Average Error: 14.1 → 0.7
Time: 22.5s
Precision: 64
Internal Precision: 320
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{x} \le -9.565220761744693 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{z}{x} \le -3.551816045633847 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{z}{x} \le 1.4103190471996078 \cdot 10^{-300}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{if}\;\frac{z}{x} \le 3.9866603406054462 \cdot 10^{+236}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 4 regimes

  2. if (/ z x) < -9.565220761744693e+244 or 3.9866603406054462e+236 < (/ z x)

    1. Initial program 3.6

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

    2. Applied simplify13.2

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

    4. Applied associate-*r/0.3

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

    6. Applied clear-num1.0

      \[\leadsto \color{blue}{\frac{1}{\frac{z}{y \cdot x}}}\]
    7. Using strategy rm

    8. Applied div-inv1.0

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

    9. Applied simplify0.4

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

    if -9.565220761744693e+244 < (/ z x) < -3.551816045633847e-115

    1. Initial program 18.3

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

    2. Applied simplify0.2

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

    if -3.551816045633847e-115 < (/ z x) < 1.4103190471996078e-300

    1. Initial program 13.3

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

    2. Applied simplify22.4

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

    4. Applied div-inv22.4

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

    5. Applied associate-*r*3.3

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

    if 1.4103190471996078e-300 < (/ z x) < 3.9866603406054462e+236

    1. Initial program 17.5

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

    2. Applied simplify0.2

      \[\leadsto \color{blue}{y \cdot \frac{x}{z}}\]
  3. Recombined 4 regimes into one program.

  4. Applied simplify0.7

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{z}{x} \le -9.565220761744693 \cdot 10^{+244}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;\frac{z}{x} \le -3.551816045633847 \cdot 10^{-115}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{z}{x} \le 1.4103190471996078 \cdot 10^{-300}:\\ \;\;\;\;\left(y \cdot x\right) \cdot \frac{1}{z}\\ \mathbf{if}\;\frac{z}{x} \le 3.9866603406054462 \cdot 10^{+236}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}}\]

Runtime

Time bar (total: 22.5s)Debug logProfile

herbie shell --seed 2019053 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))