\[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
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: 31.2 s
Input Error: 21.6
Output Error: 0.7
Log:
Profile: 🕒
\(\begin{cases} e^{\log \left(\frac{x}{y} \cdot {z}^{y}\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)} & \text{when } b \le -338.16934f0 \\ \frac{\left(\left(x \cdot {z}^{y}\right) \cdot {a}^{t}\right) \cdot {a}^{\left(-1.0\right)}}{y \cdot e^{b}} & \text{when } b \le 5.373505f0 \\ \frac{{\left(\frac{1}{{a}^{1.0}}\right)}^{1.0} \cdot x}{y \cdot e^{b}} & \text{otherwise} \end{cases}\)

    if b < -338.16934f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      20.1
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      31.0
    3. Using strategy rm
      31.0
    4. Applied pow-to-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{red}{{a}^{\left(t - 1.0\right)}}}{e^{b}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{\color{blue}{e^{\log a \cdot \left(t - 1.0\right)}}}{e^{b}}\]
      31.0
    5. Applied div-exp to get
      \[\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{red}{\frac{e^{\log a \cdot \left(t - 1.0\right)}}{e^{b}}} \leadsto \left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \color{blue}{e^{\log a \cdot \left(t - 1.0\right) - b}}\]
      26.7
    6. Applied add-exp-log to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b} \leadsto \color{blue}{e^{\log \left(\frac{x}{y} \cdot {z}^{y}\right)}} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}\]
      26.7
    7. Applied prod-exp to get
      \[\color{red}{e^{\log \left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot e^{\log a \cdot \left(t - 1.0\right) - b}} \leadsto \color{blue}{e^{\log \left(\frac{x}{y} \cdot {z}^{y}\right) + \left(\log a \cdot \left(t - 1.0\right) - b\right)}}\]
      1.0

    if -338.16934f0 < b < 5.373505f0

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      14.4
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      4.8
    3. Using strategy rm
      4.8
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      2.1
    5. Applied frac-times to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{y \cdot e^{b}}}\]
      2.1
    6. Using strategy rm
      2.1
    7. Applied sub-neg to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\color{red}{\left(t - 1.0\right)}}}{y \cdot e^{b}} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\color{blue}{\left(t + \left(-1.0\right)\right)}}}{y \cdot e^{b}}\]
      2.1
    8. Applied unpow-prod-up to get
      \[\frac{\left(x \cdot {z}^{y}\right) \cdot \color{red}{{a}^{\left(t + \left(-1.0\right)\right)}}}{y \cdot e^{b}} \leadsto \frac{\left(x \cdot {z}^{y}\right) \cdot \color{blue}{\left({a}^{t} \cdot {a}^{\left(-1.0\right)}\right)}}{y \cdot e^{b}}\]
      1.9
    9. Applied associate-*r* to get
      \[\frac{\color{red}{\left(x \cdot {z}^{y}\right) \cdot \left({a}^{t} \cdot {a}^{\left(-1.0\right)}\right)}}{y \cdot e^{b}} \leadsto \frac{\color{blue}{\left(\left(x \cdot {z}^{y}\right) \cdot {a}^{t}\right) \cdot {a}^{\left(-1.0\right)}}}{y \cdot e^{b}}\]
      1.9

    if 5.373505f0 < b

    1. Started with
      \[\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}\]
      25.3
    2. Applied simplify to get
      \[\color{red}{\frac{x \cdot e^{\left(y \cdot \log z + \left(t - 1.0\right) \cdot \log a\right) - b}}{y}} \leadsto \color{blue}{\left(\frac{x}{y} \cdot {z}^{y}\right) \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}}\]
      22.3
    3. Using strategy rm
      22.3
    4. Applied associate-*l/ to get
      \[\color{red}{\left(\frac{x}{y} \cdot {z}^{y}\right)} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}} \leadsto \color{blue}{\frac{x \cdot {z}^{y}}{y}} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}\]
      21.0
    5. Applied frac-times to get
      \[\color{red}{\frac{x \cdot {z}^{y}}{y} \cdot \frac{{a}^{\left(t - 1.0\right)}}{e^{b}}} \leadsto \color{blue}{\frac{\left(x \cdot {z}^{y}\right) \cdot {a}^{\left(t - 1.0\right)}}{y \cdot e^{b}}}\]
      21.0
    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))