\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.2 m
Input Error: 12.3
Output Error: 3.3
Log: ⚲
Profile: 🕒
\(\begin{cases} \log \left({\left(e^{\frac{x}{y}}\right)}^{\left({a}^{\left(t - 1.0\right)} \cdot \frac{{z}^{y}}{e^{b}}\right)}\right) & \text{when } y \cdot \log z \le -0.0013910353f0 \\ \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} & \text{when } y \cdot \log z \le 22465.924f0 \\ \frac{\frac{x}{e^{b}}}{y \cdot a - \left(y \cdot a\right) \cdot (\left(\log z\right) * y + \left(t \cdot \log a\right))_*} & \text{otherwise} \end{cases}\)

    if (* y (log z)) < -0.0013910353f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      6.9
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      2.9
    3. Using strategy rm
      2.9
    4. Applied add-cube-cbrt to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{{\left(\sqrt[3]{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\right)}^3}}\]
      2.9
    5. Using strategy rm
      2.9
    6. Applied add-log-exp to get
      \[\color{red}{\frac{\frac{x}{e^{b}}}{{\left(\sqrt[3]{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\right)}^3}} \leadsto \color{blue}{\log \left(e^{\frac{\frac{x}{e^{b}}}{{\left(\sqrt[3]{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\right)}^3}}\right)}\]
      3.2
    7. Applied simplify to get
      \[\log \color{red}{\left(e^{\frac{\frac{x}{e^{b}}}{{\left(\sqrt[3]{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\right)}^3}}\right)} \leadsto \log \color{blue}{\left({\left(e^{\frac{x}{y}}\right)}^{\left({a}^{\left(t - 1.0\right)} \cdot \frac{{z}^{y}}{e^{b}}\right)}\right)}\]
      1.4

    if -0.0013910353f0 < (* y (log z)) < 22465.924f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      9.0
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      2.3
    3. Using strategy rm
      2.3
    4. Applied sub-neg to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
      2.3
    5. Applied unpow-prod-up to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
      2.2

    if 22465.924f0 < (* y (log z))

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      25.1
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      31.1
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}\]
      9.7
    4. Taylor expanded around 0 to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}}\]
      9.7
    5. Applied simplify to get
      \[\color{red}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left(y \cdot a\right) \cdot (\left(\log z\right) * y + \left(t \cdot \log a\right))_*}}\]
      7.7
  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))