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Derivation

1. Split input into 2 regimes

2. if (/ y z) < 4.279263918164063e-295 or 4.999939969196146e+208 < (/ y z)

   1. Initial program 17.3

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

   2. Initial simplification4.7

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

   4. Applied associate-*r/4.5

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

   6. Applied associate-/l*4.7

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

   if 4.279263918164063e-295 < (/ y z) < 4.999939969196146e+208

   1. Initial program 8.4

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

   2. Initial simplification8.2

      \[\leadsto y \cdot \frac{x}{z}\]
   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*8.2

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

   8. Applied associate-/r/0.2

      \[\leadsto \color{blue}{\frac{y}{z} \cdot x}\]
3. Recombined 2 regimes into one program.

4. Final simplification3.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le 4.279263918164063 \cdot 10^{-295}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 4.999939969196146 \cdot 10^{+208}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Runtime

Time bar (total: 4.8s)Debug logProfile

herbie shell --seed 2018235 +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)))