\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 21.9 s
Input Error: 22.5
Output Error: 1.4
Log: ⚲
Profile: 🕒
\({a}^{t} \cdot \frac{\frac{x}{e^{b}}}{y \cdot {\left({a}^{1.0}\right)}^{1.0}}\)
  1. Started with
    \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
    22.5
  2. Applied simplify to get
    \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
    18.7
  3. Using strategy rm
    18.7
  4. Applied sub-neg to get
    \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
    18.7
  5. Applied unpow-prod-up to get
    \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
    18.7
  6. Applied *-un-lft-identity to get
    \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\frac{y}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{1 \cdot \frac{y}{{z}^{y}}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
    18.7
  7. Applied times-frac to get
    \[\frac{\frac{x}{e^{b}}}{\color{red}{\frac{1 \cdot \frac{y}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{\frac{1}{{a}^{t}} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
    18.7
  8. Applied *-un-lft-identity to get
    \[\frac{\color{red}{\frac{x}{e^{b}}}}{\frac{1}{{a}^{t}} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} \leadsto \frac{\color{blue}{1 \cdot \frac{x}{e^{b}}}}{\frac{1}{{a}^{t}} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}\]
    18.7
  9. Applied times-frac to get
    \[\color{red}{\frac{1 \cdot \frac{x}{e^{b}}}{\frac{1}{{a}^{t}} \cdot \frac{\frac{y}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}} \leadsto \color{blue}{\frac{1}{\frac{1}{{a}^{t}}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}}\]
    18.7
  10. Applied simplify to get
    \[\color{red}{\frac{1}{\frac{1}{{a}^{t}}}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} \leadsto \color{blue}{{a}^{t}} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(-1.0\right)}}}\]
    18.7
  11. Applied taylor to get
    \[{a}^{t} \cdot \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(-1.0\right)}}} \leadsto {a}^{t} \cdot \frac{\frac{x}{e^{b}}}{y \cdot {\left({a}^{1.0}\right)}^{1.0}}\]
    1.4
  12. Taylor expanded around 0 to get
    \[{a}^{t} \cdot \frac{\frac{x}{e^{b}}}{\color{red}{y \cdot {\left({a}^{1.0}\right)}^{1.0}}} \leadsto {a}^{t} \cdot \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot {\left({a}^{1.0}\right)}^{1.0}}}\]
    1.4

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))