Average Error: 14.0 → 0.3
Time: 33.4s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -3.7291468781120964 \cdot 10^{+232}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;x \cdot y \le -5.1726617773183605 \cdot 10^{-210}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;x \cdot y \le 1.963090658075571 \cdot 10^{-291}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;x \cdot y \le 1.228038068354251 \cdot 10^{+204}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -3.7291468781120964e+232 or -5.1726617773183605e-210 < (* x y) < 1.963090658075571e-291 or 1.228038068354251e+204 < (* x y)

    1. Initial program 5.8

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

    2. Applied simplify0.5

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

    if -3.7291468781120964e+232 < (* x y) < -5.1726617773183605e-210 or 1.963090658075571e-291 < (* x y) < 1.228038068354251e+204

    1. Initial program 18.0

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

    2. Applied simplify8.4

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

    4. Applied associate-*r/0.2

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

Runtime

Time bar (total: 33.4s)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' +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)))