\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.4 m
Input Error: 23.6
Output Error: 6.9
Log: ⚲
Profile: 🕒
\(\begin{cases} \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) & \text{when } y \le -4.92236056255477 \cdot 10^{+133} \\ \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{\left(\frac{-1}{y}\right)}}{\frac{y}{x}} & \text{when } y \le -5.034200074427852 \cdot 10^{-17} \\ \frac{\left(x \cdot {z}^{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}}{y} & \text{when } y \le 31.623627084778413 \\ \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{\left(\frac{-1}{y}\right)}}{\frac{y}{x}} & \text{when } y \le 2.2767442536329874 \cdot 10^{+115} \\ \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) & \text{otherwise} \end{cases}\)

    if y < -4.92236056255477e+133 or 2.2767442536329874e+115 < y

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      36.1
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      27.2
    3. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\]
      12.3
    4. Taylor expanded around 0 to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)}\]
      12.3
    5. Applied simplify to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \color{blue}{\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)}\]
      12.3

    if -4.92236056255477e+133 < y < -5.034200074427852e-17 or 31.623627084778413 < y < 2.2767442536329874e+115

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      34.3
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      37.2
    3. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      2.0
    4. Taylor expanded around inf to get
      \[\color{red}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      2.0
    5. Applied simplify to get
      \[\color{red}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{\left(\frac{-1}{y}\right)}}{\frac{y}{x}}}\]
      2.2

    if -5.034200074427852e-17 < y < 31.623627084778413

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      3.6
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      19.4
    3. Using strategy rm
      19.4
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      19.4
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      9.9
    6. Using strategy rm
      9.9
    7. Applied pow-to-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}}{y}\]
      11.2
    8. Applied div-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}}{y}\]
      3.7
  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))