\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
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: 8.4 s
Input Error: 14.3
Output Error: 1.1
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{y \cdot x}{z} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le -2.6847886448158357 \cdot 10^{+172} \\ x \cdot \frac{y}{z} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le -5.412290401010101 \cdot 10^{-271} \\ {1}^3 \cdot \frac{\frac{x}{z}}{\frac{1}{y}} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le 2.8595947605456244 \cdot 10^{-179} \\ {1}^3 \cdot \frac{x}{\frac{z}{y}} & \text{when } \frac{\frac{y}{z} \cdot t}{t} \le 9.844109873327004 \cdot 10^{+161} \\ \frac{y \cdot x}{z} & \text{otherwise} \end{cases}\)

    if (/ (* (/ y z) t) t) < -2.6847886448158357e+172 or 9.844109873327004e+161 < (/ (* (/ y z) t) t)

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      39.2
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      16.9
    3. Applied taylor to get
      \[x \cdot \frac{y}{z} \leadsto \frac{y \cdot x}{z}\]
      3.3
    4. Taylor expanded around 0 to get
      \[\color{red}{\frac{y \cdot x}{z}} \leadsto \color{blue}{\frac{y \cdot x}{z}}\]
      3.3

    if -2.6847886448158357e+172 < (/ (* (/ y z) t) t) < -5.412290401010101e-271

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      0.6
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      0.2

    if -5.412290401010101e-271 < (/ (* (/ y z) t) t) < 2.8595947605456244e-179

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      22.5
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      10.3
    3. Using strategy rm
      10.3
    4. Applied add-cube-cbrt to get
      \[\color{red}{x \cdot \frac{y}{z}} \leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      10.7
    5. Using strategy rm
      10.7
    6. Applied *-un-lft-identity to get
      \[{\color{red}{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3 \leadsto {\color{blue}{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3\]
      10.7
    7. Applied cube-prod to get
      \[\color{red}{{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto \color{blue}{{1}^3 \cdot {\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      10.7
    8. Applied simplify to get
      \[{1}^3 \cdot \color{red}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto {1}^3 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]
      11.3
    9. Using strategy rm
      11.3
    10. Applied div-inv to get
      \[{1}^3 \cdot \frac{x}{\color{red}{\frac{z}{y}}} \leadsto {1}^3 \cdot \frac{x}{\color{blue}{z \cdot \frac{1}{y}}}\]
      11.3
    11. Applied associate-/r* to get
      \[{1}^3 \cdot \color{red}{\frac{x}{z \cdot \frac{1}{y}}} \leadsto {1}^3 \cdot \color{blue}{\frac{\frac{x}{z}}{\frac{1}{y}}}\]
      1.3

    if 2.8595947605456244e-179 < (/ (* (/ y z) t) t) < 9.844109873327004e+161

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      0.6
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      0.2
    3. Using strategy rm
      0.2
    4. Applied add-cube-cbrt to get
      \[\color{red}{x \cdot \frac{y}{z}} \leadsto \color{blue}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      1.3
    5. Using strategy rm
      1.3
    6. Applied *-un-lft-identity to get
      \[{\color{red}{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3 \leadsto {\color{blue}{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}}^3\]
      1.3
    7. Applied cube-prod to get
      \[\color{red}{{\left(1 \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto \color{blue}{{1}^3 \cdot {\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3}\]
      1.3
    8. Applied simplify to get
      \[{1}^3 \cdot \color{red}{{\left(\sqrt[3]{x \cdot \frac{y}{z}}\right)}^3} \leadsto {1}^3 \cdot \color{blue}{\frac{x}{\frac{z}{y}}}\]
      0.3
  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)))