Error

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Derivation

1. Split input into 3 regimes

2. if (/ y z) < -inf.0

   1. Initial program 60.0

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

   2. Simplified0.3

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

   if -inf.0 < (/ y z) < -4.868209975303927e-240 or 3.3270316362416e-317 < (/ y z) < 5.18146444823841e+203

   1. Initial program 9.6

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

   2. Simplified8.2

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

   3. Taylor expanded around -inf 8.9

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

   5. Applied associate-/l*0.4

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

   if -4.868209975303927e-240 < (/ y z) < 3.3270316362416e-317 or 5.18146444823841e+203 < (/ y z)

   1. Initial program 24.0

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

   2. Simplified0.3

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

   3. Taylor expanded around -inf 0.4

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

4. Final simplification0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} = -\infty:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -4.868209975303927 \cdot 10^{-240}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 3.3270316362416 \cdot 10^{-317}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 5.18146444823841 \cdot 10^{+203}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019022 +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)))

Details

Time bar (total: 8.0s)Debug log