Error

Try it out

Derivation

1. Split input into 4 regimes

2. if (/ y z) < -2.789292387265011e+300

   1. Initial program 57.1

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

   2. Initial simplification0.3

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

   4. Applied associate-*r/0.2

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

   if -2.789292387265011e+300 < (/ y z) < -2.9839163918592177e-189 or 6.702964246723088e-207 < (/ y z) < 4.1600426763294235e+186

   1. Initial program 9.0

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

   2. Initial simplification8.6

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

   4. Applied associate-*r/9.1

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

   6. Applied associate-/l*8.6

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

   8. Applied associate-/r/0.2

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

   if -2.9839163918592177e-189 < (/ y z) < 6.702964246723088e-207

   1. Initial program 16.9

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

   2. Initial simplification0.6

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

   if 4.1600426763294235e+186 < (/ y z)

   1. Initial program 36.4

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

   2. Initial simplification1.3

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

   4. Applied associate-*r/1.5

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

   6. Applied associate-/l*1.3

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}}\]
3. Recombined 4 regimes into one program.

4. Final simplification0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.789292387265011 \cdot 10^{+300}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.9839163918592177 \cdot 10^{-189}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.702964246723088 \cdot 10^{-207}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 4.1600426763294235 \cdot 10^{+186}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Runtime

Time bar (total: 7.3s)Debug logProfile

herbie shell --seed 2018296 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))