Average Error: 30.2 → 1.2
Time: 7.0s
Precision: binary64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -7.60724900900460108 \cdot 10^{60} \lor \neg \left(z \le 4.5268517375082202 \cdot 10^{55}\right):\\ \;\;\;\;y \cdot \left(\frac{t}{z \cdot z} + 3.13060547622999996\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\frac{z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right) + a\right) + b}{\sqrt[3]{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004} \cdot \sqrt[3]{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}}}{\sqrt[3]{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}}\\ \end{array}\]
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 -7.60724900900460108 \cdot 10^{60} \lor \neg \left(z \le 4.5268517375082202 \cdot 10^{55}\right):\\
\;\;\;\;y \cdot \left(\frac{t}{z \cdot z} + 3.13060547622999996\right) + x\\

\mathbf{else}:\\
\;\;\;\;x + y \cdot \frac{\frac{z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right) + a\right) + b}{\sqrt[3]{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004} \cdot \sqrt[3]{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}}}{\sqrt[3]{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) (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 <= -7.607249009004601e+60) || !(z <= 4.52685173750822e+55))) {
		VAR = ((double) (((double) (y * ((double) ((t / ((double) (z * z))) + 3.13060547623)))) + x));
	} else {
		VAR = ((double) (x + ((double) (y * ((((double) (((double) (z * ((double) (((double) (z * ((double) (t + ((double) (z * ((double) (((double) (z * 3.13060547623)) + 11.1667541262)))))))) + a)))) + b)) / ((double) (((double) cbrt(((double) (((double) (z * ((double) (((double) (z * ((double) (((double) (z * ((double) (z + 15.234687407)))) + 31.4690115749)))) + 11.9400905721)))) + 0.607771387771)))) * ((double) cbrt(((double) (((double) (z * ((double) (((double) (z * ((double) (((double) (z * ((double) (z + 15.234687407)))) + 31.4690115749)))) + 11.9400905721)))) + 0.607771387771))))))) / ((double) cbrt(((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

Original30.2
Target1.1
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -7.60724900900460108e60 or 4.5268517375082202e55 < z

    1. Initial program 62.3

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

    2. Simplified60.5

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

    3. Taylor expanded around inf 8.4

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

    4. Simplified0.7

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

    5. Taylor expanded around inf 8.4

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

    6. Simplified0.5

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

    if -7.60724900900460108e60 < z < 4.5268517375082202e55

    1. Initial program 3.4

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

    2. Simplified1.5

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

    4. Applied add-cube-cbrt1.6

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

    5. Applied associate-/r*1.7

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -7.60724900900460108 \cdot 10^{60} \lor \neg \left(z \le 4.5268517375082202 \cdot 10^{55}\right):\\ \;\;\;\;y \cdot \left(\frac{t}{z \cdot z} + 3.13060547622999996\right) + x\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{\frac{z \cdot \left(z \cdot \left(t + z \cdot \left(z \cdot 3.13060547622999996 + 11.166754126200001\right)\right) + a\right) + b}{\sqrt[3]{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004} \cdot \sqrt[3]{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}}}{\sqrt[3]{z \cdot \left(z \cdot \left(z \cdot \left(z + 15.234687406999999\right) + 31.469011574900001\right) + 11.940090572100001\right) + 0.60777138777100004}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020182 
(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))))