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Derivation

1. Split input into 3 regimes

2. if (/ y z) < -3.358999357469415e+240 or 3.6376431378973445e+191 < (/ y z)

   1. Initial program 41.4

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

   2. Initial simplification1.1

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

   if -3.358999357469415e+240 < (/ y z) < -3.23428408198329e-242 or 3.314208867341187e-215 < (/ y z) < 3.6376431378973445e+191

   1. Initial program 8.8

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

   2. Initial simplification8.9

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

   3. Taylor expanded around -inf 8.8

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

   5. Applied associate-/l*0.2

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

   if -3.23428408198329e-242 < (/ y z) < 3.314208867341187e-215

   1. Initial program 18.6

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

   2. Initial simplification0.4

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

   4. Applied div-inv0.4

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

   5. Applied associate-*r*0.2

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

4. Final simplification0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.358999357469415 \cdot 10^{+240}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -3.23428408198329 \cdot 10^{-242}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 3.314208867341187 \cdot 10^{-215}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 3.6376431378973445 \cdot 10^{+191}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Runtime

Time bar (total: 7.0s)Debug logProfile

herbie shell --seed 2018351 +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)))