\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 56.2 s
Input Error: 31.2
Output Error: 4.4
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{\frac{x}{e^{\frac{1}{b}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} & \text{when } b \le -0.05251705580964073 \\ \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{\left(\sqrt{{a}^{\left(t - 1.0\right)}}\right)}^2}} & \text{when } b \le 6.190514256158086 \cdot 10^{-23} \\ \frac{\frac{x}{e^{b}}}{y \cdot a - \left(y \cdot a\right) \cdot (\left(\log z\right) * y + \left(t \cdot \log a\right))_*} & \text{otherwise} \end{cases}\)

    if b < -0.05251705580964073

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      51.2
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      62.0
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{\frac{1}{b}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      1.8
    4. Taylor expanded around inf to get
      \[\frac{\color{red}{\frac{x}{e^{\frac{1}{b}}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\color{blue}{\frac{x}{e^{\frac{1}{b}}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      1.8

    if -0.05251705580964073 < b < 6.190514256158086e-23

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      31.0
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      1.9
    3. Using strategy rm
      1.9
    4. Applied add-sqr-sqrt to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{\left(\sqrt{{a}^{\left(t - 1.0\right)}}\right)}^2}}}\]
      1.9

    if 6.190514256158086e-23 < b

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      14.7
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      30.9
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}\]
      10.9
    4. Taylor expanded around 0 to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}}\]
      10.9
    5. Applied simplify to get
      \[\color{red}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left(y \cdot a\right) \cdot (\left(\log z\right) * y + \left(t \cdot \log a\right))_*}}\]
      10.4
  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))