Error

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Derivation

1. Split input into 3 regimes

2. if (/ y z) < -3.694776946594761e-162 or 0.0 < (/ y z) < 1.4106232585641264e+84

   1. Initial program 10.5

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

   2. Simplified8.4

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

   3. Taylor expanded around 0 7.9

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

   5. Applied associate-/l*2.4

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

   if -3.694776946594761e-162 < (/ y z) < 0.0

   1. Initial program 17.4

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

   2. Simplified0.8

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

   3. Taylor expanded around 0 0.6

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

   if 1.4106232585641264e+84 < (/ y z)

   1. Initial program 27.4

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

   2. Simplified4.6

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

   3. Taylor expanded around 0 4.4

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

   5. Applied div-inv4.5

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

   7. Applied pow14.5

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

   8. Applied pow14.5

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

   9. Applied pow-prod-down4.5

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

   10. Simplified4.5

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

4. Final simplification2.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.694776946594761 \cdot 10^{-162}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 0.0:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.4106232585641264 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019005 +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)))

Details

Time bar (total: 3.8s)Debug log