Error

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Derivation

1. Split input into 3 regimes

2. if (/ y z) < -1.8334373322166774e-155 or 3.7429862945548285e-210 < (/ y z) < 5.449273013695744e+147

   1. Initial program 10.4

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

   2. Simplified8.5

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

   4. Applied associate-*r/9.5

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

   6. Applied associate-/l*8.5

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

   8. Applied associate-/r/2.8

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

   if -1.8334373322166774e-155 < (/ y z) < 3.7429862945548285e-210

   1. Initial program 16.6

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

   2. Simplified0.8

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

   if 5.449273013695744e+147 < (/ y z)

   1. Initial program 31.6

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

   2. Simplified3.1

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

   4. Applied associate-*r/2.0

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

   6. Applied associate-/l*3.2

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

4. Final simplification2.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.8334373322166774 \cdot 10^{-155}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 3.7429862945548285 \cdot 10^{-210}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 5.449273013695744 \cdot 10^{+147}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019008 
(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: 3.2s)Debug log