Error

Try it out

Derivation

1. Split input into 3 regimes

2. if x < -8.105841038305899e-158 or 2.3812906285427413e-303 < x < 2.937605696047127e-86

   1. Initial program 14.1

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

   2. Initial simplification5.5

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

   if -8.105841038305899e-158 < x < 2.3812906285427413e-303

   1. Initial program 13.0

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

   2. Initial simplification7.1

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

   3. Taylor expanded around -inf 7.2

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

   5. Applied div-inv7.3

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

   7. Applied associate-*l*6.3

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

   if 2.937605696047127e-86 < x

   1. Initial program 15.7

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

   2. Initial simplification6.2

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

   3. Taylor expanded around -inf 5.5

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

4. Final simplification5.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -8.105841038305899 \cdot 10^{-158}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;x \le 2.3812906285427413 \cdot 10^{-303}:\\ \;\;\;\;\left(\frac{1}{z} \cdot y\right) \cdot x\\ \mathbf{elif}\;x \le 2.937605696047127 \cdot 10^{-86}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Runtime

Time bar (total: 7.0s)Debug logProfile

herbie shell --seed 2018258 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))