Average Error: 14.2 → 0.4
Time: 7.9s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.437933165414712 \cdot 10^{+196}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -7.776064360420082 \cdot 10^{-255}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 7.82051862631026 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 9.73277545786147 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

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 (/ y z) < -5.437933165414712e+196 or 9.73277545786147e+210 < (/ y z)

    1. Initial program 40.0

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

    2. Initial simplification0.9

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

    4. Applied associate-*r/0.9

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

    6. Applied associate-/l*0.9

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

    if -5.437933165414712e+196 < (/ y z) < -7.776064360420082e-255 or 7.82051862631026e-310 < (/ y z) < 9.73277545786147e+210

    1. Initial program 8.6

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

    2. Initial simplification8.9

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

    4. Applied associate-*r/8.3

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

    6. Applied associate-/l*8.9

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

    8. Applied div-inv9.0

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

    9. Applied associate-/r*0.3

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

    if -7.776064360420082e-255 < (/ y z) < 7.82051862631026e-310

    1. Initial program 19.2

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

    2. Initial simplification0.1

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

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -5.437933165414712 \cdot 10^{+196}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le -7.776064360420082 \cdot 10^{-255}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{elif}\;\frac{y}{z} \le 7.82051862631026 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{y}{z} \le 9.73277545786147 \cdot 10^{+210}:\\ \;\;\;\;\frac{\frac{y}{z}}{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Runtime

Time bar (total: 7.9s)Debug logProfile

herbie shell --seed 2018217 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))