Average Error: 14.2 → 0.4
Time: 15.3s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -2.7401436256982823 \cdot 10^{+297}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -6.69633171503425 \cdot 10^{-310}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le 1.0036123500251921 \cdot 10^{-205}:\\ \;\;\;\;\frac{\frac{x}{z}}{\frac{1}{y}}\\ \mathbf{elif}\;\frac{y}{z} \le 9.096685674606636 \cdot 10^{+174}:\\ \;\;\;\;x \cdot \frac{y}{z}\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \end{array}\]

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if (/ y z) < -2.7401436256982823e+297 or 9.096685674606636e+174 < (/ y z)

    1. Initial program 42.2

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

    2. Applied simplify30.0

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

    4. Applied associate-*r/1.0

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

    if -2.7401436256982823e+297 < (/ y z) < -6.69633171503425e-310 or 1.0036123500251921e-205 < (/ y z) < 9.096685674606636e+174

    1. Initial program 8.7

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

    2. Applied simplify0.2

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

    if -6.69633171503425e-310 < (/ y z) < 1.0036123500251921e-205

    1. Initial program 18.6

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

    2. Applied simplify13.6

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

    4. Applied associate-*r/0.4

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

    6. Applied associate-/l*14.9

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

    8. Applied div-inv14.9

      \[\leadsto \frac{x}{\color{blue}{z \cdot \frac{1}{y}}}\]

    9. Applied associate-/r*0.5

      \[\leadsto \color{blue}{\frac{\frac{x}{z}}{\frac{1}{y}}}\]
  3. Recombined 3 regimes into one program.

Runtime

Time bar (total: 15.3s)Debug logProfile

herbie shell --seed 2018208 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))