Error

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Derivation

1. Split input into 3 regimes

2. if (/ (* (/ y z) t) t) < -5.995228819261882e-116 or -0.0 < (/ (* (/ y z) t) t) < 1.2042578784291804e+237

   1. Initial program 6.5

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

   2. Simplified8.9

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

   3. Taylor expanded around inf 8.0

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

   5. Applied associate-/l*2.4

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

   if -5.995228819261882e-116 < (/ (* (/ y z) t) t) < -0.0

   1. Initial program 20.5

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

   2. Simplified1.7

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

   if 1.2042578784291804e+237 < (/ (* (/ y z) t) t)

   1. Initial program 51.0

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

   2. Simplified2.4

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

   3. Taylor expanded around inf 2.4

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

4. Final simplification2.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -5.995228819261882 \cdot 10^{-116}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -0.0:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.2042578784291804 \cdot 10^{+237}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019005 
(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: 4.0s)Debug log