\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 2.7 m
Input Error: 16.4
Output Error: 2.0
Log:
Profile: 🕒
\(\begin{cases} \frac{{z}^{y} \cdot \frac{\frac{x}{y}}{e^{b}}}{{a}^{\left(\frac{1}{t} - 1.0\right)}} & \text{when } y \cdot \log z \le -4.167359238670591 \cdot 10^{+283} \\ \frac{\frac{x}{e^{\frac{1}{b}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} & \text{when } y \cdot \log z \le -2.1408169647614482 \cdot 10^{+235} \\ e^{(y * \left(\log z\right) + \left(\log a \cdot \left(t - 1.0\right)\right))_* + \left(\log \left(\frac{x}{y}\right) - b\right)} & \text{when } y \cdot \log z \le -1.6723754041891606 \cdot 10^{+125} \\ \frac{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} & \text{when } y \cdot \log z \le 11808710528.56336 \\ e^{(y * \left(\log z\right) + \left(\log a \cdot \left(t - 1.0\right)\right))_* + \left(\log \left(\frac{x}{y}\right) - b\right)} & \text{otherwise} \end{cases}\)

    if (* y (log z)) < -4.167359238670591e+283

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      1.6
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      23.7
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}}}\]
      1.6
    4. Taylor expanded around inf to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}}}}\]
      1.6
    5. Applied simplify to get
      \[\color{red}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)}}}} \leadsto \color{blue}{\frac{{z}^{y} \cdot \frac{\frac{x}{y}}{e^{b}}}{{a}^{\left(\frac{1}{t} - 1.0\right)}}}\]
      1.6

    if -4.167359238670591e+283 < (* y (log z)) < -2.1408169647614482e+235

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      15.1
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      19.4
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{\frac{1}{b}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      0.5
    4. Taylor expanded around inf to get
      \[\frac{\color{red}{\frac{x}{e^{\frac{1}{b}}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\color{blue}{\frac{x}{e^{\frac{1}{b}}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      0.5

    if -2.1408169647614482e+235 < (* y (log z)) < -1.6723754041891606e+125 or 11808710528.56336 < (* y (log z))

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      0
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      37.8
    3. Using strategy rm
      37.8
    4. Applied sub-neg to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
      37.8
    5. Applied unpow-prod-up to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
      37.8
    6. Applied div-inv to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{y \cdot \frac{1}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
      37.8
    7. Applied times-frac to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{y \cdot \frac{1}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
      37.8
    8. Applied associate-/r* to get
      \[\color{red}{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \color{blue}{\frac{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
      37.8
    9. Using strategy rm
      37.8
    10. Applied add-exp-log to get
      \[\frac{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}{\color{red}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}{\color{blue}{e^{\log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}}}\]
      37.8
    11. Applied add-exp-log to get
      \[\frac{\color{red}{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}}{e^{\log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}} \leadsto \frac{\color{blue}{e^{\log \left(\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}\right)}}}{e^{\log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}}\]
      37.8
    12. Applied div-exp to get
      \[\color{red}{\frac{e^{\log \left(\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}\right)}}{e^{\log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}}} \leadsto \color{blue}{e^{\log \left(\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}\right) - \log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}}\]
      37.8
    13. Applied simplify to get
      \[e^{\color{red}{\log \left(\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}\right) - \log \left(\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}\right)}} \leadsto e^{\color{blue}{(y * \left(\log z\right) + \left(\log a \cdot \left(t - 1.0\right)\right))_* + \left(\log \left(\frac{x}{y}\right) - b\right)}}\]
      0

    if -1.6723754041891606e+125 < (* y (log z)) < 11808710528.56336

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      19.4
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      4.2
    3. Using strategy rm
      4.2
    4. Applied sub-neg to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
      4.2
    5. Applied unpow-prod-up to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
      4.2
    6. Applied div-inv to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{y \cdot \frac{1}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
      4.2
    7. Applied times-frac to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{y \cdot \frac{1}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
      4.2
    8. Applied associate-/r* to get
      \[\color{red}{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \color{blue}{\frac{\frac{\frac{x}{e^{b}}}{\frac{y}{{a}^{t}}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
      2.4

  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))