Average Error: 0.1 → 0.1
Time: 4.5s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(y + z\right) \cdot x + \left(\left(\left(z + y\right) + t\right) \cdot x + y \cdot 5\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(y + z\right) \cdot x + \left(\left(\left(z + y\right) + t\right) \cdot x + y \cdot 5\right)
double code(double x, double y, double z, double t) {
	return ((double) (((double) (x * ((double) (((double) (((double) (((double) (y + z)) + z)) + y)) + t)))) + ((double) (y * 5.0))));
}
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (y + z)) * x)) + ((double) (((double) (((double) (((double) (z + y)) + t)) * x)) + ((double) (y * 5.0))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
  2. Using strategy rm

  3. Applied associate-+l+0.1

    \[\leadsto x \cdot \left(\color{blue}{\left(\left(y + z\right) + \left(z + y\right)\right)} + t\right) + y \cdot 5\]

  4. Applied associate-+l+0.1

    \[\leadsto x \cdot \color{blue}{\left(\left(y + z\right) + \left(\left(z + y\right) + t\right)\right)} + y \cdot 5\]

  5. Applied distribute-rgt-in0.1

    \[\leadsto \color{blue}{\left(\left(y + z\right) \cdot x + \left(\left(z + y\right) + t\right) \cdot x\right)} + y \cdot 5\]

  6. Applied associate-+l+0.1

    \[\leadsto \color{blue}{\left(y + z\right) \cdot x + \left(\left(\left(z + y\right) + t\right) \cdot x + y \cdot 5\right)}\]

  7. Final simplification0.1

    \[\leadsto \left(y + z\right) \cdot x + \left(\left(\left(z + y\right) + t\right) \cdot x + y \cdot 5\right)\]

Reproduce

herbie shell --seed 2020114 
(FPCore (x y z t)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, B"
  :precision binary64
  (+ (* x (+ (+ (+ (+ y z) z) y) t)) (* y 5)))