Error

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Derivation

1. Split input into 4 regimes

2. if (/ y z) < -7.927867421581339e+302

   1. Initial program 58.6

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

   2. Simplified0.3

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

   3. Taylor expanded around 0 0.3

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

   5. Applied clear-num0.3

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{x \cdot y}}}\]

   if -7.927867421581339e+302 < (/ y z) < -2.4897062515369744e-252 or 1.8633635984892177e-289 < (/ y z) < 4.612678511635868e+158

   1. Initial program 9.0

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

   2. Simplified8.4

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

   3. Taylor expanded around 0 8.1

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

   5. Applied associate-/l*0.2

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

   if -2.4897062515369744e-252 < (/ y z) < 1.8633635984892177e-289

   1. Initial program 18.4

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

   2. Simplified0.1

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

   4. Applied div-inv0.1

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

   5. Applied associate-*r*0.2

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

   7. Applied associate-*l*0.1

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

   if 4.612678511635868e+158 < (/ y z)

   1. Initial program 34.0

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

   2. Simplified2.3

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

4. Final simplification0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -7.927867421581339 \cdot 10^{+302}:\\ \;\;\;\;\frac{1}{\frac{z}{y \cdot x}}\\ \mathbf{elif}\;\frac{y}{z} \le -2.4897062515369744 \cdot 10^{-252}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 1.8633635984892177 \cdot 10^{-289}:\\ \;\;\;\;y \cdot \left(x \cdot \frac{1}{z}\right)\\ \mathbf{elif}\;\frac{y}{z} \le 4.612678511635868 \cdot 10^{+158}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019002 +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