Error

Derivation

1. Split input into 2 regimes

2. if (/ y z) < -4.58115826387339e-285 or 2.2692925812077e-313 < (/ y z)

   1. Initial program 12.7

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

   2. Simplified3.6

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

   if -4.58115826387339e-285 < (/ y z) < 2.2692925812077e-313

   1. Initial program 19.4

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

   2. Simplified17.8

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

   4. Applied clear-num19.0

      \[\leadsto x \cdot \color{blue}{\frac{1}{\frac{z}{y}}}\]

   5. Applied un-div-inv19.0

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

   7. Applied associate-/r/0.1

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

   9. Applied *-un-lft-identity0.1

      \[\leadsto \frac{\color{blue}{1 \cdot x}}{z} \cdot y\]

   10. Applied associate-/l*0.1

       \[\leadsto \color{blue}{\frac{1}{\frac{z}{x}}} \cdot y\]

   11. Applied associate-*l/0.1

       \[\leadsto \color{blue}{\frac{1 \cdot y}{\frac{z}{x}}}\]

   12. Simplified0.1

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

   13. Taylor expanded around inf 0.1

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

4. Final simplification3.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -4.58115826387339 \cdot 10^{-285}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 2.2692925812077 \cdot 10^{-313}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

Reproduce

herbie shell --seed 2019088 +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))