Average Error: 14.2 → 6.0
Time: 6.0s
Precision: 64
Internal Precision: 128
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le 4.1421369372308255 \cdot 10^{+170}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\frac{z}{y}}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if y < 4.1421369372308255e+170

    1. Initial program 13.6

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

    2. Initial simplification5.5

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

    3. Taylor expanded around -inf 5.4

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

    5. Applied associate-/l*5.3

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

    6. Taylor expanded around 0 5.4

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

    if 4.1421369372308255e+170 < y

    1. Initial program 21.3

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

    2. Initial simplification11.6

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

    3. Taylor expanded around -inf 12.9

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

    5. Applied associate-/l*12.1

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

    7. Applied div-inv12.6

      \[\leadsto \color{blue}{x \cdot \frac{1}{\frac{z}{y}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification6.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le 4.1421369372308255 \cdot 10^{+170}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{1}{\frac{z}{y}}\\ \end{array}\]

Runtime

Time bar (total: 6.0s)Debug logProfile

herbie shell --seed 2018277 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))