\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.7 m
Input Error: 12.1
Output Error: 2.5
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{t} \cdot {a}^{\left(-1.0\right)}}{e^{b}}}{y} & \text{when } x \le -2.2851676753931416 \cdot 10^{+159} \\ \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} & \text{when } x \le 6.095134300078123 \cdot 10^{-307} \\ \frac{e^{\log a \cdot \left(t + \left(-1.0\right)\right) + \left(y \cdot \log z + \left(\log x - b\right)\right)}}{y} & \text{otherwise} \end{cases}\)

    if x < -2.2851676753931416e+159

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      30.9
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      20.6
    3. Using strategy rm
      20.6
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      20.6
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      0.8
    6. Using strategy rm
      0.8
    7. Applied sub-neg to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{red}{\left(t - 1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y}\]
      0.8
    8. Applied unpow-prod-up to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}{e^{b}}}{y}\]
      0.8

    if -2.2851676753931416e+159 < x < 6.095134300078123e-307

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      17.7
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      8.8
    3. Using strategy rm
      8.8
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      9.5
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      3.6

    if 6.095134300078123e-307 < x

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      1.9
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      23.1
    3. Using strategy rm
      23.1
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      23.1
    5. Applied associate-*l/ to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}{y}}\]
      18.4
    6. Using strategy rm
      18.4
    7. Applied sub-neg to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{red}{\left(t - 1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y}\]
      18.4
    8. Applied unpow-prod-up to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}{e^{b}}}{y}\]
      18.4
    9. Using strategy rm
      18.4
    10. Applied pow-to-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{t} \cdot \color{red}{{a}^{\left(-1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{{a}^{t} \cdot \color{blue}{e^{\log a \cdot \left(-1.0\right)}}}{e^{b}}}{y}\]
      19.1
    11. Applied pow-to-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{t}} \cdot e^{\log a \cdot \left(-1.0\right)}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot t}} \cdot e^{\log a \cdot \left(-1.0\right)}}{e^{b}}}{y}\]
      19.1
    12. Applied prod-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{red}{e^{\log a \cdot t} \cdot e^{\log a \cdot \left(-1.0\right)}}}{e^{b}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot t + \log a \cdot \left(-1.0\right)}}}{e^{b}}}{y}\]
      19.1
    13. Applied div-exp to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot t + \log a \cdot \left(-1.0\right)}}{e^{b}}}}{y} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \color{blue}{e^{\left(\log a \cdot t + \log a \cdot \left(-1.0\right)\right) - b}}}{y}\]
      13.7
    14. Applied add-exp-log to get
      \[\frac{\color{red}{\left(x \cdot {z}^{y}\right)} \cdot e^{\left(\log a \cdot t + \log a \cdot \left(-1.0\right)\right) - b}}{y} \leadsto \frac{\color{blue}{e^{\log \left(x \cdot {z}^{y}\right)}} \cdot e^{\left(\log a \cdot t + \log a \cdot \left(-1.0\right)\right) - b}}{y}\]
      13.8
    15. Applied prod-exp to get
      \[\frac{\color{red}{e^{\log \left(x \cdot {z}^{y}\right)} \cdot e^{\left(\log a \cdot t + \log a \cdot \left(-1.0\right)\right) - b}}}{y} \leadsto \frac{\color{blue}{e^{\log \left(x \cdot {z}^{y}\right) + \left(\left(\log a \cdot t + \log a \cdot \left(-1.0\right)\right) - b\right)}}}{y}\]
      8.6
    16. Applied simplify to get
      \[\frac{e^{\color{red}{\log \left(x \cdot {z}^{y}\right) + \left(\left(\log a \cdot t + \log a \cdot \left(-1.0\right)\right) - b\right)}}}{y} \leadsto \frac{e^{\color{blue}{\log a \cdot \left(t + \left(-1.0\right)\right) + \left(y \cdot \log z + \left(\log x - b\right)\right)}}}{y}\]
      2.0
  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))