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Derivation

1. Split input into 4 regimes

2. if (/ y z) < -3.282021257746298e+200

   1. Initial program 38.6

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

   2. Initial simplification1.8

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

   4. Applied associate-*r/1.6

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

   6. Applied associate-/l*1.5

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

   if -3.282021257746298e+200 < (/ y z) < -8.6490765237775e-292 or 1.1421569379912e-312 < (/ y z) < 1.4485849901919557e+180

   1. Initial program 9.0

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

   2. Initial simplification8.7

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

   4. Applied associate-*r/8.1

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

   6. Applied associate-/l*8.6

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

   8. Applied associate-/r/0.2

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

   if -8.6490765237775e-292 < (/ y z) < 1.1421569379912e-312

   1. Initial program 20.0

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

   2. Initial simplification0.1

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

   4. Applied associate-*r/0.1

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

   if 1.4485849901919557e+180 < (/ y z)

   1. Initial program 37.3

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

   2. Initial simplification1.7

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

4. Final simplification0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.282021257746298 \cdot 10^{+200}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -8.6490765237775 \cdot 10^{-292}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.1421569379912 \cdot 10^{-312}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.4485849901919557 \cdot 10^{+180}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Runtime

Time bar (total: 4.7s)Debug logProfile

herbie shell --seed 2018297 +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)))