Average Error: 14.2 → 0.5
Time: 34.3s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.941194442644197 \cdot 10^{+228}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{y}{z} \le -2.787715053151118 \cdot 10^{-207}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 9.71584187108663 \cdot 10^{-231}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 1.4828883956537087 \cdot 10^{+129}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

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 (/ y z) < -1.941194442644197e+228 or -2.787715053151118e-207 < (/ y z) < 9.71584187108663e-231 or 1.4828883956537087e+129 < (/ y z)

    1. Initial program 24.2

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

    2. Applied simplify14.7

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

    4. Applied associate-*r/0.9

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

    if -1.941194442644197e+228 < (/ y z) < -2.787715053151118e-207 or 9.71584187108663e-231 < (/ y z) < 1.4828883956537087e+129

    1. Initial program 7.3

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

    2. Applied simplify0.2

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

Runtime

Time bar (total: 34.3s)Debug logProfile

herbie shell --seed '#(1071948828 1180510430 2986424009 997076509 406109801 420189285)' +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)))