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Derivation

1. Split input into 4 regimes

2. if (/ (* (/ y z) t) t) < -1.4424800619596556e+123

   1. Initial program 33.6

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

   2. Initial simplification3.8

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

   4. Applied div-inv3.9

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

   5. Applied associate-*r*3.2

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

   if -1.4424800619596556e+123 < (/ (* (/ y z) t) t) < -4.339640939103075e-173 or 2.1437592897272027e-51 < (/ (* (/ y z) t) t) < 1.7018916596101613e+152

   1. Initial program 0.6

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

   if -4.339640939103075e-173 < (/ (* (/ y z) t) t) < 2.1437592897272027e-51

   1. Initial program 16.1

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

   2. Initial simplification2.7

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

   if 1.7018916596101613e+152 < (/ (* (/ y z) t) t)

   1. Initial program 37.1

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

   2. Initial simplification3.4

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

   3. Taylor expanded around 0 3.1

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

4. Final simplification2.0

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.4424800619596556 \cdot 10^{+123}:\\ \;\;\;\;\frac{1}{z} \cdot \left(y \cdot x\right)\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -4.339640939103075 \cdot 10^{-173}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 2.1437592897272027 \cdot 10^{-51}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.7018916596101613 \cdot 10^{+152}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Runtime

Time bar (total: 14.0s)Debug logProfile

herbie shell --seed 2018274 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))