\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.5 m
Input Error: 24.6
Output Error: 8.8
Log: ⚲
Profile: 🕒
\(\begin{cases} \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) & \text{when } y \le -1.3927490770434836 \cdot 10^{-06} \\ \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y} & \text{when } y \le 2.3337955322339956 \cdot 10^{-206} \\ \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} & \text{when } y \le 4.3146445464559027 \cdot 10^{+101} \\ e^{\left(\log \left(\frac{x}{y}\right) + \log z \cdot y\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)} & \text{when } y \le 4.9636339424991004 \cdot 10^{+209} \\ \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) & \text{otherwise} \end{cases}\)

    if y < -1.3927490770434836e-06 or 4.9636339424991004e+209 < y

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      36.5
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      27.1
    3. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\]
      13.5
    4. Taylor expanded around 0 to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)}\]
      13.5
    5. Applied simplify to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \color{blue}{\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)}\]
      13.5

    if -1.3927490770434836e-06 < y < 2.3337955322339956e-206

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      19.2
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      16.9
    3. Using strategy rm
      16.9
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      16.9
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      2.0

    if 2.3337955322339956e-206 < y < 4.3146445464559027e+101

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      10.5
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      26.0
    3. Using strategy rm
      26.0
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      26.9
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      22.6
    6. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      10.0
    7. Taylor expanded around 0 to get
      \[\color{red}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      10.0

    if 4.3146445464559027e+101 < y < 4.9636339424991004e+209

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      0
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      28.2
    3. Using strategy rm
      28.2
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      28.2
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      23.5
    6. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot \color{red}{{z}^{y}}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\frac{x}{y} \cdot \color{blue}{e^{\log z \cdot y}}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      23.5
    7. Applied add-exp-log to get
      \[\left(\color{red}{\frac{x}{y}} \cdot e^{\log z \cdot y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\color{blue}{e^{\log \left(\frac{x}{y}\right)}} \cdot e^{\log z \cdot y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      23.5
    8. Applied prod-exp to get
      \[\color{red}{\left(e^{\log \left(\frac{x}{y}\right)} \cdot e^{\log z \cdot y}\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{e^{\log \left(\frac{x}{y}\right) + \log z \cdot y}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      20.1
    9. Applied prod-exp to get
      \[\color{red}{e^{\log \left(\frac{x}{y}\right) + \log z \cdot y} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}} \leadsto \color{blue}{e^{\left(\log \left(\frac{x}{y}\right) + \log z \cdot y\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)}}\]
      0
  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))