\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 7.4
Output Error: 2.4
Log:
Profile: 🕒
\(\begin{cases} \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} & \text{when } t \le -1.9335885f0 \\ \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left({a}^{-1.0} + \frac{1}{2} \cdot \left(\left({\left(\log a\right)}^2 \cdot {t}^2\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\right)}{e^{b}} & \text{when } t \le 1.3102372f+11 \\ \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} & \text{otherwise} \end{cases}\)

    if t < -1.9335885f0 or 1.3102372f+11 < t

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      3.0
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      16.3
    3. Using strategy rm
      16.3
    4. Applied div-inv to get
      \[\left(\color{red}{\frac{x}{y}} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      16.3
    5. Applied associate-*l* to get
      \[\color{red}{\left(\left(x \cdot \frac{1}{y}\right) \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\left(x \cdot \left(\frac{1}{y} \cdot {z}^{y}\right)\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      13.4
    6. Applied simplify to get
      \[\left(x \cdot \color{red}{\left(\frac{1}{y} \cdot {z}^{y}\right)}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(x \cdot \color{blue}{\frac{{z}^{y}}{y}}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      13.3
    7. Using strategy rm
      13.3
    8. Applied pow-to-exp to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      13.3
    9. Applied div-exp to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      7.7
    10. Applied taylor to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      3.9
    11. Taylor expanded around 0 to get
      \[\color{red}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      3.9

    if -1.9335885f0 < t < 1.3102372f+11

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      9.7
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      6.0
    3. Using strategy rm
      6.0
    4. Applied div-inv to get
      \[\left(\color{red}{\frac{x}{y}} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      6.0
    5. Applied associate-*l* to get
      \[\color{red}{\left(\left(x \cdot \frac{1}{y}\right) \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\left(x \cdot \left(\frac{1}{y} \cdot {z}^{y}\right)\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      4.4
    6. Applied simplify to get
      \[\left(x \cdot \color{red}{\left(\frac{1}{y} \cdot {z}^{y}\right)}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(x \cdot \color{blue}{\frac{{z}^{y}}{y}}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      4.3
    7. Applied taylor to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left({a}^{-1.0} + \frac{1}{2} \cdot \left(\left({\left(\log a\right)}^2 \cdot {t}^2\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\right)}{e^{b}}\]
      1.7
    8. Taylor expanded around 0 to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{red}{\left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left({a}^{-1.0} + \frac{1}{2} \cdot \left(\left({\left(\log a\right)}^2 \cdot {t}^2\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\right)}}{e^{b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{blue}{\left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left({a}^{-1.0} + \frac{1}{2} \cdot \left(\left({\left(\log a\right)}^2 \cdot {t}^2\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\right)}}{e^{b}}\]
      1.7

  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))