Average Error: 0.1 → 0.1
Time: 18.9s
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 r406876 = x;
        double r406877 = 3.0;
        double r406878 = r406876 * r406877;
        double r406879 = y;
        double r406880 = r406878 * r406879;
        double r406881 = z;
        double r406882 = r406880 - r406881;
        return r406882;
}
↓
double f(double x, double y, double z) {
        double r406883 = 3.0;
        double r406884 = x;
        double r406885 = y;
        double r406886 = r406884 * r406885;
        double r406887 = r406883 * r406886;
        double r406888 = z;
        double r406889 = r406887 - r406888;
        return r406889;
}

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
Target0.2
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 2019325 +o rules:numerics
(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))