Average Error: 14.2 → 0.6
Time: 28.4s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.2477768625223483 \cdot 10^{+176}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;x \cdot y \le -1.945227379865997 \cdot 10^{-147}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;x \cdot y \le 1.6143174686129928 \cdot 10^{-289}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;x \cdot y \le 2.534778512359649 \cdot 10^{+262}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -1.2477768625223483e+176 or -1.945227379865997e-147 < (* x y) < 1.6143174686129928e-289 or 2.534778512359649e+262 < (* x y)

    1. Initial program 7.2

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

    2. Applied simplify1.1

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

    if -1.2477768625223483e+176 < (* x y) < -1.945227379865997e-147 or 1.6143174686129928e-289 < (* x y) < 2.534778512359649e+262

    1. Initial program 18.3

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

    2. Applied simplify8.4

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

    4. Applied associate-*r/0.2

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

Runtime

Time bar (total: 28.4s)Debug logProfile

herbie shell --seed '#(1072361757 3390613284 2339397988 1175251238 145061547 3101881848)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))