\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 59.0 s
Input Error: 35.1
Output Error: 2.5
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{\frac{\frac{1}{x}}{e^{\frac{1}{b}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} & \text{when } b \le -0.49587928748277466 \\ \frac{{a}^{t}}{y} \cdot \left({a}^{\left(-1.0\right)} \cdot \left(\frac{x}{e^{b}} \cdot {z}^{y}\right)\right) & \text{when } b \le -8.571434561932433 \cdot 10^{-214} \\ \frac{{a}^{t}}{y} \cdot \left({a}^{\left(-1.0\right)} \cdot \left(\frac{x}{e^{b}} \cdot {z}^{y}\right)\right) & \text{when } b \le 1.1759021341074464 \cdot 10^{-212} \\ \frac{{a}^{t}}{y} \cdot \left({a}^{\left(-1.0\right)} \cdot \left(\frac{x}{e^{b}} \cdot {z}^{y}\right)\right) & \text{when } b \le 4.940433021970733 \cdot 10^{+66} \\ \frac{{a}^{t}}{y} \cdot \left({a}^{\left(-1.0\right)} \cdot \left(\frac{x}{e^{b}} \cdot {z}^{y}\right)\right) & \text{otherwise} \end{cases}\)

    if b < -0.49587928748277466

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      51.6
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      62.1
    3. Using strategy rm
      62.1
    4. Applied add-cube-cbrt to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{\left(\sqrt[3]{{a}^{\left(t - 1.0\right)}}\right)}^3}}}\]
      62.1
    5. Applied add-cube-cbrt to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{{\left(\sqrt[3]{{a}^{\left(t - 1.0\right)}}\right)}^3}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{{\left(\sqrt[3]{\frac{y}{{z}^{y}}}\right)}^3}}{{\left(\sqrt[3]{{a}^{\left(t - 1.0\right)}}\right)}^3}}\]
      62.1
    6. Applied cube-undiv to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{{\left(\sqrt[3]{\frac{y}{{z}^{y}}}\right)}^3}{{\left(\sqrt[3]{{a}^{\left(t - 1.0\right)}}\right)}^3}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{{\left(\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}\right)}^3}}\]
      62.1
    7. Applied add-cube-cbrt to get
      \[\frac{\color{red}{\frac{x}{e^{b}}}}{{\left(\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}\right)}^3} \leadsto \frac{\color{blue}{{\left(\sqrt[3]{\frac{x}{e^{b}}}\right)}^3}}{{\left(\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}\right)}^3}\]
      62.1
    8. Applied cube-undiv to get
      \[\color{red}{\frac{{\left(\sqrt[3]{\frac{x}{e^{b}}}\right)}^3}{{\left(\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}\right)}^3}} \leadsto \color{blue}{{\left(\frac{\sqrt[3]{\frac{x}{e^{b}}}}{\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}}\right)}^3}\]
      62.1
    9. Applied taylor to get
      \[{\left(\frac{\sqrt[3]{\frac{x}{e^{b}}}}{\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}}\right)}^3 \leadsto {\left(\frac{\sqrt[3]{\frac{1}{e^{\frac{1}{b}} \cdot x}}}{\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}}\right)}^3\]
      0.7
    10. Taylor expanded around inf to get
      \[{\left(\frac{\color{red}{\sqrt[3]{\frac{1}{e^{\frac{1}{b}} \cdot x}}}}{\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}}\right)}^3 \leadsto {\left(\frac{\color{blue}{\sqrt[3]{\frac{1}{e^{\frac{1}{b}} \cdot x}}}}{\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}}\right)}^3\]
      0.7
    11. Applied simplify to get
      \[\color{red}{{\left(\frac{\sqrt[3]{\frac{1}{e^{\frac{1}{b}} \cdot x}}}{\frac{\sqrt[3]{\frac{y}{{z}^{y}}}}{\sqrt[3]{{a}^{\left(t - 1.0\right)}}}}\right)}^3} \leadsto \color{blue}{\frac{\frac{\frac{1}{x}}{e^{\frac{1}{b}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      1.7

    if -0.49587928748277466 < b < -8.571434561932433e-214 or 1.1759021341074464e-212 < b < 4.940433021970733e+66

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      31.0
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      2.3
    3. Using strategy rm
      2.3
    4. Applied sub-neg to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
      2.3
    5. Applied unpow-prod-up to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
      2.3
    6. Applied div-inv to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{y \cdot \frac{1}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
      2.3
    7. Applied times-frac to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{y \cdot \frac{1}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
      2.3
    8. Applied *-un-lft-identity to get
      \[\frac{\color{red}{\frac{x}{e^{b}}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} \leadsto \frac{\color{blue}{1 \cdot \frac{x}{e^{b}}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}\]
      2.3
    9. Applied times-frac to get
      \[\color{red}{\frac{1 \cdot \frac{x}{e^{b}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \color{blue}{\frac{1}{\frac{y}{{a}^{t}}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
      3.4
    10. Applied simplify to get
      \[\color{red}{\frac{1}{\frac{y}{{a}^{t}}}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} \leadsto \color{blue}{\frac{{a}^{t}}{y}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}\]
      3.4
    11. Applied simplify to get
      \[\frac{{a}^{t}}{y} \cdot \color{red}{\frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \frac{{a}^{t}}{y} \cdot \color{blue}{\left({a}^{\left(-1.0\right)} \cdot \left(\frac{x}{e^{b}} \cdot {z}^{y}\right)\right)}\]
      3.4

    if -8.571434561932433e-214 < b < 1.1759021341074464e-212 or 4.940433021970733e+66 < b

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      28.1
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      2.6
    3. Using strategy rm
      2.6
    4. Applied sub-neg to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
      2.6
    5. Applied unpow-prod-up to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
      2.6
    6. Applied div-inv to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{y \cdot \frac{1}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
      2.6
    7. Applied times-frac to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{y \cdot \frac{1}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
      2.6
    8. Applied *-un-lft-identity to get
      \[\frac{\color{red}{\frac{x}{e^{b}}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} \leadsto \frac{\color{blue}{1 \cdot \frac{x}{e^{b}}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}\]
      2.6
    9. Applied times-frac to get
      \[\color{red}{\frac{1 \cdot \frac{x}{e^{b}}}{\frac{y}{{a}^{t}} \cdot \frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \color{blue}{\frac{1}{\frac{y}{{a}^{t}}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
      2.1
    10. Applied simplify to get
      \[\color{red}{\frac{1}{\frac{y}{{a}^{t}}}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} \leadsto \color{blue}{\frac{{a}^{t}}{y}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}\]
      2.1
    11. Applied simplify to get
      \[\frac{{a}^{t}}{y} \cdot \color{red}{\frac{\frac{x}{e^{b}}}{\frac{\frac{1}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \frac{{a}^{t}}{y} \cdot \color{blue}{\left({a}^{\left(-1.0\right)} \cdot \left(\frac{x}{e^{b}} \cdot {z}^{y}\right)\right)}\]
      2.1
  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))