\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 33.2 s
Input Error: 21.7
Output Error: 0.6
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{\frac{\frac{x}{e^{\frac{1}{b}}}}{e^{\frac{\log z}{y}}}}{{a}^{\left(\frac{1}{t} - 1.0\right)} \cdot y} & \text{when } b \le -2.2508123f0 \\ \frac{\left(x \cdot {z}^{y}\right) \cdot \left({a}^{t} \cdot {a}^{\left(-1.0\right)}\right)}{y \cdot e^{b}} & \text{when } b \le 54.06313f0 \\ \frac{{\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot x}{y \cdot e^{b}} & \text{otherwise} \end{cases}\)

    if b < -2.2508123f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      25.8
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      30.5
    3. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}\]
      1.8
    4. Taylor expanded around inf to get
      \[\color{red}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}} \leadsto \color{blue}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}}\]
      1.8
    5. Applied simplify to get
      \[\color{red}{\frac{e^{-1 \cdot \left(\log a \cdot \left(\frac{1}{t} - 1.0\right)\right)} \cdot \left(e^{-1 \cdot \frac{\log z}{y}} \cdot x\right)}{y \cdot e^{\frac{1}{b}}}} \leadsto \color{blue}{\frac{\frac{\frac{x}{e^{\frac{1}{b}}}}{e^{\frac{\log z}{y}}}}{{a}^{\left(\frac{1}{t} - 1.0\right)} \cdot y}}\]
      1.1

    if -2.2508123f0 < b < 54.06313f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      13.8
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      4.0
    3. Using strategy rm
      4.0
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      1.6
    5. Applied frac-times to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{y \cdot e^{b}}}\]
      1.6
    6. Using strategy rm
      1.6
    7. Applied sub-neg to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\color{red}{\left(t - 1.0\right)}}}{y \cdot e^{b}} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}{y \cdot e^{b}}\]
      1.6
    8. Applied unpow-prod-up to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}{y \cdot e^{b}} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \color{blue}{\left({a}^{t} \cdot {a}^{\left(-1.0\right)}\right)}}{y \cdot e^{b}}\]
      1.5

    if 54.06313f0 < b

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      24.9
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      22.3
    3. Using strategy rm
      22.3
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      21.0
    5. Applied frac-times to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{y \cdot e^{b}}}\]
      21.0
    6. Applied taylor to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{y \cdot e^{b}} \leadsto \frac{{\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot x}{y \cdot e^{b}}\]
      0.1
    7. Taylor expanded around 0 to get
      \[\frac{\color{red}{{\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot x}}{y \cdot e^{b}} \leadsto \frac{\color{blue}{{\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot x}}{y \cdot e^{b}}\]
      0.1
  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))