Average Error: 29.5 → 1.0
Time: 10.7s
Precision: binary64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \leq -9.197408578091303 \cdot 10^{+42} \lor \neg \left(z \leq 2.3971068713810006 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) + -36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}{z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right) + a\right) + b}}\\ \end{array}\]
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 -9.197408578091303 \cdot 10^{+42} \lor \neg \left(z \leq 2.3971068713810006 \cdot 10^{+36}\right):\\
\;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) + -36.527041698806414 \cdot \frac{y}{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 -9.197408578091303e+42) (not (<= z 2.3971068713810006e+36)))
   (+
    x
    (+ (* y (+ (/ t (* z z)) 3.13060547623)) (* -36.527041698806414 (/ y 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 <= -9.197408578091303e+42) || !(z <= 2.3971068713810006e+36)) {
		tmp = x + ((y * ((t / (z * z)) + 3.13060547623)) + (-36.527041698806414 * (y / 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

Original29.5
Target1.0
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;z < -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z < 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -9.1974085780913032e42 or 2.397106871381001e36 < z

    1. Initial program 60.4

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

    2. Taylor expanded around inf 8.6

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

    3. Simplified1.4

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

    5. Applied distribute-rgt-in_binary641.4

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

    6. Applied associate-+r+_binary641.4

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

    7. Simplified1.3

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

    if -9.1974085780913032e42 < z < 2.397106871381001e36

    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*_binary640.7

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

    4. Simplified0.7

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

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -9.197408578091303 \cdot 10^{+42} \lor \neg \left(z \leq 2.3971068713810006 \cdot 10^{+36}\right):\\ \;\;\;\;x + \left(y \cdot \left(\frac{t}{z \cdot z} + 3.13060547623\right) + -36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687407\right) + 31.4690115749\right) + 11.9400905721\right) + 0.607771387771}{z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547623 + 11.1667541262\right)\right) + a\right) + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020253 
(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))))