Average Error: 0.0 → 0.0
Time: 33.3s
Precision: 64
Internal precision: 128
\[\frac{x - y}{x + y}\]
⬇
\[\sqrt[3]{{\left(\frac{x - y}{x + y}\right)}^3}\]

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Comparison0.0
Herbie0.0
\[ \frac{x}{x + y} - \frac{y}{x + y} \]

Derivation

  1. Initial program 0.0

    \[\frac{x - y}{x + y}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube 41.7

    \[\leadsto \frac{x - y}{\color{blue}{\sqrt[3]{{\left(x + y\right)}^3}}}\]

  4. Applied add-cbrt-cube 41.9

    \[\leadsto \frac{\color{blue}{\sqrt[3]{{\left(x - y\right)}^3}}}{\sqrt[3]{{\left(x + y\right)}^3}}\]

  5. Applied cbrt-undiv 41.9

    \[\leadsto \color{blue}{\sqrt[3]{\frac{{\left(x - y\right)}^3}{{\left(x + y\right)}^3}}}\]

  6. Applied simplify 0.0

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{x - y}{x + y}\right)}^3}}\]
  7. Removed slow pow expressions

Runtime

Time bar (total: 33.3s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(3420441450 3691663780 1561847010 2338181812 1968399193 1274275240)'
(FPCore (x y)
  :name "Data.Colour.RGB:hslsv from colour-2.3.3, D"

  :target
  (- (/ x (+ x y)) (/ y (+ x y)))

  (/ (- x y) (+ x y)))