Average Error: 14.1 → 0.5
Time: 12.8s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{y} \le -2.1205953472489645 \cdot 10^{+260}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \mathbf{if}\;\frac{z}{y} \le -2.928409658617734 \cdot 10^{-171}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{z}{y} \le 2.0107945178521047 \cdot 10^{-195}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;\frac{z}{y} \le 1.7884319738416773 \cdot 10^{+213}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 3 regimes

  2. if (/ z y) < -2.1205953472489645e+260 or 1.7884319738416773e+213 < (/ z y)

    1. Initial program 17.7

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

    2. Applied simplify13.2

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

    4. Applied div-inv13.3

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

    5. Applied associate-/r*0.2

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

    if -2.1205953472489645e+260 < (/ z y) < -2.928409658617734e-171 or 2.0107945178521047e-195 < (/ z y) < 1.7884319738416773e+213

    1. Initial program 7.9

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

    2. Applied simplify0.2

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

    if -2.928409658617734e-171 < (/ z y) < 2.0107945178521047e-195

    1. Initial program 36.9

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

    2. Applied simplify20.7

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

    3. Taylor expanded around 0 2.0

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

Runtime

Time bar (total: 12.8s)Debug logProfile

herbie shell --seed '#(1070100504 930361288 1279167582 284574201 1450237281 2578255382)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))