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Derivation

1. Split input into 4 regimes

2. if (/ y z) < -inf.0

   1. Initial program 60.2

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

   2. Initial simplification0.2

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

   3. Taylor expanded around -inf 0.3

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

   5. Applied associate-/l*55.1

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

   7. Applied div-inv60.2

      \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}}\]
   8. Using strategy rm

   9. Applied associate-/r/60.2

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

   10. Applied associate-*r*0.7

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

   if -inf.0 < (/ y z) < -8.044887316823053e-181 or 1.0906822003746772e-251 < (/ y z) < 1.5151645434563507e+112

   1. Initial program 8.7

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

   2. Initial simplification8.7

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

   3. Taylor expanded around -inf 8.9

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

   5. Applied associate-/l*0.2

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

   7. Applied div-inv0.3

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

   8. Taylor expanded around 0 0.2

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

   if -8.044887316823053e-181 < (/ y z) < 1.0906822003746772e-251

   1. Initial program 17.4

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

   2. Initial simplification0.4

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

   if 1.5151645434563507e+112 < (/ y z)

   1. Initial program 27.6

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

   2. Initial simplification3.4

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

   3. Taylor expanded around -inf 3.8

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
3. Recombined 4 regimes into one program.

4. Final simplification0.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;y \cdot \left(\frac{1}{z} \cdot x\right)\\ \mathbf{elif}\;\frac{y}{z} \le -8.044887316823053 \cdot 10^{-181}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.0906822003746772 \cdot 10^{-251}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 1.5151645434563507 \cdot 10^{+112}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Runtime

Time bar (total: 6.5s)Debug logProfile

herbie shell --seed 2018346 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))