Average Error: 0.1 → 0.1
Time: 6.1s
Precision: binary64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(z + 3 \cdot x\right) + 2 \cdot y\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(z + 3 \cdot x\right) + 2 \cdot y
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (((double) (((double) (x + y)) + y)) + x)) + z)) + x));
}
↓
double code(double x, double y, double z) {
	return ((double) (((double) (z + ((double) (3.0 * x)))) + ((double) (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

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

  4. Applied distribute-lft-in0.1

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

  5. Applied associate-+r+0.1

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020182 
(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))