Average Error: 29.1 → 1.1
Time: 8.9s
Precision: binary64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -3.3456124168296954 \cdot 10^{+40} \lor \neg \left(z \leq 4.379279834858161 \cdot 10^{+52}\right):\\ \;\;\;\;x + y \cdot \left(\left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \cdot \left(z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right) + a\right) + b\right)\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}
↓
\begin{array}{l}
\mathbf{if}\;z \leq -3.3456124168296954 \cdot 10^{+40} \lor \neg \left(z \leq 4.379279834858161 \cdot 10^{+52}\right):\\
\;\;\;\;x + y \cdot \left(\left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \cdot \left(z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right) + a\right) + b\right)\\

\end{array}
(FPCore (x y z t a b)
 :precision binary64
 (+
  x
  (/
   (*
    y
    (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b))
   (+
    (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z)
    0.607771387771))))
↓
(FPCore (x y z t a b)
 :precision binary64
 (if (or (<= z -3.3456124168296954e+40) (not (<= z 4.379279834858161e+52)))
   (+ x (* y (- (+ 3.13060547623 (/ t (* z z))) (/ 36.527041698806414 z))))
   (+
    x
    (*
     (/
      y
      (+
       (* z (+ (* z (+ (* z (+ z 15.234687407)) 31.4690115749)) 11.9400905721))
       0.607771387771))
     (+
      (* z (+ (* z (+ t (* z (+ (* z 3.13060547623) 11.1667541262)))) a))
      b)))))
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (x + (((double) (y * ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (z * 3.13060547623)) + 11.1667541262)) * z)) + t)) * z)) + a)) * z)) + b)))) / ((double) (((double) (((double) (((double) (((double) (((double) (((double) (z + 15.234687407)) * z)) + 31.4690115749)) * z)) + 11.9400905721)) * z)) + 0.607771387771)))));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if (((z <= -3.3456124168296954e+40) || !(z <= 4.379279834858161e+52))) {
		tmp = ((double) (x + ((double) (y * ((double) (((double) (3.13060547623 + (t / ((double) (z * z))))) - (36.527041698806414 / z)))))));
	} else {
		tmp = ((double) (x + ((double) ((y / ((double) (((double) (z * ((double) (((double) (z * ((double) (((double) (z * ((double) (z + 15.234687407)))) + 31.4690115749)))) + 11.9400905721)))) + 0.607771387771))) * ((double) (((double) (z * ((double) (((double) (z * ((double) (t + ((double) (z * ((double) (((double) (z * 3.13060547623)) + 11.1667541262)))))))) + a)))) + b))))));
	}
	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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original29.1
Target1.0
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.3456124168296954e40 or 4.37927983485816076e52 < z

    1. Initial program 60.9

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied *-un-lft-identity_binary6460.9

      \[\leadsto x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\color{blue}{1 \cdot \left(\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771\right)}}\]

    4. Applied times-frac_binary6458.6

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}}\]

    5. Simplified58.6

      \[\leadsto x + \color{blue}{y} \cdot \frac{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]

    6. Simplified58.6

      \[\leadsto x + y \cdot \color{blue}{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}}\]

    7. Taylor expanded around inf 1.0

      \[\leadsto x + y \cdot \color{blue}{\left(\left(\frac{t}{{z}^{2}} + 3.13060547623\right) - 36.527041698806414 \cdot \frac{1}{z}\right)}\]

    8. Simplified1.0

      \[\leadsto x + y \cdot \color{blue}{\left(\left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414}{z}\right)}\]

    if -3.3456124168296954e40 < z < 4.37927983485816076e52

    1. Initial program 2.2

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
    2. Using strategy rm

    3. Applied associate-/l*_binary640.8

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]

    4. Simplified0.8

      \[\leadsto x + \frac{y}{\color{blue}{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}{z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b}}}\]
    5. Using strategy rm

    6. Applied associate-/r/_binary641.2

      \[\leadsto x + \color{blue}{\frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \cdot \left(z \cdot \left(z \cdot \left(z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right) + t\right) + a\right) + b\right)}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3456124168296954 \cdot 10^{+40} \lor \neg \left(z \leq 4.379279834858161 \cdot 10^{+52}\right):\\ \;\;\;\;x + y \cdot \left(\left(3.13060547623 + \frac{t}{z \cdot z}\right) - \frac{36.527041698806414}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771} \cdot \left(z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right) + a\right) + b\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2020210 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"
  :precision binary64

  :herbie-target
  (if (< z -6.499344996252632e+53) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0))) (if (< z 7.066965436914287e+59) (+ x (/ y (/ (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771) (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)))) (+ x (* (+ (- 3.13060547623 (/ 36.527041698806414 z)) (/ t (* z z))) (/ y 1.0)))))

  (+ x (/ (* y (+ (* (+ (* (+ (* (+ (* z 3.13060547623) 11.1667541262) z) t) z) a) z) b)) (+ (* (+ (* (+ (* (+ z 15.234687407) z) 31.4690115749) z) 11.9400905721) z) 0.607771387771))))