Average Error: 29.6 → 1.1
Time: 16.5s
Precision: binary64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.1564103734550455 \cdot 10^{28} \lor \neg \left(z \le 1.3818885668958042 \cdot 10^{37}\right):\\ \;\;\;\;x + y \cdot \left(3.13060547622999996 + \left(\frac{t}{z \cdot z} - \frac{36.527041698806414}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot \left(t + \sqrt[3]{{\left(z \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right)}^{3}}\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}\\ \end{array}\]
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 -1.1564103734550455 \cdot 10^{28} \lor \neg \left(z \le 1.3818885668958042 \cdot 10^{37}\right):\\
\;\;\;\;x + y \cdot \left(3.13060547622999996 + \left(\frac{t}{z \cdot z} - \frac{36.527041698806414}{z}\right)\right)\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot \left(t + \sqrt[3]{{\left(z \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right)}^{3}}\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}\\

\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 <= -1.1564103734550455e+28) || !(z <= 1.3818885668958042e+37))) {
		VAR = ((double) (x + ((double) (y * ((double) (3.13060547623 + ((double) (((double) (t / ((double) (z * z)))) - ((double) (36.527041698806414 / z))))))))));
	} else {
		VAR = ((double) (x + ((double) (y * ((double) (((double) (((double) (z * ((double) (((double) (z * ((double) (t + ((double) cbrt(((double) pow(((double) (z * ((double) (((double) (z * 3.13060547623)) + 11.1667541262)))), 3.0)))))))) + a)))) + b)) / ((double) (((double) (z * ((double) (((double) (z * ((double) (((double) (z * ((double) (z + 15.234687407)))) + 31.4690115749)))) + 11.9400905721)))) + 0.607771387771))))))));
	}
	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

Original29.6
Target1.0
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 < -1.1564103734550455e28 or 1.3818885668958042e37 < z

    1. Initial program 59.3

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

    2. Simplified56.7

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

    3. Taylor expanded around inf 1.6

      \[\leadsto x + y \cdot \color{blue}{\left(\left(\frac{t}{{z}^{2}} + 3.13060547622999996\right) - 36.527041698806414 \cdot \frac{1}{z}\right)}\]

    4. Simplified1.6

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

    if -1.1564103734550455e28 < z < 1.3818885668958042e37

    1. Initial program 1.3

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

    2. Simplified0.6

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

    4. Applied add-cbrt-cube0.6

      \[\leadsto x + y \cdot \frac{z \cdot \left(z \cdot \left(z \cdot \color{blue}{\sqrt[3]{\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right) \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)}} + t\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}\]

    5. Applied add-cbrt-cube0.6

      \[\leadsto x + y \cdot \frac{z \cdot \left(z \cdot \left(\color{blue}{\sqrt[3]{\left(z \cdot z\right) \cdot z}} \cdot \sqrt[3]{\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right) \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)} + t\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}\]

    6. Applied cbrt-unprod0.6

      \[\leadsto x + y \cdot \frac{z \cdot \left(z \cdot \left(\color{blue}{\sqrt[3]{\left(\left(z \cdot z\right) \cdot z\right) \cdot \left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right) \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right)}} + t\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}\]

    7. Simplified0.6

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.1564103734550455 \cdot 10^{28} \lor \neg \left(z \le 1.3818885668958042 \cdot 10^{37}\right):\\ \;\;\;\;x + y \cdot \left(3.13060547622999996 + \left(\frac{t}{z \cdot z} - \frac{36.527041698806414}{z}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z \cdot \left(z \cdot \left(t + \sqrt[3]{{\left(z \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right)}^{3}}\right) + a\right) + b}{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}\\ \end{array}\]

Reproduce

herbie shell --seed 2020179 
(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))))