Error

Try it out

Derivation

1. Split input into 3 regimes

2. if (/ y z) < -1.3785674582659613e+282 or -1.902965997773762e-220 < (/ y z) < 9.942043039681236e-228

   1. Initial program 22.4

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

   2. Simplified0.5

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

   4. Applied associate-*r/0.3

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

   if -1.3785674582659613e+282 < (/ y z) < -1.902965997773762e-220 or 9.942043039681236e-228 < (/ y z) < 4.102524940417053e+144

   1. Initial program 8.5

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

   2. Simplified8.9

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}}\]
   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*9.0

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

   8. Applied associate-/r/0.2

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

   if 4.102524940417053e+144 < (/ y z)

   1. Initial program 31.7

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

   2. Simplified2.1

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

4. Final simplification0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.3785674582659613 \cdot 10^{+282}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.902965997773762 \cdot 10^{-220}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 9.942043039681236 \cdot 10^{-228}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.102524940417053 \cdot 10^{+144}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019007 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))

Details

Time bar (total: 3.3s)Debug log