Average Error: 0.2 → 0.1
Time: 9.6s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[\left(y \cdot x\right) \cdot 3 - z\]
\left(x \cdot 3\right) \cdot y - z
↓
\left(y \cdot x\right) \cdot 3 - z
double f(double x, double y, double z) {
        double r36243472 = x;
        double r36243473 = 3.0;
        double r36243474 = r36243472 * r36243473;
        double r36243475 = y;
        double r36243476 = r36243474 * r36243475;
        double r36243477 = z;
        double r36243478 = r36243476 - r36243477;
        return r36243478;
}
↓
double f(double x, double y, double z) {
        double r36243479 = y;
        double r36243480 = x;
        double r36243481 = r36243479 * r36243480;
        double r36243482 = 3.0;
        double r36243483 = r36243481 * r36243482;
        double r36243484 = z;
        double r36243485 = r36243483 - r36243484;
        return r36243485;
}

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

Target

Original0.2
Target0.1
Herbie0.1
\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot 3\right) \cdot y - z\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{3 \cdot \left(x \cdot y\right)} - z\]

  3. Final simplification0.1

    \[\leadsto \left(y \cdot x\right) \cdot 3 - z\]

Reproduce

herbie shell --seed 2019192 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))