Average Error: 28.8 → 11.1
Time: 1.0min
Precision: binary64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \leq -5.95739283321287 \cdot 10^{+61} \lor \neg \left(y \leq 1.969901205390635 \cdot 10^{+54}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(z + y \cdot x\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array}\]
\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}
↓
\begin{array}{l}
\mathbf{if}\;y \leq -5.95739283321287 \cdot 10^{+61} \lor \neg \left(y \leq 1.969901205390635 \cdot 10^{+54}\right):\\
\;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\

\mathbf{else}:\\
\;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(z + y \cdot x\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\

\end{array}
(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
↓
(FPCore (x y z t a b c i)
 :precision binary64
 (if (or (<= y -5.95739283321287e+61) (not (<= y 1.969901205390635e+54)))
   (- (+ (/ z y) x) (/ (* x a) y))
   (/
    (+ (* y (+ (* y (+ (* y (+ z (* y x))) 27464.7644705)) 230661.510616)) t)
    (+ (* y (+ (* y (+ (* y (+ y a)) b)) c)) i))))
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double tmp;
	if ((y <= -5.95739283321287e+61) || !(y <= 1.969901205390635e+54)) {
		tmp = ((z / y) + x) - ((x * a) / y);
	} else {
		tmp = ((y * ((y * ((y * (z + (y * x))) + 27464.7644705)) + 230661.510616)) + t) / ((y * ((y * ((y * (y + a)) + b)) + c)) + i);
	}
	return tmp;
}

Error

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if y < -5.95739283321286985e61 or 1.96990120539063488e54 < y

    1. Initial program 62.5

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

    2. Taylor expanded around inf 19.9

      \[\leadsto \color{blue}{\left(\frac{z}{y} + x\right) - \frac{a \cdot x}{y}}\]

    if -5.95739283321286985e61 < y < 1.96990120539063488e54

    1. Initial program 4.7

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification11.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.95739283321287 \cdot 10^{+61} \lor \neg \left(y \leq 1.969901205390635 \cdot 10^{+54}\right):\\ \;\;\;\;\left(\frac{z}{y} + x\right) - \frac{x \cdot a}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{y \cdot \left(y \cdot \left(y \cdot \left(z + y \cdot x\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}\\ \end{array}\]

Reproduce

herbie shell --seed 2021044 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))