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Derivation

1. Split input into 2 regimes

2. if (/ y z) < 3.694440312892776e-257 or 1.858683731334887e+209 < (/ y z)

   1. Initial program 17.1

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

   2. Initial simplification4.5

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

   3. Taylor expanded around -inf 4.7

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

   if 3.694440312892776e-257 < (/ y z) < 1.858683731334887e+209

   1. Initial program 8.1

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

   2. Initial simplification8.5

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

   3. Taylor expanded around -inf 8.5

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

   5. Applied div-inv8.5

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
   6. Using strategy rm

   7. Applied pow18.5

      \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{{\left(\frac{1}{z}\right)}^{1}}\]

   8. Applied pow18.5

      \[\leadsto \color{blue}{{\left(x \cdot y\right)}^{1}} \cdot {\left(\frac{1}{z}\right)}^{1}\]

   9. Applied pow-prod-down8.5

      \[\leadsto \color{blue}{{\left(\left(x \cdot y\right) \cdot \frac{1}{z}\right)}^{1}}\]

   10. Simplified8.5

       \[\leadsto {\color{blue}{\left(\frac{y}{\frac{z}{x}}\right)}}^{1}\]
   11. Using strategy rm

   12. Applied associate-/r/0.2

       \[\leadsto {\color{blue}{\left(\frac{y}{z} \cdot x\right)}}^{1}\]
3. Recombined 2 regimes into one program.

4. Final simplification3.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 3.694440312892776 \cdot 10^{-257}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.858683731334887 \cdot 10^{+209}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Runtime

Time bar (total: 7.2s)Debug logProfile

herbie shell --seed 2018348 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))