Average Error: 29.2 → 1.1
Time: 5.1s
Precision: binary64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.63969886111990152 \cdot 10^{60} \lor \neg \left(z \le 122686767782678480\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t}{z} \cdot \frac{y}{z}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}
↓
\begin{array}{l}
\mathbf{if}\;z \le -1.63969886111990152 \cdot 10^{60} \lor \neg \left(z \le 122686767782678480\right):\\
\;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t}{z} \cdot \frac{y}{z}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\

\mathbf{else}:\\
\;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\

\end{array}
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (x + ((double) (((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 VAR;
	if (((z <= -1.6396988611199015e+60) || !(z <= 1.2268676778267848e+17))) {
		VAR = ((double) (x + ((double) (((double) (((double) (3.13060547623 * y)) + ((double) (((double) (t / z)) * ((double) (y / z)))))) - ((double) (36.527041698806414 * ((double) (y / z))))))));
	} else {
		VAR = ((double) (x + ((double) (y / ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (z + 15.234687407)) * z)) + 31.4690115749)) * z)) + 11.9400905721)) * z)) + 0.607771387771)) / ((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (z * 3.13060547623)) + 11.1667541262)) * z)) + t)) * z)) + a)) * z)) + b))))))));
	}
	return VAR;
}

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

Original29.2
Target0.9
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -1.63969886111990152e60 or 122686767782678480 < z

    1. Initial program 59.6

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]

    2. Taylor expanded around inf 8.8

      \[\leadsto x + \color{blue}{\left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)}\]
    3. Using strategy rm

    4. Applied add-sqr-sqrt34.4

      \[\leadsto x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{\color{blue}{\left(\sqrt{z} \cdot \sqrt{z}\right)}}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\]

    5. Applied unpow-prod-down34.4

      \[\leadsto x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{\color{blue}{{\left(\sqrt{z}\right)}^{2} \cdot {\left(\sqrt{z}\right)}^{2}}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\]

    6. Applied times-frac30.5

      \[\leadsto x + \left(\left(3.13060547622999996 \cdot y + \color{blue}{\frac{t}{{\left(\sqrt{z}\right)}^{2}} \cdot \frac{y}{{\left(\sqrt{z}\right)}^{2}}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\]

    7. Simplified30.5

      \[\leadsto x + \left(\left(3.13060547622999996 \cdot y + \color{blue}{\frac{t}{z}} \cdot \frac{y}{{\left(\sqrt{z}\right)}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\]

    8. Simplified1.4

      \[\leadsto x + \left(\left(3.13060547622999996 \cdot y + \frac{t}{z} \cdot \color{blue}{\frac{y}{z}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\]

    if -1.63969886111990152e60 < z < 122686767782678480

    1. Initial program 2.1

      \[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
    2. Using strategy rm

    3. Applied associate-/l*0.7

      \[\leadsto x + \color{blue}{\frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.63969886111990152 \cdot 10^{60} \lor \neg \left(z \le 122686767782678480\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t}{z} \cdot \frac{y}{z}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020153 
(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))))