Error

Try it out

Derivation

1. Split input into 2 regimes

2. if (/ (* (/ y z) t) t) < -5.579595939232642e-117 or 5.465027716549306e-309 < (/ (* (/ y z) t) t) < 1.3033798898661042e+287

   1. Initial program 6.2

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

   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*2.6

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

   if -5.579595939232642e-117 < (/ (* (/ y z) t) t) < 5.465027716549306e-309 or 1.3033798898661042e+287 < (/ (* (/ y z) t) t)

   1. Initial program 26.8

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

   2. Simplified2.0

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}}\]
3. Recombined 2 regimes into one program.

4. Final simplification2.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -5.579595939232642 \cdot 10^{-117}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 5.465027716549306 \cdot 10^{-309}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.3033798898661042 \cdot 10^{+287}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Reproduce

herbie shell --seed 2019008 +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: 4.3s)Debug log