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Derivation

1. Split input into 3 regimes

2. if (/ y z) < -8.005487962508441e+218

   1. Initial program 42.8

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

   2. Simplified0.9

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

   4. Applied associate-*r/0.6

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

   6. Applied associate-/l*1.0

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

   7. Taylor expanded around inf 0.6

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

   if -8.005487962508441e+218 < (/ y z) < -8.587130974343098e-234 or 3.032959188079464e-244 < (/ y z) < 5.171222666601488e+154

   1. Initial program 7.9

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

   2. Simplified9.0

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

   4. Applied associate-*r/8.8

      \[\leadsto \color{blue}{\frac{y \cdot x}{z}}\]
   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 -8.587130974343098e-234 < (/ y z) < 3.032959188079464e-244 or 5.171222666601488e+154 < (/ y z)

   1. Initial program 22.3

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

   2. Simplified1.0

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

4. Final simplification0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -8.005487962508441 \cdot 10^{+218}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -8.587130974343098 \cdot 10^{-234}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 3.032959188079464 \cdot 10^{-244}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 5.171222666601488 \cdot 10^{+154}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019002 
(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: 2.8s)Debug log