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Derivation

1. Split input into 3 regimes

2. if (/ (* (/ y z) t) t) < -4.783215536162634e+296 or -2.0989122530775214e-155 < (/ (* (/ y z) t) t) < 5.910443916251389e-238

   1. Initial program 26.7

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

   2. Initial simplification1.6

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

   3. Taylor expanded around 0 1.7

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

   if -4.783215536162634e+296 < (/ (* (/ y z) t) t) < -2.0989122530775214e-155

   1. Initial program 0.5

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

   if 5.910443916251389e-238 < (/ (* (/ y z) t) t)

   1. Initial program 10.1

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

   2. Initial simplification8.2

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

   3. Taylor expanded around 0 7.9

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

   5. Applied associate-/l*4.4

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

   7. Applied clear-num4.7

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

4. Final simplification2.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -4.783215536162634 \cdot 10^{+296}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -2.0989122530775214 \cdot 10^{-155}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 5.910443916251389 \cdot 10^{-238}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\frac{\frac{z}{y}}{x}}\\ \end{array}\]

Runtime

Time bar (total: 6.2s)Debug logProfile

herbie shell --seed 2018295 +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)))