\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
Test:
Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2
Bits:
128 bits
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
Bits error versus a
Bits error versus b
Time: 1.2 m
Input Error: 30.8
Output Error: 11.0
Log:
Profile: 🕒
\(\begin{cases} \frac{e^{(\left(-\log a\right) * \left(\frac{1}{t} - 1.0\right) + \left(\frac{-1}{y} \cdot \log z\right))_*}}{\frac{y}{x} \cdot e^{\frac{1}{b}}} & \text{when } b \le -68729.91375150369 \\ \frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{{a}^{\left(t - 1.0\right)}}} & \text{when } b \le 1.9367427446630768 \cdot 10^{-84} \\ \frac{\frac{x}{e^{b}}}{y \cdot a - \left(y \cdot a\right) \cdot (\left(\log z\right) * y + \left(t \cdot \log a\right))_*} & \text{otherwise} \end{cases}\)

    if b < -68729.91375150369

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      52.3
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      62.9
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}\]
      9.5
    4. Taylor expanded around inf to get
      \[\color{red}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}} \leadsto \color{blue}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}}\]
      9.5
    5. Applied simplify to get
      \[\color{red}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}} \leadsto \color{blue}{\frac{e^{(\left(-\log a\right) * \left(\frac{1}{t} - 1.0\right) + \left(\frac{-1}{y} \cdot \log z\right))_*}}{\frac{y}{x} \cdot e^{\frac{1}{b}}}}\]
      8.5

    if -68729.91375150369 < b < 1.9367427446630768e-84

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      31.8
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      21.0
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{{a}^{\left(t - 1.0\right)}}}\]
      11.9
    4. Taylor expanded around 0 to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}}{{a}^{\left(t - 1.0\right)}}}\]
      11.9

    if 1.9367427446630768e-84 < b

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      18.5
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      33.2
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}\]
      12.6
    4. Taylor expanded around 0 to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}}\]
      12.6
    5. Applied simplify to get
      \[\color{red}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left(y \cdot a\right) \cdot (\left(\log z\right) * y + \left(t \cdot \log a\right))_*}}\]
      11.2

  1. Removed slow pow expressions

Original test:


(lambda ((x default) (y default) (z default) (t default) (a default) (b default))
  #:name "Numeric.SpecFunctions:incompleteBetaWorker from math-functions-0.1.5.2"
  (/ (* x (exp (- (+ (* y (log z)) (* (- t 1.0) (log a))) b))) y))