Average Error: 13.9 → 0.3
Time: 13.1s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{x}{z} \le -1.1017547191528866 \cdot 10^{+293}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{x}{z} \le -3.4579347197799846 \cdot 10^{-183}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{x}{z} \le 5.151132160592008 \cdot 10^{-285}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{x}{z} \le 3.3015713868818398 \cdot 10^{+218}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

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 4 regimes

  2. if (/ x z) < -1.1017547191528866e+293

    1. Initial program 8.1

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

    2. Initial simplification0.2

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

    3. Taylor expanded around 0 0.3

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

    if -1.1017547191528866e+293 < (/ x z) < -3.4579347197799846e-183

    1. Initial program 18.3

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

    2. Initial simplification8.5

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

    4. Applied associate-/r/0.3

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

    if -3.4579347197799846e-183 < (/ x z) < 5.151132160592008e-285 or 3.3015713868818398e+218 < (/ x z)

    1. Initial program 5.0

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

    2. Initial simplification0.6

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

    if 5.151132160592008e-285 < (/ x z) < 3.3015713868818398e+218

    1. Initial program 17.4

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

    2. Initial simplification8.4

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

    3. Taylor expanded around 0 7.8

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

    5. Applied associate-/l*0.2

      \[\leadsto \color{blue}{\frac{y}{\frac{z}{x}}}\]
  3. Recombined 4 regimes into one program.

  4. Final simplification0.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{z} \le -1.1017547191528866 \cdot 10^{+293}:\\ \;\;\;\;\frac{y \cdot x}{z}\\ \mathbf{elif}\;\frac{x}{z} \le -3.4579347197799846 \cdot 10^{-183}:\\ \;\;\;\;\frac{x}{z} \cdot y\\ \mathbf{elif}\;\frac{x}{z} \le 5.151132160592008 \cdot 10^{-285}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \mathbf{elif}\;\frac{x}{z} \le 3.3015713868818398 \cdot 10^{+218}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\frac{z}{y}}\\ \end{array}\]

Runtime

Time bar (total: 13.1s)Debug logProfile

herbie shell --seed 2018214 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))