\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 15.6
Output Error: 4.3
Log:
Profile: 🕒
\(\begin{cases} \frac{\frac{x}{e^{\frac{1}{b}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} & \text{when } b \le -60.33268f0 \\ \frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} & \text{otherwise} \end{cases}\)

    if b < -60.33268f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      24.2
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      30.6
    3. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\frac{x}{e^{\frac{1}{b}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      2.0
    4. Taylor expanded around inf to get
      \[\frac{\color{red}{\frac{x}{e^{\frac{1}{b}}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}} \leadsto \frac{\color{blue}{\frac{x}{e^{\frac{1}{b}}}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}\]
      2.0

    if -60.33268f0 < b

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      12.9
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\left(t - 1.0\right)}}}}\]
      9.5
    3. Using strategy rm
      9.5
    4. Applied sub-neg to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{red}{\left(t - 1.0\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}}\]
      9.5
    5. Applied unpow-prod-up to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{\color{blue}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}}\]
      9.4
    6. Applied taylor to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\frac{y}{{z}^{y}}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
      4.9
    7. Taylor expanded around 0 to get
      \[\frac{\frac{x}{e^{b}}}{\frac{\color{red}{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}} \leadsto \frac{\frac{x}{e^{b}}}{\frac{\color{blue}{\left(y + \frac{1}{2} \cdot \left({y}^{3} \cdot {\left(\log z\right)}^2\right)\right) - {y}^2 \cdot \log z}}{{a}^{t} \cdot {a}^{\left(-1.0\right)}}}\]
      4.9

  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))