\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.1 m
Input Error: 29.7
Output Error: 1.4
Log:
Profile: 🕒
\(\begin{cases} \frac{e^{\log \left(x \cdot {z}^{y}\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)}}{y} & \text{when } y \le -8.881962931001398 \cdot 10^{-05} \\ \left(\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\right) \cdot \frac{1}{y} & \text{when } y \le 0.00873074001777178 \\ \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} & \text{when } y \le 3.295972573796126 \cdot 10^{+113} \\ \frac{e^{\log \left(x \cdot {z}^{y}\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)}}{y} & \text{otherwise} \end{cases}\)

    if y < -8.881962931001398e-05 or 3.295972573796126e+113 < y

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      37.1
    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. Using strategy rm
      27.2
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      27.2
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      27.2
    6. Using strategy rm
      27.2
    7. Applied pow-to-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}}{y}\]
      27.2
    8. Applied div-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}}{y}\]
      23.0
    9. Applied add-exp-log to get
      \[\frac{\color{red}{\left(x \cdot {z}^{y}\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}}{y} \leadsto \frac{\color{blue}{e^{\log \left(x \cdot {z}^{y}\right)}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}}{y}\]
      23.0
    10. Applied prod-exp to get
      \[\frac{\color{red}{e^{\log \left(x \cdot {z}^{y}\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}}}{y} \leadsto \frac{\color{blue}{e^{\log \left(x \cdot {z}^{y}\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)}}}{y}\]
      0.2

    if -8.881962931001398e-05 < y < 0.00873074001777178

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      19.6
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      14.0
    3. Using strategy rm
      14.0
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      14.0
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      2.4
    6. Using strategy rm
      2.4
    7. Applied div-inv to get
      \[\color{red}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}} \leadsto \color{blue}{\left(\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\right) \cdot \frac{1}{y}}\]
      2.4

    if 0.00873074001777178 < y < 3.295972573796126e+113

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      36.5
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      39.6
    3. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      4.2
    4. Taylor expanded around 0 to get
      \[\color{red}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      4.2

  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))