Average Error: 0.1 → 0.1
Time: 1.7s
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 r774173 = x;
        double r774174 = 3.0;
        double r774175 = r774173 * r774174;
        double r774176 = y;
        double r774177 = r774175 * r774176;
        double r774178 = z;
        double r774179 = r774177 - r774178;
        return r774179;
}
↓
double f(double x, double y, double z) {
        double r774180 = 3.0;
        double r774181 = x;
        double r774182 = y;
        double r774183 = r774181 * r774182;
        double r774184 = r774180 * r774183;
        double r774185 = z;
        double r774186 = r774184 - r774185;
        return r774186;
}

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 2020039 
(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))