Average Error: 14.1 → 0.5
Time: 15.9s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{z}{y} \le -7.477196651461092 \cdot 10^{+299}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{z}{y} \le -3.216441226474962 \cdot 10^{-233}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{if}\;\frac{z}{y} \le 1.6231268326186054 \cdot 10^{-152}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{if}\;\frac{z}{y} \le 2.9774054308490443 \cdot 10^{+181}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

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 (/ z y) < -7.477196651461092e+299 or -3.216441226474962e-233 < (/ z y) < 1.6231268326186054e-152 or 2.9774054308490443e+181 < (/ z y)

    1. Initial program 24.6

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

    2. Applied simplify15.9

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

    4. Applied associate-*r/0.9

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

    if -7.477196651461092e+299 < (/ z y) < -3.216441226474962e-233 or 1.6231268326186054e-152 < (/ z y) < 2.9774054308490443e+181

    1. Initial program 8.2

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

    2. Applied simplify0.2

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

    4. Applied associate-*r/8.9

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

    6. Applied associate-/l*0.2

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

Runtime

Time bar (total: 15.9s)Debug logProfile

herbie shell --seed 2018166 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))