\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
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: 28.8 s
Input Error: 26.4
Output Error: 1.9
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{x}{(\left({\left(e^{2.0}\right)}^{\left((a * \left(c - b\right) + \left(c \cdot 0.8333333333333334\right))_*\right)}\right) * y + x)_*} & \text{when } t \le -1.1387608974707574 \cdot 10^{-103} \\ \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t} \cdot \left(\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)\right) - \left(\frac{b - c}{\frac{z}{t}} \cdot \left(\frac{5.0}{6.0} - a\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(\frac{5.0}{6.0} + a\right) - 2.0\right)}{\frac{t}{z} \cdot \left(\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)\right)}\right)}\right) * y + x)_*} & \text{when } t \le 15879525.552212397 \\ \frac{x}{(\left({\left(e^{2.0}\right)}^{\left((\left(\frac{z}{t}\right) * \left(\sqrt{t + a}\right) + \left(\left(0.8333333333333334 + a\right) \cdot c\right))_* - b \cdot a\right)}\right) * y + x)_*} & \text{otherwise} \end{cases}\)

    if t < -1.1387608974707574e-103

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      54.1
    2. Applied simplify to get
      \[\color{red}{\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}} \leadsto \color{blue}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*}}\]
      53.8
    3. Applied taylor to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\left(0.8333333333333334 \cdot c + c \cdot a\right) - b \cdot a\right)}\right) * y + x)_*}\]
      1.3
    4. Taylor expanded around inf to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\color{red}{\left(\left(0.8333333333333334 \cdot c + c \cdot a\right) - b \cdot a\right)}}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\color{blue}{\left(\left(0.8333333333333334 \cdot c + c \cdot a\right) - b \cdot a\right)}}\right) * y + x)_*}\]
      1.3
    5. Applied simplify to get
      \[\color{red}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\left(0.8333333333333334 \cdot c + c \cdot a\right) - b \cdot a\right)}\right) * y + x)_*}} \leadsto \color{blue}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left((a * \left(c - b\right) + \left(c \cdot 0.8333333333333334\right))_*\right)}\right) * y + x)_*}}\]
      0.0

    if -1.1387608974707574e-103 < t < 15879525.552212397

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      4.5
    2. Applied simplify to get
      \[\color{red}{\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}} \leadsto \color{blue}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*}}\]
      4.9
    3. Using strategy rm
      4.9
    4. Applied flip-+ to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\color{red}{\left(\frac{5.0}{6.0} + a\right)} - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\color{blue}{\frac{{\left(\frac{5.0}{6.0}\right)}^2 - {a}^2}{\frac{5.0}{6.0} - a}} - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*}\]
      7.7
    5. Applied frac-sub to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \color{red}{\left(\frac{{\left(\frac{5.0}{6.0}\right)}^2 - {a}^2}{\frac{5.0}{6.0} - a} - \frac{2.0}{3.0 \cdot t}\right)} \cdot \left(b - c\right)\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \color{blue}{\frac{\left({\left(\frac{5.0}{6.0}\right)}^2 - {a}^2\right) \cdot \left(3.0 \cdot t\right) - \left(\frac{5.0}{6.0} - a\right) \cdot 2.0}{\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)}} \cdot \left(b - c\right)\right)}\right) * y + x)_*}\]
      7.8
    6. Applied associate-*l/ to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \color{red}{\frac{\left({\left(\frac{5.0}{6.0}\right)}^2 - {a}^2\right) \cdot \left(3.0 \cdot t\right) - \left(\frac{5.0}{6.0} - a\right) \cdot 2.0}{\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)} \cdot \left(b - c\right)}\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \color{blue}{\frac{\left(\left({\left(\frac{5.0}{6.0}\right)}^2 - {a}^2\right) \cdot \left(3.0 \cdot t\right) - \left(\frac{5.0}{6.0} - a\right) \cdot 2.0\right) \cdot \left(b - c\right)}{\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)}}\right)}\right) * y + x)_*}\]
      7.8
    7. Applied frac-sub to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\color{red}{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \frac{\left(\left({\left(\frac{5.0}{6.0}\right)}^2 - {a}^2\right) \cdot \left(3.0 \cdot t\right) - \left(\frac{5.0}{6.0} - a\right) \cdot 2.0\right) \cdot \left(b - c\right)}{\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)}\right)}}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\color{blue}{\left(\frac{\sqrt{a + t} \cdot \left(\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)\right) - \frac{t}{z} \cdot \left(\left(\left({\left(\frac{5.0}{6.0}\right)}^2 - {a}^2\right) \cdot \left(3.0 \cdot t\right) - \left(\frac{5.0}{6.0} - a\right) \cdot 2.0\right) \cdot \left(b - c\right)\right)}{\frac{t}{z} \cdot \left(\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)\right)}\right)}}\right) * y + x)_*}\]
      11.2
    8. Applied simplify to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\color{red}{\sqrt{a + t} \cdot \left(\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)\right) - \frac{t}{z} \cdot \left(\left(\left({\left(\frac{5.0}{6.0}\right)}^2 - {a}^2\right) \cdot \left(3.0 \cdot t\right) - \left(\frac{5.0}{6.0} - a\right) \cdot 2.0\right) \cdot \left(b - c\right)\right)}}{\frac{t}{z} \cdot \left(\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)\right)}\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\color{blue}{\sqrt{a + t} \cdot \left(\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)\right) - \left(\frac{b - c}{\frac{z}{t}} \cdot \left(\frac{5.0}{6.0} - a\right)\right) \cdot \left(\left(3.0 \cdot t\right) \cdot \left(\frac{5.0}{6.0} + a\right) - 2.0\right)}}{\frac{t}{z} \cdot \left(\left(\frac{5.0}{6.0} - a\right) \cdot \left(3.0 \cdot t\right)\right)}\right)}\right) * y + x)_*}\]
      5.3

    if 15879525.552212397 < t

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      8.1
    2. Applied simplify to get
      \[\color{red}{\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}} \leadsto \color{blue}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*}}\]
      6.4
    3. Applied taylor to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(b \cdot a - \left(0.8333333333333334 \cdot c + c \cdot a\right)\right)\right)}\right) * y + x)_*}\]
      1.3
    4. Taylor expanded around inf to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \color{red}{\left(b \cdot a - \left(0.8333333333333334 \cdot c + c \cdot a\right)\right)}\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \color{blue}{\left(b \cdot a - \left(0.8333333333333334 \cdot c + c \cdot a\right)\right)}\right)}\right) * y + x)_*}\]
      1.3
    5. Applied simplify to get
      \[\color{red}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(b \cdot a - \left(0.8333333333333334 \cdot c + c \cdot a\right)\right)\right)}\right) * y + x)_*}} \leadsto \color{blue}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{t + a}}{\frac{t}{z}} - \left(a \cdot b - c \cdot \left(0.8333333333333334 + a\right)\right)\right)}\right) * y + x)_*}}\]
      1.3
    6. Applied simplify to get
      \[\frac{x}{\color{red}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{t + a}}{\frac{t}{z}} - \left(a \cdot b - c \cdot \left(0.8333333333333334 + a\right)\right)\right)}\right) * y + x)_*}} \leadsto \frac{x}{\color{blue}{(\left({\left(e^{2.0}\right)}^{\left((\left(\frac{z}{t}\right) * \left(\sqrt{t + a}\right) + \left(\left(0.8333333333333334 + a\right) \cdot c\right))_* - b \cdot a\right)}\right) * y + x)_*}}\]
      1.2
  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)))))))))))