\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
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: 7.1 s
Input Error: 14.0
Output Error: 2.5
Log: ⚲
Profile: 🕒
\(\begin{cases} x \cdot \frac{y}{z} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le -1.981822314854173 \cdot 10^{-301} \\ \frac{y \cdot x}{z} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le 3.707558976003304 \cdot 10^{-304} \\ {1}^3 \cdot \frac{x}{\frac{z}{y}} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le 3.3305262352552325 \cdot 10^{+148} \\ \frac{y \cdot x}{z} & \text{otherwise} \end{cases}\)

    if (/ (* (/ y z) t) t) < -1.981822314854173e-301

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      10.6
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      4.7

    if -1.981822314854173e-301 < (/ (* (/ y z) t) t) < 3.707558976003304e-304 or 3.3305262352552325e+148 < (/ (* (/ y z) t) t)

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      29.0
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      12.3
    3. Applied taylor to get
      \[x \cdot \frac{y}{z} \leadsto \frac{y \cdot x}{z}\]
      1.7
    4. Taylor expanded around 0 to get
      \[\color{red}{\frac{y \cdot x}{z}} \leadsto \color{blue}{\frac{y \cdot x}{z}}\]
      1.7

    if 3.707558976003304e-304 < (/ (* (/ y z) t) t) < 3.3305262352552325e+148

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      0.7
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      0.2
    3. Using strategy rm
      0.2
    4. Applied add-cube-cbrt to get
      \[\color{red}{x \cdot \frac{y}{z}} \leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      1.2
    5. Using strategy rm
      1.2
    6. Applied *-un-lft-identity to get
      \[{\color{red}{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3 \leadsto {\color{blue}{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3\]
      1.2
    7. Applied cube-prod to get
      \[\color{red}{{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto \color{blue}{{1}^3 \cdot {\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      1.2
    8. Applied simplify to get
      \[{1}^3 \cdot \color{red}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto {1}^3 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]
      0.2
  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)))