Average Error: 0.0 → 0
Time: 2.3s
Precision: binary64
\[\left(x + y\right) + x\]
↓
\[\left(x + x\right) + y\]
\left(x + y\right) + x
↓
\left(x + x\right) + y
(FPCore (x y) :precision binary64 (+ (+ x y) x))
↓
(FPCore (x y) :precision binary64 (+ (+ x x) y))
double code(double x, double y) {
	return (x + y) + x;
}
↓
double code(double x, double y) {
	return (x + x) + y;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0
Herbie0
\[y + 2 \cdot x\]

Derivation

  1. Initial program 0.0

    \[\left(x + y\right) + x\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt_binary64_1408132.6

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

  4. Simplified32.6

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

  5. Simplified32.6

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

  7. Applied associate-+r+_binary64_1399132.6

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

  9. Applied associate-+r+_binary64_1399132.6

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

  11. Applied pow1_binary64_1412032.6

    \[\leadsto \sqrt{\left(x + x\right) + y} \cdot \color{blue}{{\left(\sqrt{\left(x + x\right) + y}\right)}^{1}}\]

  12. Applied pow1_binary64_1412032.6

    \[\leadsto \color{blue}{{\left(\sqrt{\left(x + x\right) + y}\right)}^{1}} \cdot {\left(\sqrt{\left(x + x\right) + y}\right)}^{1}\]

  13. Applied pow-prod-down_binary64_1413032.6

    \[\leadsto \color{blue}{{\left(\sqrt{\left(x + x\right) + y} \cdot \sqrt{\left(x + x\right) + y}\right)}^{1}}\]

  14. Simplified0

    \[\leadsto {\color{blue}{\left(\left(x + x\right) + y\right)}}^{1}\]

  15. Final simplification0

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

Reproduce

herbie shell --seed 2020344 
(FPCore (x y)
  :name "Graphics.Rendering.Plot.Render.Plot.Legend:renderLegendOutside from plot-0.2.3.4, A"
  :precision binary64

  :herbie-target
  (+ y (* 2.0 x))

  (+ (+ x y) x))