\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 1.0 m
Input Error: 14.7
Output Error: 1.8
Log: ⚲
Profile: 🕒
\(\begin{cases} \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) & \text{when } y \cdot \log z \le -172.81775f0 \\ \frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{\frac{1}{2} \cdot \left(y \cdot {b}^2\right) + \left(y + y \cdot b\right)} & \text{when } y \cdot \log z \le 31.02722f0 \\ \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{\left(\frac{-1}{y}\right)}}{\frac{y}{x}} & \text{otherwise} \end{cases}\)

    if (* y (log z)) < -172.81775f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      6.2
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      13.1
    3. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\]
      0.1
    4. Taylor expanded around 0 to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)}\]
      0.1
    5. Applied simplify to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \color{blue}{\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)}\]
      0.1

    if -172.81775f0 < (* y (log z)) < 31.02722f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      15.9
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      14.8
    3. Using strategy rm
      14.8
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      10.9
    5. Applied frac-times to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{y \cdot e^{b}}}\]
      10.9
    6. Applied taylor to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{y \cdot e^{b}} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{\frac{1}{2} \cdot \left(y \cdot {b}^2\right) + \left(y + y \cdot b\right)}\]
      2.4
    7. Taylor expanded around 0 to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{\color{red}{\frac{1}{2} \cdot \left(y \cdot {b}^2\right) + \left(y + y \cdot b\right)}} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{\color{blue}{\frac{1}{2} \cdot \left(y \cdot {b}^2\right) + \left(y + y \cdot b\right)}}\]
      2.4

    if 31.02722f0 < (* y (log z))

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      23.2
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      30.6
    3. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      1.6
    4. Taylor expanded around inf to get
      \[\color{red}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      1.6
    5. Applied simplify to get
      \[\color{red}{\frac{e^{-1 \cdot \frac{\log z}{y}} \cdot x}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \cdot \frac{{z}^{\left(\frac{-1}{y}\right)}}{\frac{y}{x}}}\]
      2.6
  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))