Error

Derivation

1. Split input into 4 regimes

2. if (* y (/ x z)) < -3.692100744515322e+294

   1. Initial program 12.4

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

   2. Applied simplify3.7

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

   if -3.692100744515322e+294 < (* y (/ x z)) < -2.503214740697761e-307 or 6.3685061748937e-321 < (* y (/ x z)) < 2.0663810401191435e+212

   1. Initial program 18.0

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

   2. Applied simplify7.8

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

   4. Applied add-cube-cbrt8.8

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \frac{y}{z}} \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right) \cdot \sqrt[3]{x \cdot \frac{y}{z}}}\]

   5. Taylor expanded around 0 56.8

      \[\leadsto \left(\color{blue}{e^{\frac{1}{3} \cdot \left(\left(\log y + \log x\right) - \log z\right)}} \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right) \cdot \sqrt[3]{x \cdot \frac{y}{z}}\]

   6. Applied simplify2.0

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{y}{\frac{z}{x}}} \cdot \sqrt[3]{\frac{y}{\frac{z}{x}}}\right) \cdot \sqrt[3]{\frac{y}{\frac{z}{x}}}}\]

   7. Taylor expanded around 0 8.8

      \[\leadsto \left(\sqrt[3]{\frac{y}{\frac{z}{x}}} \cdot \sqrt[3]{\frac{y}{\frac{z}{x}}}\right) \cdot \sqrt[3]{\color{blue}{\frac{y \cdot x}{z}}}\]

   8. Applied simplify0.9

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

   if -2.503214740697761e-307 < (* y (/ x z)) < 6.3685061748937e-321

   1. Initial program 2.0

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

   2. Applied simplify0.3

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

   4. Applied div-inv0.3

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

   5. Applied associate-*r*0.3

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

   if 2.0663810401191435e+212 < (* y (/ x z))

   1. Initial program 19.1

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

   2. Applied simplify10.3

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

   4. Applied add-cube-cbrt11.1

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \frac{y}{z}} \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right) \cdot \sqrt[3]{x \cdot \frac{y}{z}}}\]

   5. Taylor expanded around 0 48.7

      \[\leadsto \left(\color{blue}{e^{\frac{1}{3} \cdot \left(\left(\log y + \log x\right) - \log z\right)}} \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right) \cdot \sqrt[3]{x \cdot \frac{y}{z}}\]

   6. Applied simplify23.1

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{y}{\frac{z}{x}}} \cdot \sqrt[3]{\frac{y}{\frac{z}{x}}}\right) \cdot \sqrt[3]{\frac{y}{\frac{z}{x}}}}\]

   7. Taylor expanded around 0 32.5

      \[\leadsto \left(\sqrt[3]{\frac{y}{\frac{z}{x}}} \cdot \sqrt[3]{\frac{y}{\frac{z}{x}}}\right) \cdot \sqrt[3]{\color{blue}{\frac{y \cdot x}{z}}}\]

   8. Applied simplify22.4

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

   10. Applied div-inv22.5

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

   11. Applied associate-/r*10.3

       \[\leadsto \color{blue}{\frac{\frac{y}{z}}{\frac{1}{x}}}\]
3. Recombined 4 regimes into one program.

Runtime

Time bar (total: 24.9s)Debug logProfile

herbie shell --seed '#(1071948828 1180510430 2986424009 997076509 406109801 420189285)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))