\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.7 m
Input Error: 17.9
Output Error: 3.1
Log: ⚲
Profile: 🕒
\(\begin{cases} \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} & \text{when } y \le -8.965990230414458 \cdot 10^{-223} \\ \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{t} \cdot {a}^{\left(-1.0\right)}}{e^{b}}}{y} & \text{when } y \le 175704052.64168957 \\ e^{\left(\log \left(\frac{x}{y}\right) + \log z \cdot y\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)} & \text{otherwise} \end{cases}\)

    if y < -8.965990230414458e-223

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      19.7
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      9.7
    3. Using strategy rm
      9.7
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      10.3
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      4.5

    if -8.965990230414458e-223 < y < 175704052.64168957

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      21.0
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      15.9
    3. Using strategy rm
      15.9
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      15.9
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      2.5
    6. Using strategy rm
      2.5
    7. Applied sub-neg to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{red}{\left(t - 1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y}\]
      2.5
    8. Applied unpow-prod-up to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}{e^{b}}}{y}\]
      2.4

    if 175704052.64168957 < y

    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
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      28.9
    3. Using strategy rm
      28.9
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      28.9
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      24.7
    6. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot \color{red}{{z}^{y}}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\frac{x}{y} \cdot \color{blue}{e^{\log z \cdot y}}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      24.7
    7. Applied add-exp-log to get
      \[\left(\color{red}{\frac{x}{y}} \cdot e^{\log z \cdot y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\color{blue}{e^{\log \left(\frac{x}{y}\right)}} \cdot e^{\log z \cdot y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      24.7
    8. Applied prod-exp to get
      \[\color{red}{\left(e^{\log \left(\frac{x}{y}\right)} \cdot e^{\log z \cdot y}\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{e^{\log \left(\frac{x}{y}\right) + \log z \cdot y}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      22.8
    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))