Average Error: 27.5 → 1.2
Time: 26.3s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -30862913864240.8671875 \lor \neg \left(x \le 9.352513911582600409505841643271917104042 \cdot 10^{58}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\sqrt[3]{\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344} \cdot \sqrt[3]{\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344}\right) \cdot \left(\sqrt[3]{\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344} \cdot x\right) + 47.06687660600000100430406746454536914825}\\ \end{array}\]
\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 -30862913864240.8671875 \lor \neg \left(x \le 9.352513911582600409505841643271917104042 \cdot 10^{58}\right):\\
\;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\

\mathbf{else}:\\
\;\;\;\;\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(\sqrt[3]{\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344} \cdot \sqrt[3]{\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344}\right) \cdot \left(\sqrt[3]{\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344} \cdot x\right) + 47.06687660600000100430406746454536914825}\\

\end{array}
double f(double x, double y, double z) {
        double r321498 = x;
        double r321499 = 2.0;
        double r321500 = r321498 - r321499;
        double r321501 = 4.16438922228;
        double r321502 = r321498 * r321501;
        double r321503 = 78.6994924154;
        double r321504 = r321502 + r321503;
        double r321505 = r321504 * r321498;
        double r321506 = 137.519416416;
        double r321507 = r321505 + r321506;
        double r321508 = r321507 * r321498;
        double r321509 = y;
        double r321510 = r321508 + r321509;
        double r321511 = r321510 * r321498;
        double r321512 = z;
        double r321513 = r321511 + r321512;
        double r321514 = r321500 * r321513;
        double r321515 = 43.3400022514;
        double r321516 = r321498 + r321515;
        double r321517 = r321516 * r321498;
        double r321518 = 263.505074721;
        double r321519 = r321517 + r321518;
        double r321520 = r321519 * r321498;
        double r321521 = 313.399215894;
        double r321522 = r321520 + r321521;
        double r321523 = r321522 * r321498;
        double r321524 = 47.066876606;
        double r321525 = r321523 + r321524;
        double r321526 = r321514 / r321525;
        return r321526;
}
↓
double f(double x, double y, double z) {
        double r321527 = x;
        double r321528 = -30862913864240.867;
        bool r321529 = r321527 <= r321528;
        double r321530 = 9.3525139115826e+58;
        bool r321531 = r321527 <= r321530;
        double r321532 = !r321531;
        bool r321533 = r321529 || r321532;
        double r321534 = y;
        double r321535 = 2.0;
        double r321536 = pow(r321527, r321535);
        double r321537 = r321534 / r321536;
        double r321538 = 4.16438922228;
        double r321539 = r321538 * r321527;
        double r321540 = r321537 + r321539;
        double r321541 = 110.1139242984811;
        double r321542 = r321540 - r321541;
        double r321543 = 2.0;
        double r321544 = r321527 - r321543;
        double r321545 = r321527 * r321538;
        double r321546 = 78.6994924154;
        double r321547 = r321545 + r321546;
        double r321548 = r321547 * r321527;
        double r321549 = 137.519416416;
        double r321550 = r321548 + r321549;
        double r321551 = r321550 * r321527;
        double r321552 = r321551 + r321534;
        double r321553 = r321552 * r321527;
        double r321554 = z;
        double r321555 = r321553 + r321554;
        double r321556 = r321544 * r321555;
        double r321557 = 43.3400022514;
        double r321558 = r321527 + r321557;
        double r321559 = r321558 * r321527;
        double r321560 = 263.505074721;
        double r321561 = r321559 + r321560;
        double r321562 = r321561 * r321527;
        double r321563 = 313.399215894;
        double r321564 = r321562 + r321563;
        double r321565 = cbrt(r321564);
        double r321566 = r321565 * r321565;
        double r321567 = r321565 * r321527;
        double r321568 = r321566 * r321567;
        double r321569 = 47.066876606;
        double r321570 = r321568 + r321569;
        double r321571 = r321556 / r321570;
        double r321572 = r321533 ? r321542 : r321571;
        return r321572;
}

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

Original27.5
Target0.5
Herbie1.2
\[\begin{array}{l} \mathbf{if}\;x \lt -3.326128725870004842699683658678411714981 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{elif}\;x \lt 9.429991714554672672712552870340896976735 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.5050747210000281484099105000495910645 \cdot x + \left(43.3400022514000013984514225739985704422 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -30862913864240.867 or 9.3525139115826e+58 < x

    1. Initial program 59.6

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

    2. Taylor expanded around inf 1.3

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

    if -30862913864240.867 < x < 9.3525139115826e+58

    1. Initial program 1.0

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

    3. Applied add-cube-cbrt1.1

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

    4. Applied associate-*l*1.1

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

  4. Final simplification1.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -30862913864240.8671875 \lor \neg \left(x \le 9.352513911582600409505841643271917104042 \cdot 10^{58}\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\sqrt[3]{\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344} \cdot \sqrt[3]{\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344}\right) \cdot \left(\sqrt[3]{\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344} \cdot x\right) + 47.06687660600000100430406746454536914825}\\ \end{array}\]

Reproduce

herbie shell --seed 2019294 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2, C"
  :precision binary64

  :herbie-target
  (if (< x -3.3261287258700048e62) (- (+ (/ y (* x x)) (* 4.16438922227999964 x)) 110.11392429848109) (if (< x 9.4299917145546727e55) (* (/ (- x 2) 1) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922227999964) 78.6994924154000017) x) 137.51941641600001) x) y) x) z) (+ (* (+ (+ (* 263.50507472100003 x) (+ (* 43.3400022514000014 (* x x)) (* x (* x x)))) 313.399215894) x) 47.066876606000001))) (- (+ (/ y (* x x)) (* 4.16438922227999964 x)) 110.11392429848109)))

  (/ (* (- x 2) (+ (* (+ (* (+ (* (+ (* x 4.16438922227999964) 78.6994924154000017) x) 137.51941641600001) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514000014) x) 263.50507472100003) x) 313.399215894) x) 47.066876606000001)))