Average Error: 0.0 → 0.0
Time: 1.0s
Precision: 64
\[x + y \cdot \left(z + x\right)\]
↓
\[x + \left(y \cdot z + y \cdot x\right)\]
x + y \cdot \left(z + x\right)
↓
x + \left(y \cdot z + y \cdot x\right)
double f(double x, double y, double z) {
        double r120845 = x;
        double r120846 = y;
        double r120847 = z;
        double r120848 = r120847 + r120845;
        double r120849 = r120846 * r120848;
        double r120850 = r120845 + r120849;
        return r120850;
}
↓
double f(double x, double y, double z) {
        double r120851 = x;
        double r120852 = y;
        double r120853 = z;
        double r120854 = r120852 * r120853;
        double r120855 = r120852 * r120851;
        double r120856 = r120854 + r120855;
        double r120857 = r120851 + r120856;
        return r120857;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020062 
(FPCore (x y z)
  :name "Main:bigenough2 from A"
  :precision binary64
  (+ x (* y (+ z x))))