Average Error: 14.6 → 0.9
Time: 30.4s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -1.3871007602341853 \cdot 10^{+93}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;x \cdot y \le -6.092156471385546 \cdot 10^{-178}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;x \cdot y \le 1.494212723698947 \cdot 10^{-235}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{if}\;x \cdot y \le 3.6083177909184615 \cdot 10^{+278}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \end{array}\]

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) < -1.3871007602341853e+93 or -6.092156471385546e-178 < (* x y) < 1.494212723698947e-235 or 3.6083177909184615e+278 < (* x y)

    1. Initial program 8.1

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

    2. Applied simplify1.9

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

    if -1.3871007602341853e+93 < (* x y) < -6.092156471385546e-178 or 1.494212723698947e-235 < (* x y) < 3.6083177909184615e+278

    1. Initial program 19.3

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

    2. Applied simplify9.1

      \[\leadsto \color{blue}{x \cdot \frac{y}{z}}\]
    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: 30.4s)Debug logProfile

herbie shell --seed '#(1072107073 2127697367 3936270018 2300570620 2134894798 4023771849)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))