Error

Try it out

Derivation

1. Split input into 3 regimes

2. if (/ y z) < -1.3809341348223062e+256 or -3.808927552847435e-241 < (/ y z) < 1.3275543903754e-320

   1. Initial program 23.1

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

   2. Initial simplification0.3

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

   if -1.3809341348223062e+256 < (/ y z) < -3.808927552847435e-241

   1. Initial program 9.2

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

   2. Initial simplification8.8

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

   3. Taylor expanded around -inf 8.8

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

   5. Applied associate-/l*0.2

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

   7. Applied div-inv0.3

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

   8. Taylor expanded around inf 0.2

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

   if 1.3275543903754e-320 < (/ y z)

   1. Initial program 13.4

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

   2. Initial simplification7.2

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

   3. Taylor expanded around -inf 6.5

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

   5. Applied associate-/l*3.3

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

4. Final simplification1.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.3809341348223062 \cdot 10^{+256}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -3.808927552847435 \cdot 10^{-241}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 1.3275543903754 \cdot 10^{-320}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Runtime

Time bar (total: 6.5s)Debug logProfile

herbie shell --seed 2018304 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))