Average Error: 0.2 → 0.1
Time: 1.8s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[x \cdot \left(3 \cdot y\right) - z\]
\left(x \cdot 3\right) \cdot y - z
↓
x \cdot \left(3 \cdot y\right) - z
double f(double x, double y, double z) {
        double r871354 = x;
        double r871355 = 3.0;
        double r871356 = r871354 * r871355;
        double r871357 = y;
        double r871358 = r871356 * r871357;
        double r871359 = z;
        double r871360 = r871358 - r871359;
        return r871360;
}
↓
double f(double x, double y, double z) {
        double r871361 = x;
        double r871362 = 3.0;
        double r871363 = y;
        double r871364 = r871362 * r871363;
        double r871365 = r871361 * r871364;
        double r871366 = z;
        double r871367 = r871365 - r871366;
        return r871367;
}

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. Using strategy rm

  3. Applied associate-*l*0.1

    \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z\]

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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))