Average Error: 28.8 → 1.1
Time: 31.1s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -3.9856954798303585 \cdot 10^{+39}:\\ \;\;\;\;\left(3.13060547623 \cdot y + \left(\frac{y}{z} \cdot \frac{t}{z} - 36.527041698806414 \cdot \frac{y}{z}\right)\right) + x\\ \mathbf{elif}\;z \le 4.8590408174333496 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(z \cdot \left(15.234687407 + z\right) + 31.4690115749\right)\right)}{b + \left(a + z \cdot \left(t + \left(3.13060547623 \cdot z + 11.1667541262\right) \cdot z\right)\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(3.13060547623 \cdot y + \left(\frac{y}{z} \cdot \frac{t}{z} - 36.527041698806414 \cdot \frac{y}{z}\right)\right) + x\\ \end{array}\]
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 \le -3.9856954798303585 \cdot 10^{+39}:\\
\;\;\;\;\left(3.13060547623 \cdot y + \left(\frac{y}{z} \cdot \frac{t}{z} - 36.527041698806414 \cdot \frac{y}{z}\right)\right) + x\\

\mathbf{elif}\;z \le 4.8590408174333496 \cdot 10^{+55}:\\
\;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(z \cdot \left(15.234687407 + z\right) + 31.4690115749\right)\right)}{b + \left(a + z \cdot \left(t + \left(3.13060547623 \cdot z + 11.1667541262\right) \cdot z\right)\right) \cdot z}}\\

\mathbf{else}:\\
\;\;\;\;\left(3.13060547623 \cdot y + \left(\frac{y}{z} \cdot \frac{t}{z} - 36.527041698806414 \cdot \frac{y}{z}\right)\right) + x\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r22868156 = x;
        double r22868157 = y;
        double r22868158 = z;
        double r22868159 = 3.13060547623;
        double r22868160 = r22868158 * r22868159;
        double r22868161 = 11.1667541262;
        double r22868162 = r22868160 + r22868161;
        double r22868163 = r22868162 * r22868158;
        double r22868164 = t;
        double r22868165 = r22868163 + r22868164;
        double r22868166 = r22868165 * r22868158;
        double r22868167 = a;
        double r22868168 = r22868166 + r22868167;
        double r22868169 = r22868168 * r22868158;
        double r22868170 = b;
        double r22868171 = r22868169 + r22868170;
        double r22868172 = r22868157 * r22868171;
        double r22868173 = 15.234687407;
        double r22868174 = r22868158 + r22868173;
        double r22868175 = r22868174 * r22868158;
        double r22868176 = 31.4690115749;
        double r22868177 = r22868175 + r22868176;
        double r22868178 = r22868177 * r22868158;
        double r22868179 = 11.9400905721;
        double r22868180 = r22868178 + r22868179;
        double r22868181 = r22868180 * r22868158;
        double r22868182 = 0.607771387771;
        double r22868183 = r22868181 + r22868182;
        double r22868184 = r22868172 / r22868183;
        double r22868185 = r22868156 + r22868184;
        return r22868185;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r22868186 = z;
        double r22868187 = -3.9856954798303585e+39;
        bool r22868188 = r22868186 <= r22868187;
        double r22868189 = 3.13060547623;
        double r22868190 = y;
        double r22868191 = r22868189 * r22868190;
        double r22868192 = r22868190 / r22868186;
        double r22868193 = t;
        double r22868194 = r22868193 / r22868186;
        double r22868195 = r22868192 * r22868194;
        double r22868196 = 36.527041698806414;
        double r22868197 = r22868196 * r22868192;
        double r22868198 = r22868195 - r22868197;
        double r22868199 = r22868191 + r22868198;
        double r22868200 = x;
        double r22868201 = r22868199 + r22868200;
        double r22868202 = 4.8590408174333496e+55;
        bool r22868203 = r22868186 <= r22868202;
        double r22868204 = 0.607771387771;
        double r22868205 = 11.9400905721;
        double r22868206 = 15.234687407;
        double r22868207 = r22868206 + r22868186;
        double r22868208 = r22868186 * r22868207;
        double r22868209 = 31.4690115749;
        double r22868210 = r22868208 + r22868209;
        double r22868211 = r22868186 * r22868210;
        double r22868212 = r22868205 + r22868211;
        double r22868213 = r22868186 * r22868212;
        double r22868214 = r22868204 + r22868213;
        double r22868215 = b;
        double r22868216 = a;
        double r22868217 = r22868189 * r22868186;
        double r22868218 = 11.1667541262;
        double r22868219 = r22868217 + r22868218;
        double r22868220 = r22868219 * r22868186;
        double r22868221 = r22868193 + r22868220;
        double r22868222 = r22868186 * r22868221;
        double r22868223 = r22868216 + r22868222;
        double r22868224 = r22868223 * r22868186;
        double r22868225 = r22868215 + r22868224;
        double r22868226 = r22868214 / r22868225;
        double r22868227 = r22868190 / r22868226;
        double r22868228 = r22868200 + r22868227;
        double r22868229 = r22868203 ? r22868228 : r22868201;
        double r22868230 = r22868188 ? r22868201 : r22868229;
        return r22868230;
}

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

Original28.8
Target1.0
Herbie1.1
\[\begin{array}{l} \mathbf{if}\;z \lt -6.499344996252632 \cdot 10^{+53}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \mathbf{elif}\;z \lt 7.066965436914287 \cdot 10^{+59}:\\ \;\;\;\;x + \frac{y}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(3.13060547623 - \frac{36.527041698806414}{z}\right) + \frac{t}{z \cdot z}\right) \cdot \frac{y}{1}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if z < -3.9856954798303585e+39 or 4.8590408174333496e+55 < z

    1. Initial program 58.9

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

    3. Applied associate-/l*56.8

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

    5. Applied div-inv56.8

      \[\leadsto x + \color{blue}{y \cdot \frac{1}{\frac{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}{\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b}}}\]

    6. Simplified56.8

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

    7. Taylor expanded around inf 8.3

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

    8. Simplified1.3

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

    if -3.9856954798303585e+39 < z < 4.8590408174333496e+55

    1. Initial program 2.2

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

    3. Applied associate-/l*0.9

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -3.9856954798303585 \cdot 10^{+39}:\\ \;\;\;\;\left(3.13060547623 \cdot y + \left(\frac{y}{z} \cdot \frac{t}{z} - 36.527041698806414 \cdot \frac{y}{z}\right)\right) + x\\ \mathbf{elif}\;z \le 4.8590408174333496 \cdot 10^{+55}:\\ \;\;\;\;x + \frac{y}{\frac{0.607771387771 + z \cdot \left(11.9400905721 + z \cdot \left(z \cdot \left(15.234687407 + z\right) + 31.4690115749\right)\right)}{b + \left(a + z \cdot \left(t + \left(3.13060547623 \cdot z + 11.1667541262\right) \cdot z\right)\right) \cdot z}}\\ \mathbf{else}:\\ \;\;\;\;\left(3.13060547623 \cdot y + \left(\frac{y}{z} \cdot \frac{t}{z} - 36.527041698806414 \cdot \frac{y}{z}\right)\right) + x\\ \end{array}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, D"

  :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))))