\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 11.8
Output Error: 3.6
Log:
Profile: 🕒
\(\begin{cases} \frac{e^{(\left(\log a\right) * \left(t - 1.0\right) + \left(y \cdot \log z\right))_*}}{y} \cdot \left(x - \frac{x}{b}\right) & \text{when } y \cdot \log z \le -2.3494205f+18 \\ \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} & \text{when } y \cdot \log z \le 2.207478f-09 \\ \frac{\frac{x}{e^{b}}}{y \cdot a - \left(y \cdot a\right) \cdot (\left(\log z\right) * y + \left(t \cdot \log a\right))_*} & \text{otherwise} \end{cases}\)

    if (* y (log z)) < -2.3494205f+18

    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
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      11.9
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}\]
      18.1
    4. Taylor expanded around inf to get
      \[\color{red}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}} \leadsto \color{blue}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}}\]
      18.1
    5. Applied simplify to get
      \[\color{red}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}} \leadsto \color{blue}{\frac{e^{(\left(-\log a\right) * \left(\frac{1}{t} - 1.0\right) + \left(\frac{-1}{y} \cdot \log z\right))_*}}{\frac{y}{x} \cdot e^{\frac{1}{b}}}}\]
      17.4
    6. Applied taylor to get
      \[\frac{e^{(\left(-\log a\right) * \left(\frac{1}{t} - 1.0\right) + \left(\frac{-1}{y} \cdot \log z\right))_*}}{\frac{y}{x} \cdot e^{\frac{1}{b}}} \leadsto \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y} - \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y \cdot b}\]
      0
    7. Taylor expanded around inf to get
      \[\color{red}{\frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y} - \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y \cdot b}} \leadsto \color{blue}{\frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y} - \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y \cdot b}}\]
      0
    8. Applied simplify to get
      \[\frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y} - \frac{e^{(\left(-\log \left(\frac{1}{a}\right)\right) * \left(t - 1.0\right) + \left(-1 \cdot \left(y \cdot \log \left(\frac{1}{z}\right)\right)\right))_*} \cdot x}{y \cdot b} \leadsto \frac{e^{(\left(\log a\right) * \left(t - 1.0\right) + \left(y \cdot \log z\right))_*}}{y} \cdot \left(x - \frac{x}{b}\right)\]
      3.9

    9. Applied final simplification

    if -2.3494205f+18 < (* y (log z)) < 2.207478f-09

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      8.3
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      1.8
    3. Using strategy rm
      1.8
    4. Applied sub-neg to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
      1.8
    5. Applied unpow-prod-up to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
      1.7

    if 2.207478f-09 < (* y (log z))

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      22.6
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      27.9
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}\]
      8.0
    4. Taylor expanded around 0 to get
      \[\frac{\frac{x}{e^{b}}}{\color{red}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \frac{\frac{x}{e^{b}}}{\color{blue}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}}\]
      8.0
    5. Applied simplify to get
      \[\color{red}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left({y}^2 \cdot \left(\log z \cdot a\right) + y \cdot \left(\log a \cdot \left(a \cdot t\right)\right)\right)}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{y \cdot a - \left(y \cdot a\right) \cdot (\left(\log z\right) * y + \left(t \cdot \log a\right))_*}}\]
      6.4

  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))