Average Error: 0.1 → 0.1
Time: 2.6s
Precision: binary64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(x + \left(x + y\right) \cdot 2\right) + z\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(x + \left(x + y\right) \cdot 2\right) + z
(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 ((((x + y) + y) + x) + z) + x;
}
↓
double code(double x, double y, double z) {
	return (x + ((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 0.1

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

  2. Simplified0.1

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

  4. Applied associate-+r+_binary640.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020224 
(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))