Average Error: 0.1 → 0.1
Time: 3.7s
Precision: 64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[3 \cdot x + \left(z + 2 \cdot y\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
3 \cdot x + \left(z + 2 \cdot y\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 ((3.0 * x) + (z + (2.0 * y)));
}

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. Taylor expanded around 0 0.1

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

  4. Final simplification0.1

    \[\leadsto 3 \cdot x + \left(z + 2 \cdot y\right)\]

Reproduce

herbie shell --seed 2020078 
(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))