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

Average Error: 0.1 → 0.1

Time: 2.1s

Precision: binary64

Math

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

↓

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

FPCore

(FPCore (x y z) :precision binary64 (- (* (* x 3.0) y) z))

↓

(FPCore (x y z) :precision binary64 (- (* 3.0 (* y x)) 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 * (y * x)) - z;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.1
Target	0.2
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. Taylor expanded in x around 0 0.1

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

3. Final simplification 0.1

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

Reproduce

herbie shell --seed 2021352 
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))