\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 28.0 s
Input Error: 21.6
Output Error: 0.7
Log:
Profile: 🕒
\(\begin{cases} \left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right) & \text{when } b \le -1.5593f0 \\ \frac{\left(x \cdot {z}^{y}\right) \cdot {\left(\sqrt{{a}^{\left(t - 1.0\right)}}\right)}^2}{y \cdot e^{b}} & \text{when } b \le 15.794751f0 \\ \frac{{\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot x}{y \cdot e^{b}} & \text{otherwise} \end{cases}\)

    if b < -1.5593f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      24.3
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      29.7
    3. Applied taylor to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)\]
      0.8
    4. Taylor expanded around 0 to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{\left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)}\]
      0.8
    5. Applied simplify to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \left(\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} + \left(\log a \cdot t\right) \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right) - b \cdot {\left(\frac{1}{{a}^{1.0}}\right)}^{1.0}\right)} \leadsto \color{blue}{\left({\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot \left(t \cdot \log a + \left(1 - b\right)\right)\right) \cdot \left({z}^{y} \cdot \frac{x}{y}\right)}\]
      0.8

    if -1.5593f0 < b < 15.794751f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      13.2
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      4.2
    3. Using strategy rm
      4.2
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      1.8
    5. Applied frac-times to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{y \cdot e^{b}}}\]
      1.8
    6. Using strategy rm
      1.8
    7. Applied add-sqr-sqrt to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \color{red}{{a}^{\left(t - 1.0\right)}}}{y \cdot e^{b}} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \color{blue}{{\left(\sqrt{{a}^{\left(t - 1.0\right)}}\right)}^2}}{y \cdot e^{b}}\]
      1.8

    if 15.794751f0 < 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
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      22.2
    3. Using strategy rm
      22.2
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      20.8
    5. Applied frac-times to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{y \cdot e^{b}}}\]
      20.8
    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))