Average Error: 14.4 → 1.1
Time: 10.7s
Precision: 64
Internal Precision: 128
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -2.789292387265011 \cdot 10^{+300}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -2.9839163918592177 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 6.702964246723088 \cdot 10^{-207}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 4.1600426763294235 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

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) t) t) < -2.789292387265011e+300

    1. Initial program 59.4

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

    2. Initial simplification3.0

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

    if -2.789292387265011e+300 < (/ (* (/ y z) t) t) < -2.9839163918592177e-189 or 6.702964246723088e-207 < (/ (* (/ y z) t) t) < 4.1600426763294235e+186

    1. Initial program 0.6

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

    if -2.9839163918592177e-189 < (/ (* (/ y z) t) t) < 6.702964246723088e-207 or 4.1600426763294235e+186 < (/ (* (/ y z) t) t)

    1. Initial program 25.1

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

    2. Initial simplification1.5

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

    3. Taylor expanded around inf 1.7

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

    5. Applied div-inv1.8

      \[\leadsto \color{blue}{\left(x \cdot y\right) \cdot \frac{1}{z}}\]
    6. Using strategy rm

    7. Applied pow11.8

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

    8. Applied pow11.8

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

    9. Applied pow-prod-down1.8

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

    10. Simplified1.4

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\frac{y}{z} \cdot t}{t} \le -2.789292387265011 \cdot 10^{+300}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le -2.9839163918592177 \cdot 10^{-189}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 6.702964246723088 \cdot 10^{-207}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{elif}\;\frac{\frac{y}{z} \cdot t}{t} \le 4.1600426763294235 \cdot 10^{+186}:\\ \;\;\;\;x \cdot \frac{\frac{y}{z} \cdot t}{t}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \end{array}\]

Runtime

Time bar (total: 10.7s)Debug logProfile

herbie shell --seed 2018296 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))