Average Error: 0.1 → 0.1
Time: 4.5s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[2 \cdot x + \left(y \cdot 2 + \left(x + z\right)\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
2 \cdot x + \left(y \cdot 2 + \left(x + z\right)\right)
double code(double x, double y, double z) {
	return (((((x + y) + y) + x) + z) + x);
}
↓
double code(double x, double y, double z) {
	return ((2.0 * x) + ((y * 2.0) + (x + z)));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

    \[\leadsto \color{blue}{2 \cdot \left(x + y\right) + \left(x + z\right)}\]
  3. Using strategy rm

  4. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(2 \cdot x + 2 \cdot y\right)} + \left(x + z\right)\]

  5. Applied associate-+l+0.1

    \[\leadsto \color{blue}{2 \cdot x + \left(2 \cdot y + \left(x + z\right)\right)}\]

  6. Simplified0.1

    \[\leadsto 2 \cdot x + \color{blue}{\left(y \cdot 2 + \left(x + z\right)\right)}\]

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendInside from plot-0.2.3.4"
  :precision binary64
  (+ (+ (+ (+ (+ x y) y) x) z) x))