\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.4 m
Input Error: 15.2
Output Error: 10.1
Log:
Profile: 🕒
\(\begin{cases} \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{\left(\sqrt{{a}^{\left(t - 1.0\right)}}\right)}^2}{e^{b}} & \text{when } y \cdot \log z \le -3.652269526568409 \cdot 10^{-09} \\ {\left(\sqrt[3]{\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)} \cdot \sqrt[3]{e^{\log a \cdot \left(t - 1.0\right) - b}}\right)}^3 & \text{otherwise} \end{cases}\)

    if (* y (log z)) < -3.652269526568409e-09

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      14.5
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      0.8
    3. Using strategy rm
      0.8
    4. Applied add-sqr-sqrt to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{{\left(\sqrt{{a}^{\left(t - 1.0\right)}}\right)}^2}}{e^{b}}\]
      0.8

    if -3.652269526568409e-09 < (* y (log z))

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      15.6
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      33.4
    3. Using strategy rm
      33.4
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      34.3
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      30.8
    6. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      14.5
    7. Taylor expanded around 0 to get
      \[\color{red}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      14.5
    8. Using strategy rm
      14.5
    9. Applied add-cube-cbrt to get
      \[\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot \color{red}{e^{\log a \cdot \left(t - 1.0\right) - b}} \leadsto \left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right) \cdot \color{blue}{{\left(\sqrt[3]{e^{\log a \cdot \left(t - 1.0\right) - b}}\right)}^3}\]
      14.6
    10. Applied add-cube-cbrt to get
      \[\color{red}{\left(\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)\right)} \cdot {\left(\sqrt[3]{e^{\log a \cdot \left(t - 1.0\right) - b}}\right)}^3 \leadsto \color{blue}{{\left(\sqrt[3]{\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)}\right)}^3} \cdot {\left(\sqrt[3]{e^{\log a \cdot \left(t - 1.0\right) - b}}\right)}^3\]
      14.6
    11. Applied cube-unprod to get
      \[\color{red}{{\left(\sqrt[3]{\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)}\right)}^3 \cdot {\left(\sqrt[3]{e^{\log a \cdot \left(t - 1.0\right) - b}}\right)}^3} \leadsto \color{blue}{{\left(\sqrt[3]{\frac{x}{y} + \left(\log z \cdot x + \frac{1}{2} \cdot \left(y \cdot \left({\left(\log z\right)}^2 \cdot x\right)\right)\right)} \cdot \sqrt[3]{e^{\log a \cdot \left(t - 1.0\right) - b}}\right)}^3}\]
      14.6

  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))