Average Error: 13.5 → 1.0
Time: 20.6s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.0926880277021874 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.6067320136688305 \cdot 10^{-271}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.74446805017109 \cdot 10^{-121}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;\frac{y}{z} \le 4.658998730731117 \cdot 10^{+186}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \end{array}\]

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) < -1.0926880277021874e+110

    1. Initial program 26.7

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

    2. Initial simplification11.6

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

    4. Applied associate-*r/3.2

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

    if -1.0926880277021874e+110 < (/ y z) < -1.6067320136688305e-271 or 6.74446805017109e-121 < (/ y z) < 4.658998730731117e+186

    1. Initial program 6.9

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

    2. Initial simplification0.2

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

    if -1.6067320136688305e-271 < (/ y z) < 6.74446805017109e-121 or 4.658998730731117e+186 < (/ y z)

    1. Initial program 19.6

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

    2. Initial simplification11.9

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

    4. Applied div-inv11.9

      \[\leadsto x \cdot \color{blue}{\left(y \cdot \frac{1}{z}\right)}\]

    5. Applied associate-*r*1.5

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y}{z} \le -1.0926880277021874 \cdot 10^{+110}:\\ \;\;\;\;\frac{x \cdot y}{z}\\ \mathbf{elif}\;\frac{y}{z} \le -1.6067320136688305 \cdot 10^{-271}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{elif}\;\frac{y}{z} \le 6.74446805017109 \cdot 10^{-121}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \mathbf{elif}\;\frac{y}{z} \le 4.658998730731117 \cdot 10^{+186}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{z} \cdot \left(x \cdot y\right)\\ \end{array}\]

Runtime

Time bar (total: 20.6s)Debug logProfile

herbie shell --seed 2018215 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))