Error

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Derivation

1. Split input into 3 regimes

2. if (/ y z) < -9.569205628693954e+253 or 4.83810691466513e+250 < (/ y z)

   1. Initial program 46.0

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

   2. Simplified0.4

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

   if -9.569205628693954e+253 < (/ y z) < -1.5935633578943175e-185 or 1.616385694453041e-132 < (/ y z) < 4.83810691466513e+250

   1. Initial program 8.1

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

   2. Simplified9.0

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

   3. Taylor expanded around inf 10.0

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

   5. Applied associate-/l*0.3

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

   if -1.5935633578943175e-185 < (/ y z) < 1.616385694453041e-132

   1. Initial program 17.1

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

   2. Simplified1.0

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

   4. Applied div-inv1.0

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

   5. Applied associate-*r*1.3

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

4. Final simplification0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -9.569205628693954 \cdot 10^{+253}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.5935633578943175 \cdot 10^{-185}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.616385694453041 \cdot 10^{-132}:\\ \;\;\;\;\left(x \cdot y\right) \cdot \frac{1}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 4.83810691466513 \cdot 10^{+250}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x}{z}\\ \end{array}\]

Reproduce

herbie shell --seed 2019004 +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: 4.4s)Debug log