Average Error: 14.1 → 1.3
Time: 34.3s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -6.838347038772846 \cdot 10^{+135}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -1.23637162811969 \cdot 10^{-205}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le 1.6284163747782 \cdot 10^{-310}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le 6.380897058347915 \cdot 10^{+144}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 3 regimes

  2. if (/ (* (/ y z) t) t) < -6.838347038772846e+135

    1. Initial program 36.3

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

    2. Applied simplify14.6

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

    3. Taylor expanded around 0 4.2

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

    if -6.838347038772846e+135 < (/ (* (/ y z) t) t) < -1.23637162811969e-205 or 1.6284163747782e-310 < (/ (* (/ y z) t) t) < 6.380897058347915e+144

    1. Initial program 0.5

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

    2. Applied simplify0.3

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

    if -1.23637162811969e-205 < (/ (* (/ y z) t) t) < 1.6284163747782e-310 or 6.380897058347915e+144 < (/ (* (/ y z) t) t)

    1. Initial program 26.9

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

    2. Applied simplify12.1

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

    4. Applied associate-/r/1.8

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

Runtime

Time bar (total: 34.3s)Debug logProfile

herbie shell --seed '#(1063027428 1192549564 1443466578 604016274 3637110559 1698629644)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))