\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
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: 2.8 s
Input Error: 6.5
Output Error: 2.7
Log: ⚲
Profile: 🕒
\({1}^3 \cdot \left(\frac{x}{z} \cdot y\right)\)
  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 *-un-lft-identity to get
    \[{\color{red}{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3 \leadsto {\color{blue}{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3\]
    3.1
  7. Applied cube-prod to get
    \[\color{red}{{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto \color{blue}{{1}^3 \cdot {\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
    3.1
  8. Applied simplify to get
    \[{1}^3 \cdot \color{red}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto {1}^3 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]
    2.8
  9. Using strategy rm
    2.8
  10. Applied associate-/r/ to get
    \[{1}^3 \cdot \color{red}{\frac{x}{\frac{z}{y}}} \leadsto {1}^3 \cdot \color{blue}{\left(\frac{x}{z} \cdot y\right)}\]
    2.7

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)))