Average Error: 3.9 → 1.5
Time: 20.2s
Precision: 64
Internal precision: 128
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
⬇
\[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{1}{\frac{y}{\frac{t}{z \cdot 3.0}}}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original3.9
Comparison1.5
Herbie1.5
\[ \left(x - \frac{y}{z \cdot 3.0}\right) + \frac{\frac{t}{z \cdot 3.0}}{y} \]

Derivation

  1. Initial program 3.9

    \[\left(x - \frac{y}{z \cdot 3.0}\right) + \frac{t}{\left(z \cdot 3.0\right) \cdot y}\]
  2. Using strategy rm

  3. Applied associate-/r* 1.5

    \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \color{blue}{\frac{\frac{t}{z \cdot 3.0}}{y}}\]
  4. Using strategy rm

  5. Applied clear-num 1.5

    \[\leadsto \left(x - \frac{y}{z \cdot 3.0}\right) + \color{blue}{\frac{1}{\frac{y}{\frac{t}{z \cdot 3.0}}}}\]
  6. Removed slow pow expressions

Runtime

Time bar (total: 20.2s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(3446566837 287348450 1560072958 3294386672 2052617605 4013335510)'
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"

  :target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))