Average Error: 13.5 → 2.0
Time: 26.7s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{x} \le -4.714199337924424 \cdot 10^{+144}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{z}{x} \le -4.682626397675208 \cdot 10^{-203}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{if}\;\frac{z}{x} \le 2.8946106682842226 \cdot 10^{-245}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

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 x) < -4.714199337924424e+144

    1. Initial program 6.2

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

    2. Applied simplify1.3

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

    if -4.714199337924424e+144 < (/ z x) < -4.682626397675208e-203 or 2.8946106682842226e-245 < (/ z x)

    1. Initial program 16.0

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

    2. Applied simplify7.9

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

    4. Applied add-cube-cbrt8.7

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \frac{y}{z}} \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right) \cdot \sqrt[3]{x \cdot \frac{y}{z}}}\]

    5. Taylor expanded around 0 54.7

      \[\leadsto \left(\color{blue}{e^{\frac{1}{3} \cdot \left(\left(\log y + \log x\right) - \log z\right)}} \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right) \cdot \sqrt[3]{x \cdot \frac{y}{z}}\]

    6. Applied simplify3.3

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{y}{\frac{z}{x}}} \cdot \sqrt[3]{\frac{y}{\frac{z}{x}}}\right) \cdot \sqrt[3]{\frac{y}{\frac{z}{x}}}}\]

    7. Taylor expanded around 0 10.3

      \[\leadsto \left(\sqrt[3]{\frac{y}{\frac{z}{x}}} \cdot \sqrt[3]{\frac{y}{\frac{z}{x}}}\right) \cdot \sqrt[3]{\color{blue}{\frac{y \cdot x}{z}}}\]

    8. Applied simplify2.3

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

    if -4.682626397675208e-203 < (/ z x) < 2.8946106682842226e-245

    1. Initial program 9.2

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

    2. Applied simplify1.0

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

    4. Applied associate-*r/0.8

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

Runtime

Time bar (total: 26.7s)Debug logProfile

herbie shell --seed '#(1070609872 3456127585 2380521889 2328837196 1765472538 734540918)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))