        double r128019 = x;
        double r128020 = y;
        double r128021 = z;
        double r128022 = r128020 * r128021;
        double r128023 = r128019 * r128020;
        double r128024 = r128022 + r128023;
        double r128025 = r128019 + r128024;
        return r128025;
}

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

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

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))