Average Error: 0.1 → 0.1
Time: 1.6s
Precision: binary64
\[\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x\]
↓
\[\left(x \cdot 3 + y \cdot 2\right) + z\]
\left(\left(\left(\left(x + y\right) + y\right) + x\right) + z\right) + x
↓
\left(x \cdot 3 + y \cdot 2\right) + 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) (((double) (((double) (x * 3.0)) + ((double) (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+0.1

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

  6. Applied flip-+28.6

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

  7. Simplified28.6

    \[\leadsto \frac{\color{blue}{x \cdot x + \left(x + y\right) \cdot \left(\left(x + y\right) \cdot -4\right)}}{x - \left(x + y\right) \cdot 2} + z\]

  8. Simplified28.6

    \[\leadsto \frac{x \cdot x + \left(x + y\right) \cdot \left(\left(x + y\right) \cdot -4\right)}{\color{blue}{x + \left(x + y\right) \cdot -2}} + z\]

  9. Taylor expanded around 0 0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2020184 
(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))