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Derivation

1. Initial program 14.3

   \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

2. Initial simplification6.0

   \[\leadsto y \cdot \frac{x}{z}\]
3. Using strategy rm

4. Applied add-cube-cbrt6.7

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

5. Applied associate-*r*6.7

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

7. Applied cbrt-div6.6

   \[\leadsto \left(y \cdot \left(\sqrt[3]{\frac{x}{z}} \cdot \color{blue}{\frac{\sqrt[3]{x}}{\sqrt[3]{z}}}\right)\right) \cdot \sqrt[3]{\frac{x}{z}}\]
8. Using strategy rm

9. Applied div-inv6.6

   \[\leadsto \left(y \cdot \left(\sqrt[3]{\color{blue}{x \cdot \frac{1}{z}}} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right)\right) \cdot \sqrt[3]{\frac{x}{z}}\]

10. Applied cbrt-prod6.7

    \[\leadsto \left(y \cdot \left(\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{\frac{1}{z}}\right)} \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right)\right) \cdot \sqrt[3]{\frac{x}{z}}\]
11. Using strategy rm

12. Applied cbrt-div2.0

    \[\leadsto \left(y \cdot \left(\left(\sqrt[3]{x} \cdot \sqrt[3]{\frac{1}{z}}\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\right)\right) \cdot \color{blue}{\frac{\sqrt[3]{x}}{\sqrt[3]{z}}}\]

13. Final simplification2.0

    \[\leadsto \left(y \cdot \left(\frac{\sqrt[3]{x}}{\sqrt[3]{z}} \cdot \left(\sqrt[3]{\frac{1}{z}} \cdot \sqrt[3]{x}\right)\right)\right) \cdot \frac{\sqrt[3]{x}}{\sqrt[3]{z}}\]

Runtime

Time bar (total: 16.6s)Debug logProfile

herbie shell --seed 2018234 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))