Average Error: 0.1 → 0.1

Time: 2.9s

Precision: 64

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

↓

\[3 \cdot \left(y \cdot y\right) + x \cdot x\]

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

↓

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

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

↓

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

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	0.1
Target	0.1
Herbie	0.1

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

Derivation

Initial program 0.1
\[\left(\left(x \cdot x + y \cdot y\right) + y \cdot y\right) + y \cdot y\]
Simplified0.1
\[\leadsto \color{blue}{3 \cdot \left(y \cdot y\right) + x \cdot x}\]
Final simplification0.1
\[\leadsto 3 \cdot \left(y \cdot y\right) + x \cdot x\]

Reproduce

herbie shell --seed 2020075 
(FPCore (x y)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, E"
  :precision binary64

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

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