Average Error: 14.2 → 0.5
Time: 13.0s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -3.1756060618788115 \cdot 10^{+250}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{y}{z} \le -3.045170598787025 \cdot 10^{-208}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{y}{z} \le 8.4649107013579 \cdot 10^{-318}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{y}{z} \le 4.702733343193421 \cdot 10^{+136}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

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 (/ y z) < -3.1756060618788115e+250

    1. Initial program 47.5

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

    2. Applied simplify37.3

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

    4. Applied associate-*r/0.4

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

    6. Applied associate-/l*35.2

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

    8. Applied associate-/r/0.3

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

    if -3.1756060618788115e+250 < (/ y z) < -3.045170598787025e-208

    1. Initial program 9.1

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

    2. Applied simplify0.2

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

    4. Applied associate-*r/8.4

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

    6. Applied associate-/l*0.2

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

    if -3.045170598787025e-208 < (/ y z) < 8.4649107013579e-318 or 4.702733343193421e+136 < (/ y z)

    1. Initial program 21.1

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

    2. Applied simplify13.5

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

    4. Applied associate-*r/1.1

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

    if 8.4649107013579e-318 < (/ y z) < 4.702733343193421e+136

    1. Initial program 8.8

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

    2. Applied simplify0.3

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

Runtime

Time bar (total: 13.0s)Debug logProfile

herbie shell --seed 2018207 +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)))