\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
Test:
Numeric.SpecFunctions:logGamma 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
Bits error versus i
Time: 9.4 m
Input Error: 14.4
Output Error: 1.6
Log:
Profile: 🕒
\(\begin{cases} x & \text{when } y \le -59945116.0f0 \\ \frac{\left(27464.7644705 + z \cdot y\right) \cdot \left(y \cdot y\right) + \left(x \cdot {y}^{4} + \left(t + y \cdot 230661.510616\right)\right)}{\left(a \cdot y + b\right) \cdot \left(y \cdot y\right) + \left(i + \left({y}^{4} + y \cdot c\right)\right)} & \text{when } y \le 1.1986274f+10 \\ x & \text{otherwise} \end{cases}\)

    if y < -59945116.0f0 or 1.1986274f+10 < y

    1. Started with
      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
      30.4
    2. Using strategy rm
      30.4
    3. Applied clear-num to get
      \[\color{red}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]
      30.4
    4. Using strategy rm
      30.4
    5. Applied add-cube-cbrt to get
      \[\frac{1}{\color{red}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}} \leadsto \frac{1}{\color{blue}{{\left(\sqrt[3]{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}\right)}^3}}\]
      30.4
    6. Applied taylor to get
      \[\frac{1}{{\left(\sqrt[3]{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}\right)}^3} \leadsto \frac{1}{\frac{1}{x}}\]
      0.2
    7. Taylor expanded around inf to get
      \[\frac{1}{\color{red}{\frac{1}{x}}} \leadsto \frac{1}{\color{blue}{\frac{1}{x}}}\]
      0.2
    8. Applied simplify to get
      \[\frac{1}{\frac{1}{x}} \leadsto x\]
      0

    9. Applied final simplification

    if -59945116.0f0 < y < 1.1986274f+10

    1. Started with
      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
      3.3
    2. Using strategy rm
      3.3
    3. Applied add-cbrt-cube to get
      \[\color{red}{\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}} \leadsto \color{blue}{\sqrt[3]{{\left(\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right)}^3}}\]
      15.7
    4. Applied taylor to get
      \[\sqrt[3]{{\left(\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\right)}^3} \leadsto \sqrt[3]{{\left(\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}\right)}^3}\]
      15.0
    5. Taylor expanded around 0 to get
      \[\sqrt[3]{\color{red}{{\left(\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}\right)}^3}} \leadsto \sqrt[3]{\color{blue}{{\left(\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}\right)}^3}}\]
      15.0
    6. Applied simplify to get
      \[\sqrt[3]{{\left(\frac{230661.510616 \cdot y + \left({y}^{3} \cdot z + \left(t + \left({y}^{4} \cdot x + 27464.7644705 \cdot {y}^2\right)\right)\right)}{{y}^{3} \cdot a + \left(y \cdot c + \left({y}^{4} + \left(i + {y}^2 \cdot b\right)\right)\right)}\right)}^3} \leadsto \frac{\left(\left(27464.7644705 \cdot y\right) \cdot y + \left({y}^{4} \cdot x + t\right)\right) + \left(y \cdot 230661.510616 + {y}^3 \cdot z\right)}{\left(c \cdot y + {y}^3 \cdot a\right) + \left(b \cdot \left(y \cdot y\right) + \left({y}^{4} + i\right)\right)}\]
      2.8

    7. Applied final simplification
    8. Applied simplify to get
      \[\color{red}{\frac{\left(\left(27464.7644705 \cdot y\right) \cdot y + \left({y}^{4} \cdot x + t\right)\right) + \left(y \cdot 230661.510616 + {y}^3 \cdot z\right)}{\left(c \cdot y + {y}^3 \cdot a\right) + \left(b \cdot \left(y \cdot y\right) + \left({y}^{4} + i\right)\right)}} \leadsto \color{blue}{\frac{\left(27464.7644705 + z \cdot y\right) \cdot \left(y \cdot y\right) + \left(x \cdot {y}^{4} + \left(t + y \cdot 230661.510616\right)\right)}{\left(a \cdot y + b\right) \cdot \left(y \cdot y\right) + \left(i + \left({y}^{4} + y \cdot c\right)\right)}}\]
      2.7

  1. Removed slow pow expressions

Original test:


(lambda ((x default) (y default) (z default) (t default) (a default) (b default) (c default) (i default))
  #:name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))