Average Error: 28.8 → 1.1
Time: 24.6s
Precision: 64
\[x + \frac{y \cdot \left(\left(\left(\left(z \cdot 3.13060547623 + 11.1667541262\right) \cdot z + t\right) \cdot z + a\right) \cdot z + b\right)}{\left(\left(\left(z + 15.234687407\right) \cdot z + 31.4690115749\right) \cdot z + 11.9400905721\right) \cdot z + 0.607771387771}\]
↓
\[\begin{array}{l} \mathbf{if}\;z \le -1.0597997332978914 \cdot 10^{+45}:\\ \;\;\;\;x + \left(3.13060547623 \cdot y + \left(\frac{t}{\frac{z}{\sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}} \cdot \sqrt[3]{y} - \frac{y \cdot 36.527041698806414}{z}\right)\right)\\ \mathbf{elif}\;z \le 1.3590012002674587 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right) + 0.607771387771}{b + z \cdot \left(a + \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right) \cdot z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 \cdot y + \left(\frac{t}{\frac{z}{\sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}} \cdot \sqrt[3]{y} - \frac{y \cdot 36.527041698806414}{z}\right)\right)\\ \end{array}\]
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 -1.0597997332978914 \cdot 10^{+45}:\\
\;\;\;\;x + \left(3.13060547623 \cdot y + \left(\frac{t}{\frac{z}{\sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}} \cdot \sqrt[3]{y} - \frac{y \cdot 36.527041698806414}{z}\right)\right)\\

\mathbf{elif}\;z \le 1.3590012002674587 \cdot 10^{+52}:\\
\;\;\;\;x + \frac{y}{\frac{z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right) + 0.607771387771}{b + z \cdot \left(a + \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right) \cdot z\right)}}\\

\mathbf{else}:\\
\;\;\;\;x + \left(3.13060547623 \cdot y + \left(\frac{t}{\frac{z}{\sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}} \cdot \sqrt[3]{y} - \frac{y \cdot 36.527041698806414}{z}\right)\right)\\

\end{array}
double f(double x, double y, double z, double t, double a, double b) {
        double r21390313 = x;
        double r21390314 = y;
        double r21390315 = z;
        double r21390316 = 3.13060547623;
        double r21390317 = r21390315 * r21390316;
        double r21390318 = 11.1667541262;
        double r21390319 = r21390317 + r21390318;
        double r21390320 = r21390319 * r21390315;
        double r21390321 = t;
        double r21390322 = r21390320 + r21390321;
        double r21390323 = r21390322 * r21390315;
        double r21390324 = a;
        double r21390325 = r21390323 + r21390324;
        double r21390326 = r21390325 * r21390315;
        double r21390327 = b;
        double r21390328 = r21390326 + r21390327;
        double r21390329 = r21390314 * r21390328;
        double r21390330 = 15.234687407;
        double r21390331 = r21390315 + r21390330;
        double r21390332 = r21390331 * r21390315;
        double r21390333 = 31.4690115749;
        double r21390334 = r21390332 + r21390333;
        double r21390335 = r21390334 * r21390315;
        double r21390336 = 11.9400905721;
        double r21390337 = r21390335 + r21390336;
        double r21390338 = r21390337 * r21390315;
        double r21390339 = 0.607771387771;
        double r21390340 = r21390338 + r21390339;
        double r21390341 = r21390329 / r21390340;
        double r21390342 = r21390313 + r21390341;
        return r21390342;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r21390343 = z;
        double r21390344 = -1.0597997332978914e+45;
        bool r21390345 = r21390343 <= r21390344;
        double r21390346 = x;
        double r21390347 = 3.13060547623;
        double r21390348 = y;
        double r21390349 = r21390347 * r21390348;
        double r21390350 = t;
        double r21390351 = cbrt(r21390348);
        double r21390352 = r21390343 / r21390351;
        double r21390353 = r21390352 * r21390352;
        double r21390354 = r21390350 / r21390353;
        double r21390355 = r21390354 * r21390351;
        double r21390356 = 36.527041698806414;
        double r21390357 = r21390348 * r21390356;
        double r21390358 = r21390357 / r21390343;
        double r21390359 = r21390355 - r21390358;
        double r21390360 = r21390349 + r21390359;
        double r21390361 = r21390346 + r21390360;
        double r21390362 = 1.3590012002674587e+52;
        bool r21390363 = r21390343 <= r21390362;
        double r21390364 = 11.9400905721;
        double r21390365 = 31.4690115749;
        double r21390366 = 15.234687407;
        double r21390367 = r21390343 + r21390366;
        double r21390368 = r21390343 * r21390367;
        double r21390369 = r21390365 + r21390368;
        double r21390370 = r21390343 * r21390369;
        double r21390371 = r21390364 + r21390370;
        double r21390372 = r21390343 * r21390371;
        double r21390373 = 0.607771387771;
        double r21390374 = r21390372 + r21390373;
        double r21390375 = b;
        double r21390376 = a;
        double r21390377 = 11.1667541262;
        double r21390378 = r21390347 * r21390343;
        double r21390379 = r21390377 + r21390378;
        double r21390380 = r21390343 * r21390379;
        double r21390381 = r21390380 + r21390350;
        double r21390382 = r21390381 * r21390343;
        double r21390383 = r21390376 + r21390382;
        double r21390384 = r21390343 * r21390383;
        double r21390385 = r21390375 + r21390384;
        double r21390386 = r21390374 / r21390385;
        double r21390387 = r21390348 / r21390386;
        double r21390388 = r21390346 + r21390387;
        double r21390389 = r21390363 ? r21390388 : r21390361;
        double r21390390 = r21390345 ? r21390361 : r21390389;
        return r21390390;
}

