Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Average Error: 0.1 → 0.1

Time: 2.8s

Precision: 64

Math

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

↓

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

C

double code(double x, double y, double z) {
	return (((x * 3.0) * y) - z);
}

↓

double code(double x, double y, double z) {
	return ((3.0 * (x * y)) - z);
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.1
Herbie	0.1

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

Derivation

1. Initial program 0.1

   \[\left(x \cdot 3\right) \cdot y - z\]
2. Using strategy rm

3. Applied *-un-lft-identity 0.1

   \[\leadsto \left(x \cdot 3\right) \cdot y - \color{blue}{1 \cdot z}\]

4. Applied *-un-lft-identity 0.1

   \[\leadsto \color{blue}{1 \cdot \left(\left(x \cdot 3\right) \cdot y\right)} - 1 \cdot z\]

5. Applied distribute-lft-out-- 0.1

   \[\leadsto \color{blue}{1 \cdot \left(\left(x \cdot 3\right) \cdot y - z\right)}\]

6. Simplified 0.1

   \[\leadsto 1 \cdot \color{blue}{\left(3 \cdot \left(x \cdot y\right) - z\right)}\]

7. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(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))