Average Error: 0.1 → 0.7
Time: 16.5s
Precision: 64
Internal precision: 128
\[x \cdot \sin y + z \cdot \cos y\]
⬇
\[{\left(\sqrt[3]{x} \cdot \sqrt[3]{\sin y}\right)}^{3} + z \cdot \cos y\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Comparison0.1
Herbie0.7
\[ x \cdot \sin y + z \cdot \cos y \]

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt 0.6

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

  5. Applied cbrt-prod 0.7

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

  7. Applied pow3 0.7

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

Runtime

Time bar (total: 16.5s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(1320679906 1155795288 1117127776 3758588396 822811180 592207429)'
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"

  :target
  (+ (* x (sin y)) (* z (cos y)))

  (+ (* x (sin y)) (* z (cos y))))