\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
Test:
Numeric.SpecFunctions:invIncompleteBetaWorker 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
Bits error versus c
Time: 33.3 s
Input Error: 3.6
Output Error: 2.9
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\frac{2.0}{t \cdot 3.0} + \left(a + \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t} - \left(t \cdot \left(b - c\right)\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}{t \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right)}}} & \text{when } \frac{z \cdot \sqrt{t + a}}{t} \le -inf.0 \\ \frac{x}{{\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\frac{5.0}{6.0} + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(b - c\right)\right)} \cdot y + x} & \text{when } \frac{z \cdot \sqrt{t + a}}{t} \le 2.5343662298162753 \cdot 10^{+304} \\ \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\frac{2.0}{t \cdot 3.0} + \left(a + \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t} - \left(t \cdot \left(b - c\right)\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}{t \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right)}}} & \text{otherwise} \end{cases}\)

    if (/ (* z (sqrt (+ t a))) t) or 2.5343662298162753e+304 < (/ (* z (sqrt (+ t a))) t)

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      16.5
    2. Using strategy rm
      16.5
    3. Applied flip-- to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{red}{\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{blue}{\frac{{\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2}{\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}}}\right)}}\]
      29.7
    4. Applied associate-*r/ to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{red}{\left(b - c\right) \cdot \frac{{\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2}{\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}}}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{\left(b - c\right) \cdot \left({\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2\right)}{\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}}}\right)}}\]
      30.8
    5. Applied frac-sub to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \color{red}{\left(\frac{z \cdot \sqrt{t + a}}{t} - \frac{\left(b - c\right) \cdot \left({\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2\right)}{\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}}\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right) - t \cdot \left(\left(b - c\right) \cdot \left({\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2\right)\right)}{t \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right)}}}}\]
      35.9
    6. Applied simplify to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{red}{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right) - t \cdot \left(\left(b - c\right) \cdot \left({\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2\right)\right)}}{t \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{blue}{\left(\frac{2.0}{t \cdot 3.0} + \left(a + \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t} - \left(t \cdot \left(b - c\right)\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}{t \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right)}}}\]
      12.0

    if (/ (* z (sqrt (+ t a))) t) < 2.5343662298162753e+304

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      0.0
    2. Using strategy rm
      0.0
    3. Applied add-log-exp to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{red}{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)}\right)}}\]
      2.6
    4. Applied add-log-exp to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{red}{\frac{z \cdot \sqrt{t + a}}{t}} - \log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\log \left(e^{\frac{z \cdot \sqrt{t + a}}{t}}\right)} - \log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)\right)}}\]
      12.5
    5. Applied diff-log to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \color{red}{\left(\log \left(e^{\frac{z \cdot \sqrt{t + a}}{t}}\right) - \log \left(e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}}\right)}}}\]
      12.5
    6. Applied taylor to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{0.6666666666666666}{t}\right)}}\right)}}\]
      12.5
    7. Taylor expanded around 0 to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \color{red}{\frac{0.6666666666666666}{t}}\right)}}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \color{blue}{\frac{0.6666666666666666}{t}}\right)}}\right)}}\]
      12.5
    8. Applied simplify to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \log \left(\frac{e^{\frac{z \cdot \sqrt{t + a}}{t}}}{e^{\left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{0.6666666666666666}{t}\right)}}\right)}} \leadsto \frac{x}{{\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\frac{5.0}{6.0} + \left(a - \frac{0.6666666666666666}{t}\right)\right) \cdot \left(b - c\right)\right)} \cdot y + x}\]
      0.4
    9. Applied final simplification
  1. Removed slow pow expressions

Original test:


(lambda ((x default) (y default) (z default) (t default) (a default) (b default) (c default))
  #:name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2"
  (/ x (+ x (* y (exp (* 2.0 (- (/ (* z (sqrt (+ t a))) t) (* (- b c) (- (+ a (/ 5.0 6.0)) (/ 2.0 (* t 3.0)))))))))))