Average Error: 14.9 → 0.4
Time: 28.1s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \cdot x \le -5.856186853950634 \cdot 10^{+206}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;y \cdot x \le -8.229232975891601 \cdot 10^{-171}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;y \cdot x \le 4.829633011818158 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;y \cdot x \le 2.2050564879853263 \cdot 10^{+235}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

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) < -5.856186853950634e+206 or -8.229232975891601e-171 < (* x y) < 4.829633011818158e-230

    1. Initial program 5.7

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

    2. Applied simplify0.7

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

    if -5.856186853950634e+206 < (* x y) < -8.229232975891601e-171 or 4.829633011818158e-230 < (* x y) < 2.2050564879853263e+235

    1. Initial program 20.1

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

    2. Applied simplify9.9

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

    4. Applied associate-*r/0.2

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

    if 2.2050564879853263e+235 < (* x y)

    1. Initial program 11.5

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

    2. Applied simplify0.8

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

    4. Applied div-inv0.9

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

    5. Applied associate-*r*34.2

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

    7. Applied pow134.2

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

    8. Applied pow134.2

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

    9. Applied pow-prod-down34.2

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

    10. Applied simplify0.7

      \[\leadsto {\color{blue}{\left(\frac{y}{\frac{z}{x}}\right)}}^{1}\]
  3. Recombined 3 regimes into one program.

  4. Applied simplify0.4

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;y \cdot x \le -5.856186853950634 \cdot 10^{+206}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;y \cdot x \le -8.229232975891601 \cdot 10^{-171}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;y \cdot x \le 4.829633011818158 \cdot 10^{-230}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;y \cdot x \le 2.2050564879853263 \cdot 10^{+235}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}}\]

Runtime

Time bar (total: 28.1s)Debug logProfile

herbie shell --seed '#(1072967564 1937075727 894099792 790700740 1036514779 1027793188)' +o rules:numerics
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))