Average Error: 0.2 → 0.1
Time: 1.6s
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 r811255 = x;
        double r811256 = 3.0;
        double r811257 = r811255 * r811256;
        double r811258 = y;
        double r811259 = r811257 * r811258;
        double r811260 = z;
        double r811261 = r811259 - r811260;
        return r811261;
}
↓
double f(double x, double y, double z) {
        double r811262 = 3.0;
        double r811263 = x;
        double r811264 = y;
        double r811265 = r811263 * r811264;
        double r811266 = r811262 * r811265;
        double r811267 = z;
        double r811268 = r811266 - r811267;
        return r811268;
}

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

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

Reproduce

herbie shell --seed 2020065 
(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))