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Derivation

1. Split input into 2 regimes

2. if y < 3.2416694185665217e+162

   1. Initial program 13.6

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

   2. Initial simplification5.6

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

   4. Applied div-inv5.7

      \[\leadsto y \cdot \color{blue}{\left(x \cdot \frac{1}{z}\right)}\]

   5. Applied associate-*r*5.4

      \[\leadsto \color{blue}{\left(y \cdot x\right) \cdot \frac{1}{z}}\]

   if 3.2416694185665217e+162 < y

   1. Initial program 20.8

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

   2. Initial simplification10.9

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

   4. Applied div-inv11.0

      \[\leadsto y \cdot \color{blue}{\left(x \cdot \frac{1}{z}\right)}\]

   5. Applied associate-*r*12.6

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

   7. Applied pow112.6

      \[\leadsto \left(y \cdot x\right) \cdot \color{blue}{{\left(\frac{1}{z}\right)}^{1}}\]

   8. Applied pow112.6

      \[\leadsto \color{blue}{{\left(y \cdot x\right)}^{1}} \cdot {\left(\frac{1}{z}\right)}^{1}\]

   9. Applied pow-prod-down12.6

      \[\leadsto \color{blue}{{\left(\left(y \cdot x\right) \cdot \frac{1}{z}\right)}^{1}}\]

   10. Simplified11.7

       \[\leadsto {\color{blue}{\left(\frac{x}{\frac{z}{y}}\right)}}^{1}\]
3. Recombined 2 regimes into one program.

4. Final simplification6.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 3.2416694185665217 \cdot 10^{+162}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Runtime

Time bar (total: 7.4s)Debug logProfile

herbie shell --seed 2018277 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))