Average Error: 14.7 → 0.9
Time: 30.4s
Precision: 64
Internal Precision: 384
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y = -\infty:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{if}\;x \cdot y \le -4.5164478497014764 \cdot 10^{-274}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;x \cdot y \le 6.6426518701512256 \cdot 10^{-248}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;x \cdot y \le 5.3560873381746105 \cdot 10^{+101}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Derivation

  1. Split input into 3 regimes

  2. if (* x y) < -inf.0

    1. Initial program 10.5

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

    if -inf.0 < (* x y) < -4.5164478497014764e-274 or 6.6426518701512256e-248 < (* x y) < 5.3560873381746105e+101

    1. Initial program 18.0

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

    2. Applied simplify8.5

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

    4. Applied associate-*r/0.2

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

    if -4.5164478497014764e-274 < (* x y) < 6.6426518701512256e-248 or 5.3560873381746105e+101 < (* x y)

    1. Initial program 8.0

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

    2. Applied simplify1.6

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

Runtime

Time bar (total: 30.4s)Debug logProfile

herbie shell --seed '#(1070864556 424010669 783715395 1203517814 4070606583 4107618214)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))