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Derivation

1. Split input into 4 regimes

2. if (/ y z) < -5.124513885490297e+99

   1. Initial program 28.9

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

   2. Initial simplification4.3

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

   4. Applied associate-*r/3.6

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

   5. Taylor expanded around 0 3.6

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

   if -5.124513885490297e+99 < (/ y z) < 9.401674186844705e-264

   1. Initial program 12.2

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

   2. Initial simplification4.9

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

   4. Applied associate-*r/5.1

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

   6. Applied associate-/l*4.9

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

   if 9.401674186844705e-264 < (/ y z) < 3.731806655551077e+162

   1. Initial program 7.7

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

   2. Initial simplification9.4

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

   4. Applied associate-*r/8.3

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

   6. Applied associate-/l*9.5

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

   8. Applied associate-/r/0.2

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

   if 3.731806655551077e+162 < (/ y z)

   1. Initial program 32.2

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

   2. Initial simplification1.9

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

   4. Applied associate-*r/1.9

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

   6. Applied clear-num2.0

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot x}}}\]
3. Recombined 4 regimes into one program.

4. Final simplification3.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.124513885490297 \cdot 10^{+99}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 9.401674186844705 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 3.731806655551077 \cdot 10^{+162}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{z}{x \cdot y}}\\ \end{array}\]

Runtime

Time bar (total: 7.2s)Debug logProfile

herbie shell --seed 2018286 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))