\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 50.2 s
Input Error: 11.0
Output Error: 0.6
Log:
Profile: 🕒
\(\begin{cases} \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) & \text{when } y \le -48.584396f0 \\ \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot {e}^{\left(\log a \cdot \left(t - 1.0\right) - b\right)} & \text{when } y \le 2.8667614f0 \\ \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) & \text{otherwise} \end{cases}\)

    if y < -48.584396f0 or 2.8667614f0 < y

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      17.3
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      13.0
    3. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\]
      0.0
    4. Taylor expanded around 0 to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)}\]
      0.0
    5. Applied simplify to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \color{blue}{\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)}\]
      0.0

    if -48.584396f0 < y < 2.8667614f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      1.1
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      9.0
    3. Using strategy rm
      9.0
    4. Applied div-inv to get
      \[\left(\color{red}{\frac{x}{y}} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      9.0
    5. Applied associate-*l* to get
      \[\color{red}{\left(\left(x \cdot \frac{1}{y}\right) \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\left(x \cdot \left(\frac{1}{y} \cdot {z}^{y}\right)\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      4.0
    6. Applied simplify to get
      \[\left(x \cdot \color{red}{\left(\frac{1}{y} \cdot {z}^{y}\right)}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(x \cdot \color{blue}{\frac{{z}^{y}}{y}}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      3.9
    7. Using strategy rm
      3.9
    8. Applied pow-to-exp to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      4.5
    9. Applied div-exp to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      1.3
    10. Using strategy rm
      1.3
    11. Applied *-un-lft-identity to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot e^{\color{red}{\log a \cdot \left(t - 1.0\right) - b}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot e^{\color{blue}{1 \cdot \left(\log a \cdot \left(t - 1.0\right) - b\right)}}\]
      1.3
    12. Applied exp-prod to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{red}{e^{1 \cdot \left(\log a \cdot \left(t - 1.0\right) - b\right)}} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot \color{blue}{{\left(e^{1}\right)}^{\left(\log a \cdot \left(t - 1.0\right) - b\right)}}\]
      1.4
    13. Applied simplify to get
      \[\left(x \cdot \frac{{z}^{y}}{y}\right) \cdot {\color{red}{\left(e^{1}\right)}}^{\left(\log a \cdot \left(t - 1.0\right) - b\right)} \leadsto \left(x \cdot \frac{{z}^{y}}{y}\right) \cdot {\color{blue}{e}}^{\left(\log a \cdot \left(t - 1.0\right) - b\right)}\]
      1.4

  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))