Error

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Derivation

1. Split input into 4 regimes

2. if y < -2.4167143474665745e-201 or 3.9387554926515795e-199 < y < 9.86503952705176e+94

   1. Initial program 13.9

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

   2. Initial simplification4.7

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

   3. Taylor expanded around -inf 4.9

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

   5. Applied div-inv5.0

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

   if -2.4167143474665745e-201 < y < 3.9387554926515795e-199

   1. Initial program 12.6

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

   2. Initial simplification7.8

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

   3. Taylor expanded around -inf 7.9

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

   5. Applied div-inv7.9

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

   7. Applied associate-*l*6.7

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

   if 9.86503952705176e+94 < y < 1.2026216740967171e+290

   1. Initial program 17.4

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

   2. Initial simplification8.5

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

   if 1.2026216740967171e+290 < y

   1. Initial program 24.4

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

   2. Initial simplification22.2

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

   3. Taylor expanded around -inf 12.1

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

   5. Applied associate-/l*10.2

      \[\leadsto \color{blue}{\frac{x}{\frac{z}{y}}}\]
3. Recombined 4 regimes into one program.

4. Final simplification5.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -2.4167143474665745 \cdot 10^{-201}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \le 3.9387554926515795 \cdot 10^{-199}:\\ \;\;\;\;x \cdot \left(\frac{1}{z} \cdot y\right)\\ \mathbf{elif}\;y \le 9.86503952705176 \cdot 10^{+94}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;y \le 1.2026216740967171 \cdot 10^{+290}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2018365 
(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: 2.7s)Debug log