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

    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
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      25.8
    3. Using strategy rm
      25.8
    4. Applied add-sqr-sqrt to get
      \[\color{red}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}} \leadsto \color{blue}{{\left(\sqrt{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\right)}^2}\]
      25.9
    5. Applied taylor to get
      \[{\left(\sqrt{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\right)}^2 \leadsto {0}^2\]
      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
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      1.8
    3. Using strategy rm
      1.8
    4. Applied add-sqr-sqrt to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{\left(\sqrt{{a}^{\left(t - 1.0\right)}}\right)}^2}}}\]
      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))