Average Error: 14.5 → 0.3
Time: 36.7s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -4.0489496635322154 \cdot 10^{+300}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;x \cdot y \le -3.671985826538214 \cdot 10^{-194}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;x \cdot y \le 4.150998984392305 \cdot 10^{-192}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{if}\;x \cdot y \le 1.1751250528686869 \cdot 10^{+229}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -4.0489496635322154e+300

    1. Initial program 8.4

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

    2. Applied simplify0.2

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

    if -4.0489496635322154e+300 < (* x y) < -3.671985826538214e-194 or 4.150998984392305e-192 < (* x y) < 1.1751250528686869e+229

    1. Initial program 19.4

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

    2. Applied simplify9.2

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

    4. Applied associate-*r/0.2

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

    if -3.671985826538214e-194 < (* x y) < 4.150998984392305e-192 or 1.1751250528686869e+229 < (* x y)

    1. Initial program 5.9

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

    2. Applied simplify0.8

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

    4. Applied add-cube-cbrt1.4

      \[\leadsto \color{blue}{\left(\sqrt[3]{x \cdot \frac{y}{z}} \cdot \sqrt[3]{x \cdot \frac{y}{z}}\right) \cdot \sqrt[3]{x \cdot \frac{y}{z}}}\]
    5. Using strategy rm

    6. Applied add-cbrt-cube1.4

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

    7. Applied simplify1.5

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

    8. Taylor expanded around 0 14.8

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

    9. Applied simplify0.5

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

Runtime

Time bar (total: 36.7s)Debug logProfile

herbie shell --seed 2018195 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))