Average Error: 14.5 → 0.3
Time: 25.4s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -3.3292212885791176 \cdot 10^{+213}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;x \cdot y \le -5.111311550452874 \cdot 10^{-171}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;x \cdot y \le 2.2378145291046333 \cdot 10^{-303}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{if}\;x \cdot y \le 1.2401857462065563 \cdot 10^{+246}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -3.3292212885791176e+213 or 1.2401857462065563e+246 < (* x y)

    1. Initial program 9.3

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

    2. Applied simplify0.6

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

    if -3.3292212885791176e+213 < (* x y) < -5.111311550452874e-171 or 2.2378145291046333e-303 < (* x y) < 1.2401857462065563e+246

    1. Initial program 18.7

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

    2. Applied simplify8.9

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

    4. Applied associate-*r/0.2

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

    if -5.111311550452874e-171 < (* x y) < 2.2378145291046333e-303

    1. Initial program 4.9

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

    2. Applied simplify0.6

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

    4. Applied add-cube-cbrt1.1

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

    5. Taylor expanded around 0 57.9

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

    6. Applied simplify1.1

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

    7. Taylor expanded around 0 13.3

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

    8. Applied simplify0.6

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

Runtime

Time bar (total: 25.4s)Debug logProfile

herbie shell --seed 2018199 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))