Average Error: 0.0 → 0.0
Time: 6.5s
Precision: 64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[\left(y \cdot z + x \cdot z\right) + 1 \cdot \left(x + y\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
\left(y \cdot z + x \cdot z\right) + 1 \cdot \left(x + y\right)
double f(double x, double y, double z) {
        double r40781 = x;
        double r40782 = y;
        double r40783 = r40781 + r40782;
        double r40784 = z;
        double r40785 = 1.0;
        double r40786 = r40784 + r40785;
        double r40787 = r40783 * r40786;
        return r40787;
}
↓
double f(double x, double y, double z) {
        double r40788 = y;
        double r40789 = z;
        double r40790 = r40788 * r40789;
        double r40791 = x;
        double r40792 = r40791 * r40789;
        double r40793 = r40790 + r40792;
        double r40794 = 1.0;
        double r40795 = r40791 + r40788;
        double r40796 = r40794 * r40795;
        double r40797 = r40793 + r40796;
        return r40797;
}

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

    \[\left(x + y\right) \cdot \left(z + 1\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(y + x\right) \cdot \left(z + 1\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(y + x\right) \cdot z + \left(y + x\right) \cdot 1}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{z \cdot \left(y + x\right)} + \left(y + x\right) \cdot 1\]
  6. Using strategy rm

  7. Applied distribute-lft-in0.0

    \[\leadsto \color{blue}{\left(z \cdot y + z \cdot x\right)} + \left(y + x\right) \cdot 1\]

  8. Simplified0.0

    \[\leadsto \left(\color{blue}{y \cdot z} + z \cdot x\right) + \left(y + x\right) \cdot 1\]

  9. Final simplification0.0

    \[\leadsto \left(y \cdot z + x \cdot z\right) + 1 \cdot \left(x + y\right)\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  (* (+ x y) (+ z 1.0)))