\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
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: 47.5 s
Input Error: 3.8
Output Error: 2.6
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\left(\frac{2.0}{t \cdot 3.0} + \left(a + \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t} - \left(t \cdot \left(b - c\right)\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}{t \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right)}}} & \text{when } t \le 2.0009290028352183 \cdot 10^{-168} \\ \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z}{\frac{t}{\sqrt{t + a}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}} & \text{otherwise} \end{cases}\)

    if t < 2.0009290028352183e-168

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      6.5
    2. Using strategy rm
      6.5
    3. Applied flip-- to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{red}{\left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \color{blue}{\frac{{\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2}{\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}}}\right)}}\]
      18.0
    4. Applied associate-*r/ to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{red}{\left(b - c\right) \cdot \frac{{\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2}{\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}}}\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \color{blue}{\frac{\left(b - c\right) \cdot \left({\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2\right)}{\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}}}\right)}}\]
      18.4
    5. Applied frac-sub to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \color{red}{\left(\frac{z \cdot \sqrt{t + a}}{t} - \frac{\left(b - c\right) \cdot \left({\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2\right)}{\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}}\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \color{blue}{\frac{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right) - t \cdot \left(\left(b - c\right) \cdot \left({\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2\right)\right)}{t \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right)}}}}\]
      23.7
    6. Applied simplify to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{red}{\left(z \cdot \sqrt{t + a}\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right) - t \cdot \left(\left(b - c\right) \cdot \left({\left(a + \frac{5.0}{6.0}\right)}^2 - {\left(\frac{2.0}{t \cdot 3.0}\right)}^2\right)\right)}}{t \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right)}}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \frac{\color{blue}{\left(\frac{2.0}{t \cdot 3.0} + \left(a + \frac{5.0}{6.0}\right)\right) \cdot \left(z \cdot \sqrt{a + t} - \left(t \cdot \left(b - c\right)\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}{t \cdot \left(\left(a + \frac{5.0}{6.0}\right) + \frac{2.0}{t \cdot 3.0}\right)}}}\]
      5.9

    if 2.0009290028352183e-168 < t

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      2.3
    2. Using strategy rm
      2.3
    3. Applied associate-/l* to get
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{red}{\frac{z \cdot \sqrt{t + a}}{t}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}} \leadsto \frac{x}{x + y \cdot e^{2.0 \cdot \left(\color{blue}{\frac{z}{\frac{t}{\sqrt{t + a}}}} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      0.7
  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)))))))))))