\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
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: 8.6 s
Input Error: 14.0
Output Error: 3.3
Log: ⚲
Profile: 🕒
\(\begin{cases} {1}^3 \cdot \frac{x}{\frac{z}{y}} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le -2.7103728391399204 \cdot 10^{-293} \\ \left(x \cdot y\right) \cdot \frac{1}{z} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le 4.8533841877051176 \cdot 10^{-225} \\ {1}^3 \cdot \frac{x}{\frac{z}{y}} & \text{otherwise} \end{cases}\)

    if (/ (* (/ y z) t) t) < -2.7103728391399204e-293 or 4.8533841877051176e-225 < (/ (* (/ y z) t) t)

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      10.2
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      4.4
    3. Using strategy rm
      4.4
    4. Applied add-cube-cbrt to get
      \[\color{red}{x \cdot \frac{y}{z}} \leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      5.4
    5. Using strategy rm
      5.4
    6. Applied *-un-lft-identity to get
      \[{\color{red}{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3 \leadsto {\color{blue}{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3\]
      5.4
    7. Applied cube-prod to get
      \[\color{red}{{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto \color{blue}{{1}^3 \cdot {\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      5.4
    8. Applied simplify to get
      \[{1}^3 \cdot \color{red}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto {1}^3 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]
      4.0

    if -2.7103728391399204e-293 < (/ (* (/ y z) t) t) < 4.8533841877051176e-225

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      24.5
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      9.9
    3. Using strategy rm
      9.9
    4. Applied div-inv to get
      \[x \cdot \color{red}{\frac{y}{z}} \leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]
      9.9
    5. Applied associate-*r* to get
      \[\color{red}{x \cdot \left(y \cdot \frac{1}{z}\right)} \leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
      1.3
  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)))