\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
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: 6.9 s
Input Error: 6.5
Output Error: 1.5
Log: ⚲
Profile: 🕒
\(\begin{cases} {1}^3 \cdot \frac{x}{\frac{z}{y}} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le -1.6784522f-18 \\ \frac{y \cdot x}{z} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le 1.263616f-29 \\ {1}^3 \cdot \frac{x}{\frac{z}{y}} & \text{otherwise} \end{cases}\)

    if (/ (* (/ y z) t) t) < -1.6784522f-18 or 1.263616f-29 < (/ (* (/ y z) t) t)

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      5.6
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      2.4
    3. Using strategy rm
      2.4
    4. Applied add-cube-cbrt to get
      \[\color{red}{x \cdot \frac{y}{z}} \leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      2.9
    5. Using strategy rm
      2.9
    6. Applied *-un-lft-identity to get
      \[{\color{red}{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3 \leadsto {\color{blue}{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3\]
      2.9
    7. Applied cube-prod to get
      \[\color{red}{{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto \color{blue}{{1}^3 \cdot {\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      2.9
    8. Applied simplify to get
      \[{1}^3 \cdot \color{red}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto {1}^3 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]
      1.8

    if -1.6784522f-18 < (/ (* (/ y z) t) t) < 1.263616f-29

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      8.5
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      3.6
    3. Applied taylor to get
      \[x \cdot \frac{y}{z} \leadsto \frac{y \cdot x}{z}\]
      0.7
    4. Taylor expanded around 0 to get
      \[\color{red}{\frac{y \cdot x}{z}} \leadsto \color{blue}{\frac{y \cdot x}{z}}\]
      0.7
  1. 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)))