Error

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Derivation

1. Split input into 2 regimes

2. if (/ y z) < -5.897662964381415e+305 or -2.537105397623105e-218 < (/ y z) < 1.4297097965547508e-295

   1. Initial program 22.4

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

   2. Simplified0.2

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

   4. Applied associate-*r/0.3

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

   6. Applied associate-/l*0.2

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

   if -5.897662964381415e+305 < (/ y z) < -2.537105397623105e-218 or 1.4297097965547508e-295 < (/ y z)

   1. Initial program 11.3

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

   2. Simplified8.0

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

   4. Applied div-inv8.0

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

   5. Applied associate-*r*7.7

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

   7. Applied pow17.7

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

   8. Applied pow17.7

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

   9. Applied pow-prod-down7.7

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

   10. Simplified1.9

       \[\leadsto {\color{blue}{\left(\frac{x}{\frac{z}{y}}\right)}}^{1}\]
3. Recombined 2 regimes into one program.

4. Final simplification1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.897662964381415 \cdot 10^{+305}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.537105397623105 \cdot 10^{-218}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.4297097965547508 \cdot 10^{-295}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019016 +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: 4.2s)Debug log