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Derivation

1. Split input into 2 regimes

2. if (/ y z) < -2.917171288068428e+301 or -1.2286817288539788e-238 < (/ y z) < 2.020881514954108e-79

   1. Initial program 19.7

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

   2. Initial simplification1.7

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

   if -2.917171288068428e+301 < (/ y z) < -1.2286817288539788e-238 or 2.020881514954108e-79 < (/ y z)

   1. Initial program 11.8

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

   2. Initial simplification8.8

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

   4. Applied associate-*r/8.4

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

   6. Applied associate-/l*8.8

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

   8. Applied associate-/r/2.7

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

4. Final simplification2.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.917171288068428 \cdot 10^{+301}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.2286817288539788 \cdot 10^{-238}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 2.020881514954108 \cdot 10^{-79}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Runtime

Time bar (total: 7.1s)Debug logProfile

herbie shell --seed 2018290 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))