Error

Derivation

1. Initial program 13.9

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

2. Applied simplify5.9

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

4. Applied add-cube-cbrt6.7

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

5. Applied associate-*r*6.7

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

7. Applied cbrt-div6.6

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

8. Applied cbrt-div6.7

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

9. Applied frac-times6.7

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

11. Applied div-inv6.6

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

12. Applied cbrt-prod1.7

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

Runtime

Time bar (total: 29.7s)Debug logProfile

herbie shell --seed '#(1070960995 739739648 2531964651 3069671617 351857262 3877178482)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))