Average Error: 0.0 → 0.0

Time: 2.4s

Precision: binary64

Cost: 448

\[2 \cdot \left(x \cdot x + x \cdot y\right)\]

↓

\[2 \cdot \left(x \cdot \left(x + y\right)\right)\]

2 \cdot \left(x \cdot x + x \cdot y\right)

↓

2 \cdot \left(x \cdot \left(x + y\right)\right)

(FPCore (x y) :precision binary64 (* 2.0 (+ (* x x) (* x y))))

↓

(FPCore (x y) :precision binary64 (* 2.0 (* x (+ x y))))

double code(double x, double y) {
	return 2.0 * ((x * x) + (x * y));
}

↓

double code(double x, double y) {
	return 2.0 * (x * (x + y));
}

Error

The X axis uses an exponential scale — Bits error versus `x`

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.0
Target	0.0
Herbie	0.0

\[\left(x \cdot 2\right) \cdot \left(x + y\right)\]

Alternatives

Alternative 1
Error	8.1
Cost	648

\[\begin{array}{l} \mathbf{if}\;y \leq -4.833138391616769 \cdot 10^{-22} \lor \neg \left(y \leq 2.490381128317894 \cdot 10^{-77}\right):\\ \;\;\;\;2 \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;2 \cdot \left(x \cdot x\right)\\ \end{array}\]

Alternative 2
Error	32.8
Cost	320

\[2 \cdot \left(x \cdot x\right)\]

Alternative 3
Error	54.0
Cost	64

\[0\]

Alternative 4
Error	61.3
Cost	64

\[1\]

Error

Derivation

Initial program 0.0
\[2 \cdot \left(x \cdot x + x \cdot y\right)\]
Simplified0.0
\[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(x + y\right)\right)}\]
Simplified0.0
\[\leadsto \color{blue}{2 \cdot \left(x \cdot \left(x + y\right)\right)}\]
Final simplification0.0
\[\leadsto 2 \cdot \left(x \cdot \left(x + y\right)\right)\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (* (* x 2.0) (+ x y))

  (* 2.0 (+ (* x x) (* x y))))