Average Error: 29.8 → 2.0
Time: 28.5s
Precision: binary64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -9.79520177736085 \cdot 10^{+56} \lor \neg \left(z \leq 3.2572397592828936 \cdot 10^{+20}\right):\\ \;\;\;\;x + \frac{y}{\left(0.31942702700572795 + \frac{3.7269864963038164}{z}\right) - \left(0.10203362558171805 \cdot \frac{t}{z \cdot z} + \frac{3.241970391368046}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}{z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right) + a\right) + b}}\\ \end{array}\]
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 -9.79520177736085 \cdot 10^{+56} \lor \neg \left(z \leq 3.2572397592828936 \cdot 10^{+20}\right):\\
\;\;\;\;x + \frac{y}{\left(0.31942702700572795 + \frac{3.7269864963038164}{z}\right) - \left(0.10203362558171805 \cdot \frac{t}{z \cdot z} + \frac{3.241970391368046}{z \cdot z}\right)}\\

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

\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 -9.79520177736085e+56) (not (<= z 3.2572397592828936e+20)))
   (+
    x
    (/
     y
     (-
      (+ 0.31942702700572795 (/ 3.7269864963038164 z))
      (+
       (* 0.10203362558171805 (/ t (* z z)))
       (/ 3.241970391368046 (* z 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 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));
}
↓
double code(double x, double y, double z, double t, double a, double b) {
	double tmp;
	if ((z <= -9.79520177736085e+56) || !(z <= 3.2572397592828936e+20)) {
		tmp = x + (y / ((0.31942702700572795 + (3.7269864963038164 / z)) - ((0.10203362558171805 * (t / (z * z))) + (3.241970391368046 / (z * z)))));
	} else {
		tmp = 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)));
	}
	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

Original29.8
Target0.8
Herbie2.0
\[\begin{array}{l} \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.79520177736085014e56 or 325723975928289362000 < z

    1. Initial program 60.0

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

    3. Applied associate-/l*_binary64_1161757.8

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

    4. Simplified57.8

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

    5. Taylor expanded around inf 3.5

      \[\leadsto x + \frac{y}{\color{blue}{\left(3.7269864963038164 \cdot \frac{1}{z} + 0.31942702700572795\right) - \left(0.10203362558171805 \cdot \frac{t}{{z}^{2}} + 3.241970391368046 \cdot \frac{1}{{z}^{2}}\right)}}\]

    6. Simplified3.5

      \[\leadsto x + \frac{y}{\color{blue}{\left(0.31942702700572795 + \frac{3.7269864963038164}{z}\right) - \left(0.10203362558171805 \cdot \frac{t}{z \cdot z} + \frac{3.241970391368046}{z \cdot z}\right)}}\]

    if -9.79520177736085014e56 < z < 325723975928289362000

    1. Initial program 1.8

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

    3. Applied associate-/l*_binary64_116170.6

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

  4. Final simplification2.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.79520177736085 \cdot 10^{+56} \lor \neg \left(z \leq 3.2572397592828936 \cdot 10^{+20}\right):\\ \;\;\;\;x + \frac{y}{\left(0.31942702700572795 + \frac{3.7269864963038164}{z}\right) - \left(0.10203362558171805 \cdot \frac{t}{z \cdot z} + \frac{3.241970391368046}{z \cdot z}\right)}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}{z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right) + a\right) + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2021043 
(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))))