Average Error: 0.0 → 0.0
Time: 7.7s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[x \cdot y + \left(x + y \cdot z\right)\]
x + y \cdot \left(z + x\right)
↓
x \cdot y + \left(x + y \cdot z\right)
double f(double x, double y, double z) {
        double r82194 = x;
        double r82195 = y;
        double r82196 = z;
        double r82197 = r82196 + r82194;
        double r82198 = r82195 * r82197;
        double r82199 = r82194 + r82198;
        return r82199;
}
↓
double f(double x, double y, double z) {
        double r82200 = x;
        double r82201 = y;
        double r82202 = r82200 * r82201;
        double r82203 = z;
        double r82204 = r82201 * r82203;
        double r82205 = r82200 + r82204;
        double r82206 = r82202 + r82205;
        return r82206;
}

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. Applied associate-+r+0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))