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Derivation

1. Split input into 3 regimes

2. if z < -6.961428734902451e+143

   1. Initial program 12.0

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

   2. Initial simplification7.3

      \[\leadsto y \cdot \frac{x}{z}\]
   3. Using strategy rm

   4. Applied associate-*r/7.0

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

   6. Applied div-inv7.1

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

   8. Applied pow17.1

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

   9. Applied pow17.1

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

   10. Applied pow-prod-down7.1

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

   11. Simplified7.2

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

   if -6.961428734902451e+143 < z < 2.485245629353602e-229 or 9.804480552862454e+180 < z

   1. Initial program 15.3

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

   2. Initial simplification6.2

      \[\leadsto y \cdot \frac{x}{z}\]
   3. Using strategy rm

   4. Applied associate-*r/6.4

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

   if 2.485245629353602e-229 < z < 9.804480552862454e+180

   1. Initial program 13.8

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

   2. Initial simplification4.9

      \[\leadsto y \cdot \frac{x}{z}\]
   3. Using strategy rm

   4. Applied associate-*r/5.3

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

   6. Applied associate-/l*4.7

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

4. Final simplification6.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -6.961428734902451 \cdot 10^{+143}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;z \le 2.485245629353602 \cdot 10^{-229}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;z \le 9.804480552862454 \cdot 10^{+180}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Runtime

Time bar (total: 7.1s)Debug logProfile

herbie shell --seed 2018256 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))