\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.3 m
Input Error: 26.5
Output Error: 1.6
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{t} \cdot {a}^{\left(-1.0\right)}}{e^{b}}}{y} & \text{when } x \le -1.5508057375082158 \cdot 10^{+38} \\ e^{\left(\log \left(\frac{x}{y}\right) + \log z \cdot y\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)} & \text{when } x \le -3.9027600347390286 \cdot 10^{-29} \\ \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{t} \cdot {a}^{\left(-1.0\right)}}{e^{b}}}{y} & \text{when } x \le 2.494535994100433 \cdot 10^{-272} \\ \frac{e^{\log \left(x \cdot {z}^{y}\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)}}{y} & \text{otherwise} \end{cases}\)

    if x < -1.5508057375082158e+38

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      31.2
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      15.7
    3. Using strategy rm
      15.7
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      15.7
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      0.6
    6. Using strategy rm
      0.6
    7. Applied sub-neg to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{red}{\left(t - 1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y}\]
      0.6
    8. Applied unpow-prod-up to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}{e^{b}}}{y}\]
      0.6

    if -1.5508057375082158e+38 < x < -3.9027600347390286e-29

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      0.6
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      16.1
    3. Using strategy rm
      16.1
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      16.6
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      11.0
    6. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot \color{red}{{z}^{y}}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\frac{x}{y} \cdot \color{blue}{e^{\log z \cdot y}}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      11.0
    7. Applied add-exp-log to get
      \[\left(\color{red}{\frac{x}{y}} \cdot e^{\log z \cdot y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\color{blue}{e^{\log \left(\frac{x}{y}\right)}} \cdot e^{\log z \cdot y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      11.1
    8. Applied prod-exp to get
      \[\color{red}{\left(e^{\log \left(\frac{x}{y}\right)} \cdot e^{\log z \cdot y}\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{e^{\log \left(\frac{x}{y}\right) + \log z \cdot y}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      11.1
    9. Applied prod-exp to get
      \[\color{red}{e^{\log \left(\frac{x}{y}\right) + \log z \cdot y} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}} \leadsto \color{blue}{e^{\left(\log \left(\frac{x}{y}\right) + \log z \cdot y\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)}}\]
      1.1

    if -3.9027600347390286e-29 < x < 2.494535994100433e-272

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      28.4
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      0.9
    3. Using strategy rm
      0.9
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      0.9
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      2.8
    6. Using strategy rm
      2.8
    7. Applied sub-neg to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{red}{\left(t - 1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y}\]
      2.8
    8. Applied unpow-prod-up to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}{e^{b}}}{y}\]
      2.7

    if 2.494535994100433e-272 < x

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      24.5
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      23.4
    3. Using strategy rm
      23.4
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      23.5
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      19.7
    6. Using strategy rm
      19.7
    7. Applied pow-to-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}}{y}\]
      20.2
    8. Applied div-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}}{y}\]
      15.7
    9. Applied add-exp-log to get
      \[\frac{\color{red}{\left(x \cdot {z}^{y}\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}}{y} \leadsto \frac{\color{blue}{e^{\log \left(x \cdot {z}^{y}\right)}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}}{y}\]
      15.7
    10. Applied prod-exp to get
      \[\frac{\color{red}{e^{\log \left(x \cdot {z}^{y}\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}}}{y} \leadsto \frac{\color{blue}{e^{\log \left(x \cdot {z}^{y}\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)}}}{y}\]
      1.4
  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))