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Derivation

1. Split input into 3 regimes

2. if y < -6.0371201832147224e+203

   1. Initial program 22.0

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

   2. Initial simplification11.6

      \[\leadsto y \cdot \frac{x}{z}\]

   3. Taylor expanded around 0 13.4

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
   4. Using strategy rm

   5. Applied clear-num13.5

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]

   if -6.0371201832147224e+203 < y < -9.89710938050192e-294 or 5.0038104182459124e-185 < y

   1. Initial program 13.8

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

   2. Initial simplification5.1

      \[\leadsto y \cdot \frac{x}{z}\]

   3. Taylor expanded around 0 5.6

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
   4. Using strategy rm

   5. Applied associate-/l*5.2

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]

   if -9.89710938050192e-294 < y < 5.0038104182459124e-185

   1. Initial program 12.1

      \[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]

   2. Initial simplification7.8

      \[\leadsto y \cdot \frac{x}{z}\]
3. Recombined 3 regimes into one program.

4. Final simplification6.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -6.0371201832147224 \cdot 10^{+203}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \mathbf{elif}\;y \le -9.89710938050192 \cdot 10^{-294}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;y \le 5.0038104182459124 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Runtime

Time bar (total: 13.2s)Debug logProfile

herbie shell --seed 2018263 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))