Error

Try it out

Derivation

1. Split input into 4 regimes

2. if (/ z x) < -3.222695108487588e+245 or 3.9866603406054462e+236 < (/ z x)

   1. Initial program 3.6

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

   2. Applied simplify13.3

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

   4. Applied associate-*r/0.3

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

   6. Applied clear-num1.0

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot x}}}\]
   7. Using strategy rm

   8. Applied div-inv1.0

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

   9. Applied simplify0.4

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

   if -3.222695108487588e+245 < (/ z x) < -3.627028867899059e-102

   1. Initial program 18.3

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

   2. Applied simplify0.2

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

   if -3.627028867899059e-102 < (/ z x) < 1.4103190471996078e-300

   1. Initial program 13.7

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

   2. Applied simplify20.8

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

   4. Applied div-inv20.9

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

   5. Applied associate-*r*3.7

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

   if 1.4103190471996078e-300 < (/ z x) < 3.9866603406054462e+236

   1. Initial program 17.5

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

   2. Applied simplify0.2

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

4. Applied simplify0.8

   \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{z}{x} \le -3.222695108487588 \cdot 10^{+245}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{z}{x} \le -3.627028867899059 \cdot 10^{-102}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{z}{x} \le 1.4103190471996078 \cdot 10^{-300}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{if}\;\frac{z}{x} \le 3.9866603406054462 \cdot 10^{+236}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}}\]

Runtime

Time bar (total: 22.6s)Debug logProfile

herbie shell --seed 2019053 +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)))