\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 53.2 s
Input Error: 25.0
Output Error: 0.3
Log: ⚲
Profile: 🕒
\(\begin{cases} {0}^2 & \text{when } b \le -1.5593f0 \\ \frac{\left(x \cdot {z}^{y}\right) \cdot {\left(\sqrt{{a}^{\left(t - 1.0\right)}}\right)}^2}{y \cdot e^{b}} & \text{when } b \le 0.0006072211f0 \\ {0}^2 & \text{otherwise} \end{cases}\)

    if b < -1.5593f0 or 0.0006072211f0 < b

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      27.3
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      26.5
    3. Using strategy rm
      26.5
    4. Applied add-sqr-sqrt to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{{\left(\sqrt{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\right)}^2}\]
      26.5
    5. Applied taylor to get
      \[{\left(\sqrt{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\right)}^2 \leadsto {0}^2\]
      0
    6. Taylor expanded around inf to get
      \[{\color{red}{0}}^2 \leadsto {\color{blue}{0}}^2\]
      0
    7. Applied simplify to get
      \[{0}^2 \leadsto {0}^2\]
      0
    8. Applied final simplification

    if -1.5593f0 < b < 0.0006072211f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      13.4
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      4.1
    3. Using strategy rm
      4.1
    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
  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))