Average Error: 0.1 → 0.1
Time: 2.0s
Precision: 64
\[x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5\]
↓
\[\left(x \cdot z + x \cdot z\right) + \left(\left(\left(y + y\right) + t\right) \cdot x + y \cdot 5\right)\]
x \cdot \left(\left(\left(\left(y + z\right) + z\right) + y\right) + t\right) + y \cdot 5
↓
\left(x \cdot z + x \cdot z\right) + \left(\left(\left(y + y\right) + t\right) \cdot x + y \cdot 5\right)
double code(double x, double y, double z, double t) {
	return ((x * ((((y + z) + z) + y) + t)) + (y * 5.0));
}
↓
double code(double x, double y, double z, double t) {
	return (((x * z) + (x * z)) + ((((y + y) + t) * x) + (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 +-commutative0.1

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

  4. Applied associate-+l+0.1

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

  5. Applied associate-+l+0.1

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

  6. Applied associate-+l+0.1

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

  7. Applied distribute-lft-in0.1

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

  9. Applied +-commutative0.1

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

  10. Applied associate-+l+0.1

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

  11. Applied associate-+l+0.1

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

  12. Applied distribute-lft-in0.1

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

  13. Applied associate-+r+0.1

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

  14. Applied associate-+l+0.1

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

  15. Simplified0.1

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

  16. Final simplification0.1

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

Reproduce

herbie shell --seed 2020078 
(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)))