Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 8.7s

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 r69481 = x;
        double r69482 = y;
        double r69483 = r69481 * r69482;
        double r69484 = z;
        double r69485 = r69483 + r69484;
        double r69486 = r69485 * r69482;
        double r69487 = 27464.7644705;
        double r69488 = r69486 + r69487;
        double r69489 = r69488 * r69482;
        double r69490 = 230661.510616;
        double r69491 = r69489 + r69490;
        double r69492 = r69491 * r69482;
        double r69493 = t;
        double r69494 = r69492 + r69493;
        double r69495 = a;
        double r69496 = r69482 + r69495;
        double r69497 = r69496 * r69482;
        double r69498 = b;
        double r69499 = r69497 + r69498;
        double r69500 = r69499 * r69482;
        double r69501 = c;
        double r69502 = r69500 + r69501;
        double r69503 = r69502 * r69482;
        double r69504 = i;
        double r69505 = r69503 + r69504;
        double r69506 = r69494 / r69505;
        return r69506;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69507 = x;
        double r69508 = y;
        double r69509 = r69507 * r69508;
        double r69510 = z;
        double r69511 = r69509 + r69510;
        double r69512 = r69511 * r69508;
        double r69513 = 27464.7644705;
        double r69514 = r69512 + r69513;
        double r69515 = cbrt(r69514);
        double r69516 = r69515 * r69515;
        double r69517 = r69515 * r69508;
        double r69518 = r69516 * r69517;
        double r69519 = 230661.510616;
        double r69520 = r69518 + r69519;
        double r69521 = r69520 * r69508;
        double r69522 = t;
        double r69523 = r69521 + r69522;
        double r69524 = a;
        double r69525 = r69508 + r69524;
        double r69526 = r69525 * r69508;
        double r69527 = b;
        double r69528 = r69526 + r69527;
        double r69529 = r69528 * r69508;
        double r69530 = c;
        double r69531 = r69529 + r69530;
        double r69532 = r69531 * r69508;
        double r69533 = i;
        double r69534 = r69532 + r69533;
        double r69535 = r69523 / r69534;
        return r69535;
}

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 29.1

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

3. Applied add-cube-cbrt 29.2

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

4. Applied associate-*l* 29.2

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

5. Final simplification 29.2

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

Reproduce

herbie shell --seed 2019362 
(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)))