Average Error: 0.0 → 0.0
Time: 14.7s
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 r105943 = x;
        double r105944 = y;
        double r105945 = z;
        double r105946 = r105945 + r105943;
        double r105947 = r105944 * r105946;
        double r105948 = r105943 + r105947;
        return r105948;
}
↓
double f(double x, double y, double z) {
        double r105949 = x;
        double r105950 = z;
        double r105951 = y;
        double r105952 = r105950 * r105951;
        double r105953 = r105951 * r105949;
        double r105954 = r105952 + r105953;
        double r105955 = r105949 + r105954;
        return r105955;
}

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 2019326 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))