Average Error: 0.0 → 0.0
Time: 1.5s
Precision: 64
\[\left(x + y\right) \cdot \left(z + 1\right)\]
↓
\[z \cdot x + \left(y \cdot z + 1 \cdot \left(x + y\right)\right)\]
\left(x + y\right) \cdot \left(z + 1\right)
↓
z \cdot x + \left(y \cdot z + 1 \cdot \left(x + y\right)\right)
double f(double x, double y, double z) {
        double r44086 = x;
        double r44087 = y;
        double r44088 = r44086 + r44087;
        double r44089 = z;
        double r44090 = 1.0;
        double r44091 = r44089 + r44090;
        double r44092 = r44088 * r44091;
        return r44092;
}
↓
double f(double x, double y, double z) {
        double r44093 = z;
        double r44094 = x;
        double r44095 = r44093 * r44094;
        double r44096 = y;
        double r44097 = r44096 * r44093;
        double r44098 = 1.0;
        double r44099 = r44094 + r44096;
        double r44100 = r44098 * r44099;
        double r44101 = r44097 + r44100;
        double r44102 = r44095 + r44101;
        return r44102;
}

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. Using strategy rm

  3. Applied distribute-lft-in0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  7. Applied distribute-lft-in0.0

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

  8. Applied associate-+l+0.0

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020036 
(FPCore (x y z)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, G"
  :precision binary64
  (* (+ x y) (+ z 1)))