\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.8 m
Input Error: 16.4
Output Error: 7.7
Log:
Profile: 🕒
\(\begin{cases} {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(\left(\left(1 - b\right) + \log a \cdot \left(-t\right)\right) \cdot \frac{{z}^{y}}{\frac{y}{x}}\right) & \text{when } y \cdot \log z \le -0.0005338382708144056 \\ \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} & \text{when } y \cdot \log z \le 8.372833883618234 \cdot 10^{-292} \\ \frac{x}{e^{b}} \cdot \frac{\frac{{z}^{\left(\frac{-1}{y}\right)}}{y}}{{a}^{\left(\frac{1}{t} - 1.0\right)}} & \text{when } y \cdot \log z \le 4.631397527329793 \cdot 10^{-195} \\ \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} & \text{otherwise} \end{cases}\)

    if (* y (log z)) < -0.0005338382708144056

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      13.2
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      27.9
    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
    6. Applied taylor to get
      \[\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) \leadsto \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(-1 \cdot \left(\log a \cdot t\right) + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)\]
      13.3
    7. Taylor expanded around inf to get
      \[\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(\color{red}{-1 \cdot \left(\log a \cdot t\right)} + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) \leadsto \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(\color{blue}{-1 \cdot \left(\log a \cdot t\right)} + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)\]
      13.3
    8. Applied simplify to get
      \[\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(-1 \cdot \left(\log a \cdot t\right) + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) \leadsto {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(\left(\left(1 - b\right) + \log a \cdot \left(-t\right)\right) \cdot \frac{{z}^{y}}{\frac{y}{x}}\right)\]
      0.3

    9. Applied final simplification

    if -0.0005338382708144056 < (* y (log z)) < 8.372833883618234e-292 or 4.631397527329793e-195 < (* y (log z))

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      16.8
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      34.1
    3. Using strategy rm
      34.1
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      34.9
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      31.5
    6. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      13.5
    7. Taylor expanded around 0 to get
      \[\color{red}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      13.5

    if 8.372833883618234e-292 < (* y (log z)) < 4.631397527329793e-195

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      31.5
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      45.9
    3. Using strategy rm
      45.9
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      45.9
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      45.2
    6. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      18.2
    7. Taylor expanded around inf to get
      \[\color{red}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      18.2
    8. Applied simplify to get
      \[\color{red}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}} \leadsto \color{blue}{\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot {a}^{\left(t - 1.0\right)}\right)}\]
      21.8
    9. Applied taylor to get
      \[\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot {a}^{\left(t - 1.0\right)}\right) \leadsto \frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}\right)\]
      3.9
    10. Taylor expanded around inf to get
      \[\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot \color{red}{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}}\right) \leadsto \frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot \color{blue}{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}}\right)\]
      3.9
    11. Applied simplify to get
      \[\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \left(\frac{x}{e^{b}} \cdot e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}\right) \leadsto \left(\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \frac{x}{e^{b}}\right) \cdot e^{\left(-\log a\right) \cdot \left(\frac{1}{t} - 1.0\right)}\]
      1.0

    12. Applied final simplification
    13. Applied simplify to get
      \[\color{red}{\left(\frac{{z}^{\left(\frac{-1}{y}\right)}}{y} \cdot \frac{x}{e^{b}}\right) \cdot e^{\left(-\log a\right) \cdot \left(\frac{1}{t} - 1.0\right)}} \leadsto \color{blue}{\frac{x}{e^{b}} \cdot \frac{\frac{{z}^{\left(\frac{-1}{y}\right)}}{y}}{{a}^{\left(\frac{1}{t} - 1.0\right)}}}\]
      1.0

  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))