Average Error: 14.2 → 0.8
Time: 11.3s
Precision: 64
Internal Precision: 576
\[x \cdot \frac{\frac{y}{z} \cdot t}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{y}{\frac{z}{x}} = -\infty:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{if}\;\frac{y}{\frac{z}{x}} \le -6.9515036369863 \cdot 10^{-320}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{if}\;\frac{y}{\frac{z}{x}} \le 2.1660847804611 \cdot 10^{-313}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{if}\;\frac{y}{\frac{z}{x}} \le 2.3774293887972803 \cdot 10^{+250}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}\]

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 (pow (/ y (/ z x)) 1) < -inf.0 or -6.9515036369863e-320 < (pow (/ y (/ z x)) 1) < 2.1660847804611e-313 or 2.3774293887972803e+250 < (pow (/ y (/ z x)) 1)

    1. Initial program 4.2

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

    2. Applied simplify1.4

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

    if -inf.0 < (pow (/ y (/ z x)) 1) < -6.9515036369863e-320 or 2.1660847804611e-313 < (pow (/ y (/ z x)) 1) < 2.3774293887972803e+250

    1. Initial program 18.5

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

    2. Applied simplify8.0

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

    4. Applied div-inv8.1

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

    5. Applied associate-*r*7.5

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

    7. Applied pow17.5

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

    8. Applied pow17.5

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

    9. Applied pow-prod-down7.5

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

    10. Applied simplify0.5

      \[\leadsto {\color{blue}{\left(\frac{y}{\frac{z}{x}}\right)}}^{1}\]
  3. Recombined 2 regimes into one program.

  4. Applied simplify0.8

    \[\leadsto \color{blue}{\begin{array}{l} \mathbf{if}\;\frac{y}{\frac{z}{x}} = -\infty:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{if}\;\frac{y}{\frac{z}{x}} \le -6.9515036369863 \cdot 10^{-320}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{if}\;\frac{y}{\frac{z}{x}} \le 2.1660847804611 \cdot 10^{-313}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \mathbf{if}\;\frac{y}{\frac{z}{x}} \le 2.3774293887972803 \cdot 10^{+250}:\\ \;\;\;\;\frac{y}{\frac{z}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{z} \cdot x\\ \end{array}}\]

Runtime

Time bar (total: 11.3s)Debug logProfile

herbie shell --seed '#(1072743783 989954326 4239155542 3782239461 3602631542 1719177920)' 
(FPCore (x y z t)
  :name "Graphics.Rendering.Chart.Backend.Diagrams:calcFontMetrics from Chart-diagrams-1.5.1"
  (* x (/ (* (/ y z) t) t)))