Average Error: 14.2 → 0.7
Time: 14.2s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{x} \le -7.92684161151757 \cdot 10^{+299}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{if}\;\frac{z}{x} \le -1.3844937451963608 \cdot 10^{-237}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{if}\;\frac{z}{x} \le 1.5139712940123256 \cdot 10^{-195}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{z}{x} \le 1.3189206670934682 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

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 (/ z x) < -7.92684161151757e+299 or 1.3189206670934682e+102 < (/ z x)

    1. Initial program 6.7

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

    2. Applied simplify1.6

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

    if -7.92684161151757e+299 < (/ z x) < -1.3844937451963608e-237 or 1.5139712940123256e-195 < (/ z x) < 1.3189206670934682e+102

    1. Initial program 18.3

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

    2. Applied simplify8.9

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

    4. Applied div-inv9.0

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

    5. Applied associate-*r*9.6

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
    6. Using strategy rm

    7. Applied pow19.6

      \[\leadsto \left(x \cdot y\right) \cdot \color{blue}{{\left(\frac{1}{z}\right)}^{1}}\]

    8. Applied pow19.6

      \[\leadsto \color{blue}{{\left(x \cdot y\right)}^{1}} \cdot {\left(\frac{1}{z}\right)}^{1}\]

    9. Applied pow-prod-down9.6

      \[\leadsto \color{blue}{{\left(\left(x \cdot y\right) \cdot \frac{1}{z}\right)}^{1}}\]

    10. Applied simplify0.2

      \[\leadsto {\color{blue}{\left(\frac{y}{\frac{z}{x}}\right)}}^{1}\]

    if -1.3844937451963608e-237 < (/ z x) < 1.5139712940123256e-195

    1. Initial program 10.8

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

    2. Applied simplify0.7

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

    4. Applied associate-*r/0.7

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

    6. Applied associate-/l*0.7

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

  4. Applied simplify0.7

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{z}{x} \le -7.92684161151757 \cdot 10^{+299}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{if}\;\frac{z}{x} \le -1.3844937451963608 \cdot 10^{-237}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{if}\;\frac{z}{x} \le 1.5139712940123256 \cdot 10^{-195}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{z}{x} \le 1.3189206670934682 \cdot 10^{+102}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}}\]

Runtime

Time bar (total: 14.2s)Debug logProfile

herbie shell --seed 2018201 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))