Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.2 → 29.3

Time: 28.4s

Precision: 64

Math

\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

↓

\[\frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65496 = x;
        double r65497 = y;
        double r65498 = r65496 * r65497;
        double r65499 = z;
        double r65500 = r65498 + r65499;
        double r65501 = r65500 * r65497;
        double r65502 = 27464.7644705;
        double r65503 = r65501 + r65502;
        double r65504 = r65503 * r65497;
        double r65505 = 230661.510616;
        double r65506 = r65504 + r65505;
        double r65507 = r65506 * r65497;
        double r65508 = t;
        double r65509 = r65507 + r65508;
        double r65510 = a;
        double r65511 = r65497 + r65510;
        double r65512 = r65511 * r65497;
        double r65513 = b;
        double r65514 = r65512 + r65513;
        double r65515 = r65514 * r65497;
        double r65516 = c;
        double r65517 = r65515 + r65516;
        double r65518 = r65517 * r65497;
        double r65519 = i;
        double r65520 = r65518 + r65519;
        double r65521 = r65509 / r65520;
        return r65521;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65522 = x;
        double r65523 = y;
        double r65524 = r65522 * r65523;
        double r65525 = z;
        double r65526 = r65524 + r65525;
        double r65527 = r65526 * r65523;
        double r65528 = 27464.7644705;
        double r65529 = r65527 + r65528;
        double r65530 = cbrt(r65529);
        double r65531 = r65530 * r65530;
        double r65532 = r65530 * r65523;
        double r65533 = r65531 * r65532;
        double r65534 = 230661.510616;
        double r65535 = r65533 + r65534;
        double r65536 = r65535 * r65523;
        double r65537 = t;
        double r65538 = r65536 + r65537;
        double r65539 = a;
        double r65540 = r65523 + r65539;
        double r65541 = r65540 * r65523;
        double r65542 = b;
        double r65543 = r65541 + r65542;
        double r65544 = r65543 * r65523;
        double r65545 = c;
        double r65546 = r65544 + r65545;
        double r65547 = r65546 * r65523;
        double r65548 = i;
        double r65549 = r65547 + r65548;
        double r65550 = r65538 / r65549;
        return r65550;
}

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

Bits error versus c

Bits error versus i

Derivation

1. Initial program 29.2

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
2. Using strategy rm

3. Applied add-cube-cbrt 29.3

   \[\leadsto \frac{\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right)} \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

4. Applied associate-*l* 29.3

   \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right)} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

5. Final simplification 29.3

   \[\leadsto \frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))