Average Error: 0.1 → 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 r965580 = x;
        double r965581 = 3.0;
        double r965582 = r965580 * r965581;
        double r965583 = y;
        double r965584 = r965582 * r965583;
        double r965585 = z;
        double r965586 = r965584 - r965585;
        return r965586;
}
↓
double f(double x, double y, double z) {
        double r965587 = x;
        double r965588 = 3.0;
        double r965589 = y;
        double r965590 = r965588 * r965589;
        double r965591 = r965587 * r965590;
        double r965592 = z;
        double r965593 = r965591 - r965592;
        return r965593;
}

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
Target0.1
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. 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 2020057 
(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))