\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
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: 5.8 s
Input Error: 14.4
Output Error: 6.0
Log: ⚲
Profile: 🕒
\(\begin{cases} \left(x \cdot y\right) \cdot \frac{1}{z} & \text{when } t \le -3.273924478542282 \cdot 10^{+58} \\ x \cdot \frac{y}{z} & \text{when } t \le 2.3171949870445494 \cdot 10^{-176} \\ \left(x \cdot y\right) \cdot \frac{1}{z} & \text{when } t \le 9.065596326568504 \cdot 10^{-13} \\ \frac{y}{\frac{z}{x}} & \text{otherwise} \end{cases}\)

    if t < -3.273924478542282e+58 or 2.3171949870445494e-176 < t < 9.065596326568504e-13

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      14.3
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      6.3
    3. Using strategy rm
      6.3
    4. Applied div-inv to get
      \[x \cdot \color{red}{\frac{y}{z}} \leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]
      6.4
    5. Applied associate-*r* to get
      \[\color{red}{x \cdot \left(y \cdot \frac{1}{z}\right)} \leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
      5.9

    if -3.273924478542282e+58 < t < 2.3171949870445494e-176

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      14.6
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      5.6

    if 9.065596326568504e-13 < t

    1. Started with
      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
      14.1
    2. Applied simplify to get
      \[\color{red}{x \cdot \frac{\frac{y}{z} \cdot t}{t}} \leadsto \color{blue}{x \cdot \frac{y}{z}}\]
      6.7
    3. Applied taylor to get
      \[x \cdot \frac{y}{z} \leadsto \frac{y \cdot x}{z}\]
      5.9
    4. Taylor expanded around 0 to get
      \[\color{red}{\frac{y \cdot x}{z}} \leadsto \color{blue}{\frac{y \cdot x}{z}}\]
      5.9
    5. Using strategy rm
      5.9
    6. Applied associate-/l* to get
      \[\color{red}{\frac{y \cdot x}{z}} \leadsto \color{blue}{\frac{y}{\frac{z}{x}}}\]
      6.6
  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)))