Average Error: 14.6 → 1.1
Time: 33.5s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le -2.701705248459643 \cdot 10^{+97}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;x \cdot y \le -1.2460807539482867 \cdot 10^{-130}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;x \cdot y \le 3.084811635157326 \cdot 10^{-167}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{if}\;x \cdot y \le 1.6843692024798482 \cdot 10^{+225}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < -2.701705248459643e+97 or -1.2460807539482867e-130 < (* x y) < 3.084811635157326e-167 or 1.6843692024798482e+225 < (* x y)

    1. Initial program 8.9

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

    2. Applied simplify1.8

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

    if -2.701705248459643e+97 < (* x y) < -1.2460807539482867e-130 or 3.084811635157326e-167 < (* x y) < 1.6843692024798482e+225

    1. Initial program 20.6

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

    2. Applied simplify9.8

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

    4. Applied associate-*l/0.3

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

Runtime

Time bar (total: 33.5s)Debug logProfile

herbie shell --seed 2020178 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))