Average Error: 0.1 → 0.1

Time: 2.5s

Precision: 64

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

↓

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

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

↓

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

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

↓

double code(double x, double y, double z) {
	return ((3.0 * (z * z)) + (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	0.1
Target	0.1
Herbie	0.1

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

Derivation

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

Reproduce

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

  :herbie-target
  (+ (* (* 3 z) z) (* y x))

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