Average Error: 0.0 → 0.1
Time: 12.1s
Precision: 64
Internal precision: 128
\[\frac{x + y}{x - y}\]
⬇
\[{\left(\sqrt[3]{\frac{x + y}{x - y}}\right)}^3\]

Error

Bits error versus x

Bits error versus y

Target

Original0.0
Comparison0.0
Herbie0.1
\[ \frac{1}{\frac{x}{x + y} - \frac{y}{x + y}} \]

Derivation

  1. Initial program 0.0

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

  3. Applied add-cube-cbrt 0.1

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

Runtime

Time bar (total: 12.1s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(3101247804 3881553178 3971534918 22366080 903419769 3302647428)'
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"

  :target
  (/ 1 (- (/ x (+ x y)) (/ y (+ x y))))

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