Average Error: 0.1 → 0.1
Time: 21.0s
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 r40265696 = x;
        double r40265697 = 3.0;
        double r40265698 = r40265696 * r40265697;
        double r40265699 = y;
        double r40265700 = r40265698 * r40265699;
        double r40265701 = z;
        double r40265702 = r40265700 - r40265701;
        return r40265702;
}
↓
double f(double x, double y, double z) {
        double r40265703 = y;
        double r40265704 = x;
        double r40265705 = r40265703 * r40265704;
        double r40265706 = 3.0;
        double r40265707 = r40265705 * r40265706;
        double r40265708 = z;
        double r40265709 = r40265707 - r40265708;
        return r40265709;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

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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

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

Reproduce

herbie shell --seed 2019169 
(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))