\[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
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: 29.5 s
Input Error: 6.0
Output Error: 1.1
Log: ⚲
Profile: 🕒
\(\begin{cases} \frac{x}{(\left({\left(e^{2.0}\right)}^{\left((\left(\frac{z}{t}\right) * \left(\sqrt{t + a}\right) + \left(\frac{0.6666666666666666}{t} \cdot \left(b - c\right)\right))_* - b \cdot 0.8333333333333334\right)}\right) * y + x)_*} & \text{when } \frac{z \cdot \sqrt{t + a}}{t} \le -2.7731225f-28 \\ \frac{x}{(\left({\left(e^{2.0}\right)}^{\left((a * \left(c - b\right) + \left(c \cdot 0.8333333333333334\right))_*\right)}\right) * y + x)_*} & \text{when } \frac{z \cdot \sqrt{t + a}}{t} \le 5.632792f-22 \\ \frac{x}{(\left({\left(e^{2.0}\right)}^{\left((\left(\frac{z}{t}\right) * \left(\sqrt{t + a}\right) + \left(\frac{0.6666666666666666}{t} \cdot \left(b - c\right)\right))_* - b \cdot 0.8333333333333334\right)}\right) * y + x)_*} & \text{otherwise} \end{cases}\)

    if (/ (* z (sqrt (+ t a))) t) < -2.7731225f-28 or 5.632792f-22 < (/ (* z (sqrt (+ t a))) t)

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      6.2
    2. Applied simplify to get
      \[\color{red}{\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}} \leadsto \color{blue}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*}}\]
      6.6
    3. Applied taylor to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(0.8333333333333334 \cdot b + 0.6666666666666666 \cdot \frac{c}{t}\right) - 0.6666666666666666 \cdot \frac{b}{t}\right)\right)}\right) * y + x)_*}\]
      1.8
    4. Taylor expanded around 0 to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \color{red}{\left(\left(0.8333333333333334 \cdot b + 0.6666666666666666 \cdot \frac{c}{t}\right) - 0.6666666666666666 \cdot \frac{b}{t}\right)}\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \color{blue}{\left(\left(0.8333333333333334 \cdot b + 0.6666666666666666 \cdot \frac{c}{t}\right) - 0.6666666666666666 \cdot \frac{b}{t}\right)}\right)}\right) * y + x)_*}\]
      1.8
    5. Applied simplify to get
      \[\color{red}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(0.8333333333333334 \cdot b + 0.6666666666666666 \cdot \frac{c}{t}\right) - 0.6666666666666666 \cdot \frac{b}{t}\right)\right)}\right) * y + x)_*}} \leadsto \color{blue}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left((\left(\frac{z}{t}\right) * \left(\sqrt{t + a}\right) + \left(\frac{0.6666666666666666}{t} \cdot \left(b - c\right)\right))_* - b \cdot 0.8333333333333334\right)}\right) * y + x)_*}}\]
      1.3

    if -2.7731225f-28 < (/ (* z (sqrt (+ t a))) t) < 5.632792f-22

    1. Started with
      \[\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}\]
      5.3
    2. Applied simplify to get
      \[\color{red}{\frac{x}{x + y \cdot e^{2.0 \cdot \left(\frac{z \cdot \sqrt{t + a}}{t} - \left(b - c\right) \cdot \left(\left(a + \frac{5.0}{6.0}\right) - \frac{2.0}{t \cdot 3.0}\right)\right)}}} \leadsto \color{blue}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*}}\]
      5.4
    3. Applied taylor to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\frac{\sqrt{a + t}}{\frac{t}{z}} - \left(\left(\frac{5.0}{6.0} + a\right) - \frac{2.0}{3.0 \cdot t}\right) \cdot \left(b - c\right)\right)}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\left(0.8333333333333334 \cdot c + c \cdot a\right) - b \cdot a\right)}\right) * y + x)_*}\]
      0.4
    4. Taylor expanded around inf to get
      \[\frac{x}{(\left({\left(e^{2.0}\right)}^{\color{red}{\left(\left(0.8333333333333334 \cdot c + c \cdot a\right) - b \cdot a\right)}}\right) * y + x)_*} \leadsto \frac{x}{(\left({\left(e^{2.0}\right)}^{\color{blue}{\left(\left(0.8333333333333334 \cdot c + c \cdot a\right) - b \cdot a\right)}}\right) * y + x)_*}\]
      0.4
    5. Applied simplify to get
      \[\color{red}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left(\left(0.8333333333333334 \cdot c + c \cdot a\right) - b \cdot a\right)}\right) * y + x)_*}} \leadsto \color{blue}{\frac{x}{(\left({\left(e^{2.0}\right)}^{\left((a * \left(c - b\right) + \left(c \cdot 0.8333333333333334\right))_*\right)}\right) * y + x)_*}}\]
      0.1
  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)))))))))))