Average Error: 0.1 → 0.1
Time: 23.0s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[3 \cdot \left(x \cdot y\right) - z\]
\left(x \cdot 3\right) \cdot y - z
↓
3 \cdot \left(x \cdot y\right) - z
double f(double x, double y, double z) {
        double r81658 = x;
        double r81659 = 3.0;
        double r81660 = r81658 * r81659;
        double r81661 = y;
        double r81662 = r81660 * r81661;
        double r81663 = z;
        double r81664 = r81662 - r81663;
        return r81664;
}
↓
double f(double x, double y, double z) {
        double r81665 = 3.0;
        double r81666 = x;
        double r81667 = y;
        double r81668 = r81666 * r81667;
        double r81669 = r81665 * r81668;
        double r81670 = z;
        double r81671 = r81669 - r81670;
        return r81671;
}

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

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

Derivation

  1. Initial program 0.1

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

  2. Taylor expanded around 0 0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019315 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3 y)) z)

  (- (* (* x 3) y) z))