Average Error: 0.0 → 0.0
Time: 5.0s
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 r79195 = x;
        double r79196 = y;
        double r79197 = z;
        double r79198 = r79197 + r79195;
        double r79199 = r79196 * r79198;
        double r79200 = r79195 + r79199;
        return r79200;
}
↓
double f(double x, double y, double z) {
        double r79201 = x;
        double r79202 = y;
        double r79203 = r79201 * r79202;
        double r79204 = z;
        double r79205 = r79202 * r79204;
        double r79206 = r79201 + r79205;
        double r79207 = r79203 + r79206;
        return r79207;
}

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 2019179 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  (+ x (* y (+ z x))))