Average Error: 30.0 → 4.2
Time: 7.3s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -2.5655762721640628 \cdot 10^{51} \lor \neg \left(z \le 4.0260214363493681 \cdot 10^{53}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\frac{\left({\left(z \cdot 3.13060547622999996\right)}^{3} + {11.166754126200001}^{3}\right) \cdot z}{\left(z \cdot 3.13060547622999996\right) \cdot \left(z \cdot 3.13060547622999996\right) + \left(11.166754126200001 \cdot 11.166754126200001 - \left(z \cdot 3.13060547622999996\right) \cdot 11.166754126200001\right)} + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]
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 -2.5655762721640628 \cdot 10^{51} \lor \neg \left(z \le 4.0260214363493681 \cdot 10^{53}\right):\\
\;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\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(\frac{\left({\left(z \cdot 3.13060547622999996\right)}^{3} + {11.166754126200001}^{3}\right) \cdot z}{\left(z \cdot 3.13060547622999996\right) \cdot \left(z \cdot 3.13060547622999996\right) + \left(11.166754126200001 \cdot 11.166754126200001 - \left(z \cdot 3.13060547622999996\right) \cdot 11.166754126200001\right)} + 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 (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 VAR;
	if (((z <= -2.5655762721640628e+51) || !(z <= 4.026021436349368e+53))) {
		VAR = (x + (((3.13060547623 * y) + ((t * y) / pow(z, 2.0))) - (36.527041698806414 * (y / z))));
	} else {
		VAR = (x + (y / ((((((((z + 15.234687407) * z) + 31.4690115749) * z) + 11.9400905721) * z) + 0.607771387771) / ((((((((pow((z * 3.13060547623), 3.0) + pow(11.1667541262, 3.0)) * z) / (((z * 3.13060547623) * (z * 3.13060547623)) + ((11.1667541262 * 11.1667541262) - ((z * 3.13060547623) * 11.1667541262)))) + 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

Original30.0
Target1.0
Herbie4.2
\[\begin{array}{l} \mathbf{if}\;z \lt -6.4993449962526318 \cdot 10^{53}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.0669654369142868 \cdot 10^{59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\left(z \cdot 3.13060547622999996 + 11.166754126200001\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547622999996 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -2.5655762721640628e+51 or 4.026021436349368e+53 < z

    1. Initial program 61.8

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

    2. Taylor expanded around inf 7.8

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

    if -2.5655762721640628e+51 < z < 4.026021436349368e+53

    1. Initial program 2.7

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

    3. Applied associate-/l*1.1

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

    5. Applied flip3-+1.1

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

    6. Applied associate-*l/1.1

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

  4. Final simplification4.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -2.5655762721640628 \cdot 10^{51} \lor \neg \left(z \le 4.0260214363493681 \cdot 10^{53}\right):\\ \;\;\;\;x + \left(\left(3.13060547622999996 \cdot y + \frac{t \cdot y}{{z}^{2}}\right) - 36.527041698806414 \cdot \frac{y}{z}\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687406999999\right) \cdot z + 31.469011574900001\right) \cdot z + 11.940090572100001\right) \cdot z + 0.60777138777100004}{\left(\left(\frac{\left({\left(z \cdot 3.13060547622999996\right)}^{3} + {11.166754126200001}^{3}\right) \cdot z}{\left(z \cdot 3.13060547622999996\right) \cdot \left(z \cdot 3.13060547622999996\right) + \left(11.166754126200001 \cdot 11.166754126200001 - \left(z \cdot 3.13060547622999996\right) \cdot 11.166754126200001\right)} + t\right) \cdot z + a\right) \cdot z + b}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020075 
(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))) (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)))))

  (+ 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))))