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Derivation

1. Split input into 3 regimes

2. if (/ y z) < -inf.0 or -6.003458830815731e-264 < (/ y z) < -0.0 or 1.434781732036167e+288 < (/ y z)

   1. Initial program 28.9

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

   2. Initial simplification0.2

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

   3. Taylor expanded around -inf 0.1

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

   5. Applied div-inv0.2

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

   7. Applied pow10.2

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

   8. Applied pow10.2

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

   9. Applied pow-prod-down0.2

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

   10. Simplified0.2

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

   if -inf.0 < (/ y z) < -6.003458830815731e-264

   1. Initial program 9.7

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

   2. Initial simplification7.7

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

   3. Taylor expanded around -inf 8.1

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

   5. Applied div-inv8.2

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

   7. Applied pow18.2

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

   8. Applied pow18.2

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

   9. Applied pow-prod-down8.2

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

   10. Simplified7.6

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

   12. Applied associate-/r/0.2

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

   if -0.0 < (/ y z) < 1.434781732036167e+288

   1. Initial program 10.8

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

   2. Initial simplification7.2

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

   3. Taylor expanded around -inf 7.6

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

   5. Applied associate-/l*0.8

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

4. Final simplification0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -6.003458830815731 \cdot 10^{-264}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le -0.0:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.434781732036167 \cdot 10^{+288}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Runtime

Time bar (total: 6.0s)Debug logProfile

herbie shell --seed 2018340 +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)))