\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
Test:
Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
Time: 5.5 s
Input Error: 6.5
Output Error: 2.7
Log: ⚲
Profile: 🕒
\(\frac{y}{\frac{z}{x}}\)
  1. Started with
    \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
    6.5
  2. Applied simplify to get
    \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    2.8
  3. Using strategy rm
    2.8
  4. Applied add-cube-cbrt to get
    \[\color{red}{x \cdot \frac{y}{z}} \leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
    3.1
  5. Using strategy rm
    3.1
  6. Applied add-cbrt-cube to get
    \[\color{red}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto \color{blue}{\sqrt[3]{{\left({\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3\right)}^3}}\]
    14.9
  7. Applied simplify to get
    \[\sqrt[3]{\color{red}{{\left({\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3\right)}^3}} \leadsto \sqrt[3]{\color{blue}{{\left(\frac{x}{z} \cdot y\right)}^3}}\]
    14.7
  8. Applied taylor to get
    \[\sqrt[3]{{\left(\frac{x}{z} \cdot y\right)}^3} \leadsto \sqrt[3]{{\left(\frac{y \cdot x}{z}\right)}^3}\]
    14.6
  9. Taylor expanded around 0 to get
    \[\sqrt[3]{{\color{red}{\left(\frac{y \cdot x}{z}\right)}}^3} \leadsto \sqrt[3]{{\color{blue}{\left(\frac{y \cdot x}{z}\right)}}^3}\]
    14.6
  10. Applied simplify to get
    \[\sqrt[3]{{\left(\frac{y \cdot x}{z}\right)}^3} \leadsto \frac{y}{\frac{z}{x}}\]
    2.7
  11. Applied final simplification
  12. Removed slow pow expressions

Original test:


(lambda ((x default) (y default) (z default) (t default))
  #:name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))