Average Error: 13.7 → 5.8
Time: 5.2s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le 2.441393482817533 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

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 2 regimes

  2. if y < 2.441393482817533e-302

    1. Initial program 13.9

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

    2. Initial simplification6.0

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

    3. Taylor expanded around inf 6.4

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

    5. Applied associate-/l*5.6

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

    if 2.441393482817533e-302 < y

    1. Initial program 13.5

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

    2. Initial simplification6.2

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

    3. Taylor expanded around inf 6.0

      \[\leadsto \color{blue}{\frac{x \cdot y}{z}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification5.8

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 2.441393482817533 \cdot 10^{-302}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Runtime

Time bar (total: 5.2s)Debug logProfile

herbie shell --seed 2018251 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))