Average Error: 0.1 → 0.4
Time: 45.8s
Precision: 64
Internal Precision: 384
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \log \left(e^{\sqrt[3]{\cos y}}\right)\right)\right) \cdot \sqrt[3]{\cos y}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

    \[\leadsto x \cdot \sin y + z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)}\]

  4. Applied associate-*r*0.4

    \[\leadsto x \cdot \sin y + \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}}\]
  5. Using strategy rm

  6. Applied add-log-exp0.4

    \[\leadsto x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{\log \left(e^{\sqrt[3]{\cos y}}\right)}\right)\right) \cdot \sqrt[3]{\cos y}\]
  7. Removed slow pow expressions.

Runtime

Time bar (total: 45.8s)Debug log

herbie shell --seed '#(1567391828 2030694642 2833800258 828025724 3004380912 3532991858)' +o setup:early-exit
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))