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Derivation

1. Split input into 3 regimes

2. if x < -6.527818448277319e-113

   1. Initial program 15.2

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

   2. Simplified6.2

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

   3. Taylor expanded around -inf 6.0

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

   5. Applied div-inv6.0

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
   6. Using strategy rm

   7. Applied pow16.0

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

   8. Applied pow16.0

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

   9. Applied pow-prod-down6.0

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

   10. Simplified6.0

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

   if -6.527818448277319e-113 < x < 3.458399982184495e-126

   1. Initial program 11.9

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

   2. Simplified5.7

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

   3. Taylor expanded around -inf 7.0

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

   5. Applied div-inv7.1

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

   6. Taylor expanded around inf 7.0

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

   if 3.458399982184495e-126 < x

   1. Initial program 15.1

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

   2. Simplified5.1

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

4. Final simplification6.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -6.527818448277319 \cdot 10^{-113}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;x \le 3.458399982184495 \cdot 10^{-126}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019004 
(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: 3.7s)Debug log