\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
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: 28.9 s
Input Error: 4.0
Output Error: 1.4
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}} & \text{when } t \le -7.6629611465298 \cdot 10^{-58} \\ \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left({t}^2 \cdot 3.0\right)}}} & \text{when } t \le 1.7070708274716628 \cdot 10^{-171} \\ \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}} & \text{otherwise} \end{cases}\)

    if t < -7.6629611465298e-58 or 1.7070708274716628e-171 < t

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      2.8
    2. Using strategy rm
      2.8
    3. Applied associate-/l* to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{red}{\frac{z \cdot \sqrt{t + a}}{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\frac{t}{\sqrt{t + a}}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      0.6

    if -7.6629611465298e-58 < t < 1.7070708274716628e-171

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      7.1
    2. Using strategy rm
      7.1
    3. Applied flip-+ to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{red}{\left(a + \frac{5.0}{6.0}\right)} - \frac{2.0}{t \cdot 3.0}\right)\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\color{blue}{\frac{{a}^2 - {\left(\frac{5.0}{6.0}\right)}^2}{a - \frac{5.0}{6.0}}} - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      10.9
    4. Applied frac-sub to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{red}{\left(\frac{{a}^2 - {\left(\frac{5.0}{6.0}\right)}^2}{a - \frac{5.0}{6.0}} - \frac{2.0}{t \cdot 3.0}\right)}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{blue}{\frac{\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]
      10.9
    5. Applied associate-*r/ to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{red}{\left(b - c\right) \cdot \frac{\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}}\right)}}\]
      11.0
    6. Applied frac-sub to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \color{red}{\left(\frac{z \cdot \sqrt{t + a}}{t} - \frac{\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)}{\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)}\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}}\]
      8.7
    7. Applied simplify to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{red}{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right) - t \cdot \left(\left(b - c\right) \cdot \left(\left({a}^2 - {\left(\frac{5.0}{6.0}\right)}^2\right) \cdot \left(t \cdot 3.0\right) - \left(a - \frac{5.0}{6.0}\right) \cdot 2.0\right)\right)}}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{blue}{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}\]
      3.3
    8. Applied simplify to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}{\color{red}{t \cdot \left(\left(a - \frac{5.0}{6.0}\right) \cdot \left(t \cdot 3.0\right)\right)}}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\left(3.0 \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t}\right) - \left(\left(\left(b - c\right) \cdot t\right) \cdot \left(a - \frac{5.0}{6.0}\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(a + \frac{5.0}{6.0}\right) - 2.0\right)}{\color{blue}{\left(a - \frac{5.0}{6.0}\right) \cdot \left({t}^2 \cdot 3.0\right)}}}}\]
      3.3
  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)))))))))))