Average Error: 0.2 → 0.1
Time: 11.6s
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 r493426 = x;
        double r493427 = 3.0;
        double r493428 = r493426 * r493427;
        double r493429 = y;
        double r493430 = r493428 * r493429;
        double r493431 = z;
        double r493432 = r493430 - r493431;
        return r493432;
}
↓
double f(double x, double y, double z) {
        double r493433 = 3.0;
        double r493434 = x;
        double r493435 = y;
        double r493436 = r493434 * r493435;
        double r493437 = r493433 * r493436;
        double r493438 = z;
        double r493439 = r493437 - r493438;
        return r493439;
}

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
Target0.2
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 2019199 +o rules:numerics
(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))