Error

Derivation

1. Split input into 3 regimes

2. if (/ y z) < -2.0582081373525886e-266 or 2.975739674819211e-193 < (/ y z) < 2.9135451819351904e+171

   1. Initial program 10.6

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

   2. Simplified2.5

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

   if -2.0582081373525886e-266 < (/ y z) < 2.975739674819211e-193

   1. Initial program 18.1

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

   2. Simplified12.4

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

   3. Taylor expanded around 0 0.3

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

   if 2.9135451819351904e+171 < (/ y z)

   1. Initial program 33.3

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

   2. Simplified19.4

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

   4. Applied div-inv19.5

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

   5. Applied associate-*r*2.1

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

4. Final simplification1.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.0582081373525886 \cdot 10^{-266}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 2.975739674819211 \cdot 10^{-193}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 2.9135451819351904 \cdot 10^{+171}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019050 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))