Average Error: 26.8 → 0.6
Time: 20.6s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -9.168391507400123006303027147886417404254 \cdot 10^{69} \lor \neg \left(x \le 1.930869431253392580588428718419400205994 \cdot 10^{69}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{else}:\\ \;\;\;\;\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]
\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}
↓
\begin{array}{l}
\mathbf{if}\;x \le -9.168391507400123006303027147886417404254 \cdot 10^{69} \lor \neg \left(x \le 1.930869431253392580588428718419400205994 \cdot 10^{69}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\

\mathbf{else}:\\
\;\;\;\;\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}}\\

\end{array}
double f(double x, double y, double z) {
        double r221449 = x;
        double r221450 = 2.0;
        double r221451 = r221449 - r221450;
        double r221452 = 4.16438922228;
        double r221453 = r221449 * r221452;
        double r221454 = 78.6994924154;
        double r221455 = r221453 + r221454;
        double r221456 = r221455 * r221449;
        double r221457 = 137.519416416;
        double r221458 = r221456 + r221457;
        double r221459 = r221458 * r221449;
        double r221460 = y;
        double r221461 = r221459 + r221460;
        double r221462 = r221461 * r221449;
        double r221463 = z;
        double r221464 = r221462 + r221463;
        double r221465 = r221451 * r221464;
        double r221466 = 43.3400022514;
        double r221467 = r221449 + r221466;
        double r221468 = r221467 * r221449;
        double r221469 = 263.505074721;
        double r221470 = r221468 + r221469;
        double r221471 = r221470 * r221449;
        double r221472 = 313.399215894;
        double r221473 = r221471 + r221472;
        double r221474 = r221473 * r221449;
        double r221475 = 47.066876606;
        double r221476 = r221474 + r221475;
        double r221477 = r221465 / r221476;
        return r221477;
}
↓
double f(double x, double y, double z) {
        double r221478 = x;
        double r221479 = -9.168391507400123e+69;
        bool r221480 = r221478 <= r221479;
        double r221481 = 1.9308694312533926e+69;
        bool r221482 = r221478 <= r221481;
        double r221483 = !r221482;
        bool r221484 = r221480 || r221483;
        double r221485 = y;
        double r221486 = 2.0;
        double r221487 = pow(r221478, r221486);
        double r221488 = r221485 / r221487;
        double r221489 = 4.16438922228;
        double r221490 = r221489 * r221478;
        double r221491 = r221488 + r221490;
        double r221492 = 110.1139242984811;
        double r221493 = r221491 - r221492;
        double r221494 = 2.0;
        double r221495 = r221478 - r221494;
        double r221496 = 43.3400022514;
        double r221497 = r221478 + r221496;
        double r221498 = r221497 * r221478;
        double r221499 = 263.505074721;
        double r221500 = r221498 + r221499;
        double r221501 = r221500 * r221478;
        double r221502 = 313.399215894;
        double r221503 = r221501 + r221502;
        double r221504 = r221503 * r221478;
        double r221505 = 47.066876606;
        double r221506 = r221504 + r221505;
        double r221507 = r221478 * r221489;
        double r221508 = 78.6994924154;
        double r221509 = r221507 + r221508;
        double r221510 = r221509 * r221478;
        double r221511 = 137.519416416;
        double r221512 = r221510 + r221511;
        double r221513 = r221512 * r221478;
        double r221514 = r221513 + r221485;
        double r221515 = r221514 * r221478;
        double r221516 = z;
        double r221517 = r221515 + r221516;
        double r221518 = r221506 / r221517;
        double r221519 = r221495 / r221518;
        double r221520 = r221484 ? r221493 : r221519;
        return r221520;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original26.8
Target0.6
Herbie0.6
\[\begin{array}{l} \mathbf{if}\;x \lt -3.326128725870004842699683658678411714981 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{elif}\;x \lt 9.429991714554672672712552870340896976735 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.5050747210000281484099105000495910645 \cdot x + \left(43.3400022514000013984514225739985704422 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -9.168391507400123e+69 or 1.9308694312533926e+69 < x

    1. Initial program 64.0

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\]

    2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229}\]

    if -9.168391507400123e+69 < x < 1.9308694312533926e+69

    1. Initial program 3.4

      \[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\]
    2. Using strategy rm

    3. Applied associate-/l*1.0

      \[\leadsto \color{blue}{\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}}}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.6

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -9.168391507400123006303027147886417404254 \cdot 10^{69} \lor \neg \left(x \le 1.930869431253392580588428718419400205994 \cdot 10^{69}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{else}:\\ \;\;\;\;\frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.326128725870005e+62) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811) (if (< x 9.429991714554673e+55) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (+ (* (+ (+ (* 263.505074721 x) (+ (* 43.3400022514 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606))) (- (+ (/ y (* x x)) (* 4.16438922228 x)) 110.1139242984811)))

  (/ (* (- x 2) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))