Error

Try it out

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -4.672154975256748e+209 or -2.537105397623105e-218 < (/ y z) < -0.0

   1. Initial program 23.3

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

   2. Simplified0.3

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

   if -4.672154975256748e+209 < (/ y z) < -2.537105397623105e-218 or -0.0 < (/ y z)

   1. Initial program 10.7

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

   2. Simplified8.1

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

   3. Taylor expanded around inf 7.8

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

   5. Applied associate-/l*2.1

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
3. Recombined 2 regimes into one program.

4. Final simplification1.7

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.672154975256748 \cdot 10^{+209}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -2.537105397623105 \cdot 10^{-218}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019016 
(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: 3.5s)Debug log