Average Error: 26.4 → 0.9
Time: 13.8s
Precision: 64
\[\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \le -3.240573328946715190890073478060839868024 \cdot 10^{52} \lor \neg \left(x \le 98007668318672541904438026043392\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x\right) \cdot \left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x\right) - 263.5050747210000281484099105000495910645 \cdot 263.5050747210000281484099105000495910645\right) \cdot x}{\left(x + 43.3400022514000013984514225739985704422\right) \cdot x - 263.5050747210000281484099105000495910645} + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\\ \end{array}\]
\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 -3.240573328946715190890073478060839868024 \cdot 10^{52} \lor \neg \left(x \le 98007668318672541904438026043392\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(\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x\right) \cdot \left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x\right) - 263.5050747210000281484099105000495910645 \cdot 263.5050747210000281484099105000495910645\right) \cdot x}{\left(x + 43.3400022514000013984514225739985704422\right) \cdot x - 263.5050747210000281484099105000495910645} + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\\

\end{array}
double f(double x, double y, double z) {
        double r401515 = x;
        double r401516 = 2.0;
        double r401517 = r401515 - r401516;
        double r401518 = 4.16438922228;
        double r401519 = r401515 * r401518;
        double r401520 = 78.6994924154;
        double r401521 = r401519 + r401520;
        double r401522 = r401521 * r401515;
        double r401523 = 137.519416416;
        double r401524 = r401522 + r401523;
        double r401525 = r401524 * r401515;
        double r401526 = y;
        double r401527 = r401525 + r401526;
        double r401528 = r401527 * r401515;
        double r401529 = z;
        double r401530 = r401528 + r401529;
        double r401531 = r401517 * r401530;
        double r401532 = 43.3400022514;
        double r401533 = r401515 + r401532;
        double r401534 = r401533 * r401515;
        double r401535 = 263.505074721;
        double r401536 = r401534 + r401535;
        double r401537 = r401536 * r401515;
        double r401538 = 313.399215894;
        double r401539 = r401537 + r401538;
        double r401540 = r401539 * r401515;
        double r401541 = 47.066876606;
        double r401542 = r401540 + r401541;
        double r401543 = r401531 / r401542;
        return r401543;
}
↓
double f(double x, double y, double z) {
        double r401544 = x;
        double r401545 = -3.240573328946715e+52;
        bool r401546 = r401544 <= r401545;
        double r401547 = 9.800766831867254e+31;
        bool r401548 = r401544 <= r401547;
        double r401549 = !r401548;
        bool r401550 = r401546 || r401549;
        double r401551 = y;
        double r401552 = 2.0;
        double r401553 = pow(r401544, r401552);
        double r401554 = r401551 / r401553;
        double r401555 = 4.16438922228;
        double r401556 = r401555 * r401544;
        double r401557 = r401554 + r401556;
        double r401558 = 110.1139242984811;
        double r401559 = r401557 - r401558;
        double r401560 = 2.0;
        double r401561 = r401544 - r401560;
        double r401562 = r401544 * r401555;
        double r401563 = 78.6994924154;
        double r401564 = r401562 + r401563;
        double r401565 = r401564 * r401544;
        double r401566 = 137.519416416;
        double r401567 = r401565 + r401566;
        double r401568 = r401567 * r401544;
        double r401569 = r401568 + r401551;
        double r401570 = r401569 * r401544;
        double r401571 = z;
        double r401572 = r401570 + r401571;
        double r401573 = r401561 * r401572;
        double r401574 = 43.3400022514;
        double r401575 = r401544 + r401574;
        double r401576 = r401575 * r401544;
        double r401577 = r401576 * r401576;
        double r401578 = 263.505074721;
        double r401579 = r401578 * r401578;
        double r401580 = r401577 - r401579;
        double r401581 = r401580 * r401544;
        double r401582 = r401576 - r401578;
        double r401583 = r401581 / r401582;
        double r401584 = 313.399215894;
        double r401585 = r401583 + r401584;
        double r401586 = r401585 * r401544;
        double r401587 = 47.066876606;
        double r401588 = r401586 + r401587;
        double r401589 = r401573 / r401588;
        double r401590 = r401550 ? r401559 : r401589;
        return r401590;
}

