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Derivation

1. Split input into 2 regimes

2. if (/ y z) < -inf.0 or -5.031109885997233e-230 < (/ y z) < -0.0 or 1.434781732036167e+288 < (/ y z)

   1. Initial program 27.6

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

   2. Initial simplification0.3

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

   3. Taylor expanded around -inf 0.3

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

   5. Applied clear-num0.7

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

   7. Applied associate-/r*0.8

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

   if -inf.0 < (/ y z) < -5.031109885997233e-230 or -0.0 < (/ y z) < 1.434781732036167e+288

   1. Initial program 10.1

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

   2. Initial simplification7.6

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

   3. Taylor expanded around -inf 8.0

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

   5. Applied associate-/l*0.5

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

4. Final simplification0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -5.031109885997233 \cdot 10^{-230}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.434781732036167 \cdot 10^{+288}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \end{array}\]

Runtime

Time bar (total: 6.1s)Debug logProfile

herbie shell --seed 2018340 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))