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 < -1.0597997332978914e+45 or 1.3590012002674587e+52 < z

    1. Initial program 59.2

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

    2. Taylor expanded around inf 7.8

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

    3. Simplified1.1

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

    5. Applied add-cube-cbrt1.2

      \[\leadsto x + \left(3.13060547623 \cdot y + \left(\frac{t}{z \cdot z} \cdot \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} - \frac{y \cdot 36.527041698806414}{z}\right)\right)\]

    6. Applied associate-*r*1.2

      \[\leadsto x + \left(3.13060547623 \cdot y + \left(\color{blue}{\left(\frac{t}{z \cdot z} \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}} - \frac{y \cdot 36.527041698806414}{z}\right)\right)\]

    7. Simplified1.3

      \[\leadsto x + \left(3.13060547623 \cdot y + \left(\color{blue}{\frac{t}{\frac{z}{\sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}}} \cdot \sqrt[3]{y} - \frac{y \cdot 36.527041698806414}{z}\right)\right)\]

    if -1.0597997332978914e+45 < z < 1.3590012002674587e+52

    1. Initial program 1.9

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

    3. Applied associate-/l*0.8

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

  4. Final simplification1.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;z \le -1.0597997332978914 \cdot 10^{+45}:\\ \;\;\;\;x + \left(3.13060547623 \cdot y + \left(\frac{t}{\frac{z}{\sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}} \cdot \sqrt[3]{y} - \frac{y \cdot 36.527041698806414}{z}\right)\right)\\ \mathbf{elif}\;z \le 1.3590012002674587 \cdot 10^{+52}:\\ \;\;\;\;x + \frac{y}{\frac{z \cdot \left(11.9400905721 + z \cdot \left(31.4690115749 + z \cdot \left(z + 15.234687407\right)\right)\right) + 0.607771387771}{b + z \cdot \left(a + \left(z \cdot \left(11.1667541262 + 3.13060547623 \cdot z\right) + t\right) \cdot z\right)}}\\ \mathbf{else}:\\ \;\;\;\;x + \left(3.13060547623 \cdot y + \left(\frac{t}{\frac{z}{\sqrt[3]{y}} \cdot \frac{z}{\sqrt[3]{y}}} \cdot \sqrt[3]{y} - \frac{y \cdot 36.527041698806414}{z}\right)\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 
(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))))