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

Original26.4
Target0.5
Herbie0.9
\[\begin{array}{l} \mathbf{if}\;x \lt -3.326128725870004842699683658678411714981 \cdot 10^{62}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{elif}\;x \lt 9.429991714554672672712552870340896976735 \cdot 10^{55}:\\ \;\;\;\;\frac{x - 2}{1} \cdot \frac{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}{\left(\left(263.5050747210000281484099105000495910645 \cdot x + \left(43.3400022514000013984514225739985704422 \cdot \left(x \cdot x\right) + x \cdot \left(x \cdot x\right)\right)\right) + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\\ \mathbf{else}:\\ \;\;\;\;\left(\frac{y}{x \cdot x} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if x < -3.240573328946715e+52 or 9.800766831867254e+31 < x

    1. Initial program 60.4

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

    3. Applied associate-/l*56.7

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

    5. Applied *-un-lft-identity56.7

      \[\leadsto \frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}{\color{blue}{1 \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}}}\]

    6. Applied *-un-lft-identity56.7

      \[\leadsto \frac{x - 2}{\frac{\color{blue}{1 \cdot \left(\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825\right)}}{1 \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}}\]

    7. Applied times-frac56.7

      \[\leadsto \frac{x - 2}{\color{blue}{\frac{1}{1} \cdot \frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}}}\]

    8. Applied *-un-lft-identity56.7

      \[\leadsto \frac{\color{blue}{1 \cdot \left(x - 2\right)}}{\frac{1}{1} \cdot \frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}}\]

    9. Applied times-frac56.7

      \[\leadsto \color{blue}{\frac{1}{\frac{1}{1}} \cdot \frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}}}\]

    10. Simplified56.7

      \[\leadsto \color{blue}{1} \cdot \frac{x - 2}{\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}{\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z}}\]

    11. Simplified56.7

      \[\leadsto 1 \cdot \color{blue}{\left(\left(z + \left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x\right) \cdot \frac{x - 2}{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x + 263.5050747210000281484099105000495910645\right) \cdot x + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\right)}\]

    12. Taylor expanded around inf 0.9

      \[\leadsto 1 \cdot \color{blue}{\left(\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\right)}\]

    if -3.240573328946715e+52 < x < 9.800766831867254e+31

    1. Initial program 0.9

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

    3. Applied flip-+0.9

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

    4. Applied associate-*l/0.9

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

  4. Final simplification0.9

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3.240573328946715190890073478060839868024 \cdot 10^{52} \lor \neg \left(x \le 98007668318672541904438026043392\right):\\ \;\;\;\;\left(\frac{y}{{x}^{2}} + 4.16438922227999963610045597306452691555 \cdot x\right) - 110.1139242984810948655649553984403610229\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(x - 2\right) \cdot \left(\left(\left(\left(x \cdot 4.16438922227999963610045597306452691555 + 78.69949241540000173245061887428164482117\right) \cdot x + 137.5194164160000127594685181975364685059\right) \cdot x + y\right) \cdot x + z\right)}{\left(\frac{\left(\left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x\right) \cdot \left(\left(x + 43.3400022514000013984514225739985704422\right) \cdot x\right) - 263.5050747210000281484099105000495910645 \cdot 263.5050747210000281484099105000495910645\right) \cdot x}{\left(x + 43.3400022514000013984514225739985704422\right) \cdot x - 263.5050747210000281484099105000495910645} + 313.3992158940000081202015280723571777344\right) \cdot x + 47.06687660600000100430406746454536914825}\\ \end{array}\]

Reproduce

herbie shell --seed 2019350 
(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)))