Average Error: 0.0 → 0.0
Time: 16.9s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[x + \left(z \cdot y + y \cdot x\right)\]
x + y \cdot \left(z + x\right)
↓
x + \left(z \cdot y + y \cdot x\right)
double f(double x, double y, double z) {
        double r85143 = x;
        double r85144 = y;
        double r85145 = z;
        double r85146 = r85145 + r85143;
        double r85147 = r85144 * r85146;
        double r85148 = r85143 + r85147;
        return r85148;
}
↓
double f(double x, double y, double z) {
        double r85149 = x;
        double r85150 = z;
        double r85151 = y;
        double r85152 = r85150 * r85151;
        double r85153 = r85151 * r85149;
        double r85154 = r85152 + r85153;
        double r85155 = r85149 + r85154;
        return r85155;
}

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

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))