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Derivation

1. Split input into 3 regimes

2. if (/ y z) < -inf.0

   1. Initial program 60.2

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

   2. Initial simplification0.3

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

   4. Applied associate-*r/0.3

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

   6. Applied associate-/l*0.3

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

   8. Applied clear-num0.4

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

   if -inf.0 < (/ y z) < -2.0989122530775214e-155 or 8.544848973252619e-242 < (/ y z)

   1. Initial program 11.3

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

   2. Initial simplification8.3

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

   4. Applied associate-*r/8.7

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
   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/2.6

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

   if -2.0989122530775214e-155 < (/ y z) < 8.544848973252619e-242

   1. Initial program 16.8

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

   2. Initial simplification0.8

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

4. Final simplification2.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{x}}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.0989122530775214 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 8.544848973252619 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Runtime

Time bar (total: 4.3s)Debug logProfile

herbie shell --seed 2018295 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))