Average Error: 0.1 → 0.1
Time: 3.8s
Precision: binary64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[x + \left(\left(x + y\right) \cdot 2 + z\right)\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
x + \left(\left(x + y\right) \cdot 2 + z\right)
(FPCore (x y z) :precision binary64 (+ (+ (+ (+ (+ x y) y) x) z) x))
↓
(FPCore (x y z) :precision binary64 (+ x (+ (* (+ x y) 2.0) z)))
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) (x + ((double) (((double) (((double) (x + y)) * 2.0)) + 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 Error: 0.1 bits

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

  2. SimplifiedError: 0.1 bits

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

  3. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020204 
(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))