\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 43.5 s
Input Error: 25.1
Output Error: 1.7
Log:
Profile: 🕒
\(\begin{cases} \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \frac{{z}^{y}}{\frac{y}{x}}\right) \cdot (t * \left(\log a\right) + \left(1 - b\right))_* & \text{when } y \le -3.323283894772062 \cdot 10^{-05} \\ \frac{x}{1} \cdot \left(e^{\log a \cdot \left(t - 1.0\right) - b} \cdot \frac{{z}^{y}}{y}\right) & \text{when } y \le 401965514.1159669 \\ \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \frac{{z}^{y}}{\frac{y}{x}}\right) \cdot (t * \left(\log a\right) + \left(1 - b\right))_* & \text{otherwise} \end{cases}\)

    if y < -3.323283894772062e-05 or 401965514.1159669 < y

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      37.8
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      27.3
    3. Using strategy rm
      27.3
    4. Applied *-un-lft-identity to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{1 \cdot {a}^{\left(t - 1.0\right)}}}}\]
      27.3
    5. Applied *-un-lft-identity to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{1 \cdot {a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{1 \cdot \frac{y}{{z}^{y}}}}{1 \cdot {a}^{\left(t - 1.0\right)}}}\]
      27.3
    6. Applied times-frac to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{1 \cdot \frac{y}{{z}^{y}}}{1 \cdot {a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      27.3
    7. Applied div-inv to get
      \[\frac{\color{red}{\frac{x}{e^{b}}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\color{blue}{x \cdot \frac{1}{e^{b}}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      27.3
    8. Applied times-frac to get
      \[\color{red}{\frac{x \cdot \frac{1}{e^{b}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \color{blue}{\frac{x}{\frac{1}{1}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      27.3
    9. Applied simplify to get
      \[\color{red}{\frac{x}{\frac{1}{1}}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \color{blue}{\frac{x}{1}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      27.3
    10. Applied simplify to get
      \[\frac{x}{1} \cdot \color{red}{\frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{x}{1} \cdot \color{blue}{\left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right)}\]
      27.3
    11. Applied taylor to get
      \[\frac{x}{1} \cdot \left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right) \leadsto \frac{x}{1} \cdot \left(\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) \cdot \frac{{z}^{y}}{y}\right)\]
      13.4
    12. Taylor expanded around 0 to get
      \[\frac{x}{1} \cdot \left(\color{red}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \cdot \frac{{z}^{y}}{y}\right) \leadsto \frac{x}{1} \cdot \left(\color{blue}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \cdot \frac{{z}^{y}}{y}\right)\]
      13.4
    13. Applied simplify to get
      \[\color{red}{\frac{x}{1} \cdot \left(\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) \cdot \frac{{z}^{y}}{y}\right)} \leadsto \color{blue}{\left(\frac{\frac{{z}^{y}}{\frac{y}{x}}}{1} \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) \cdot (t * \left(\log a\right) + \left(1 - b\right))_*}\]
      0.3
    14. Applied simplify to get
      \[\color{red}{\left(\frac{\frac{{z}^{y}}{\frac{y}{x}}}{1} \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \cdot (t * \left(\log a\right) + \left(1 - b\right))_* \leadsto \color{blue}{\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \frac{{z}^{y}}{\frac{y}{x}}\right)} \cdot (t * \left(\log a\right) + \left(1 - b\right))_*\]
      0.3

    if -3.323283894772062e-05 < y < 401965514.1159669

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      3.5
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      12.7
    3. Using strategy rm
      12.7
    4. Applied *-un-lft-identity to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{1 \cdot {a}^{\left(t - 1.0\right)}}}}\]
      12.7
    5. Applied *-un-lft-identity to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{1 \cdot {a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{1 \cdot \frac{y}{{z}^{y}}}}{1 \cdot {a}^{\left(t - 1.0\right)}}}\]
      12.7
    6. Applied times-frac to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{1 \cdot \frac{y}{{z}^{y}}}{1 \cdot {a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      12.7
    7. Applied div-inv to get
      \[\frac{\color{red}{\frac{x}{e^{b}}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\color{blue}{x \cdot \frac{1}{e^{b}}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      12.7
    8. Applied times-frac to get
      \[\color{red}{\frac{x \cdot \frac{1}{e^{b}}}{\frac{1}{1} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \color{blue}{\frac{x}{\frac{1}{1}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      12.8
    9. Applied simplify to get
      \[\color{red}{\frac{x}{\frac{1}{1}}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \color{blue}{\frac{x}{1}} \cdot \frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      12.8
    10. Applied simplify to get
      \[\frac{x}{1} \cdot \color{red}{\frac{\frac{1}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{x}{1} \cdot \color{blue}{\left(\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right)}\]
      9.8
    11. Using strategy rm
      9.8
    12. Applied pow-to-exp to get
      \[\frac{x}{1} \cdot \left(\frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right) \leadsto \frac{x}{1} \cdot \left(\frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}} \cdot \frac{{z}^{y}}{y}\right)\]
      11.1
    13. Applied div-exp to get
      \[\frac{x}{1} \cdot \left(\color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \cdot \frac{{z}^{y}}{y}\right) \leadsto \frac{x}{1} \cdot \left(\color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}} \cdot \frac{{z}^{y}}{y}\right)\]
      4.0

  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))