Average Error: 29.2 → 29.3
Time: 10.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\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(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69479 = x;
        double r69480 = y;
        double r69481 = r69479 * r69480;
        double r69482 = z;
        double r69483 = r69481 + r69482;
        double r69484 = r69483 * r69480;
        double r69485 = 27464.7644705;
        double r69486 = r69484 + r69485;
        double r69487 = r69486 * r69480;
        double r69488 = 230661.510616;
        double r69489 = r69487 + r69488;
        double r69490 = r69489 * r69480;
        double r69491 = t;
        double r69492 = r69490 + r69491;
        double r69493 = a;
        double r69494 = r69480 + r69493;
        double r69495 = r69494 * r69480;
        double r69496 = b;
        double r69497 = r69495 + r69496;
        double r69498 = r69497 * r69480;
        double r69499 = c;
        double r69500 = r69498 + r69499;
        double r69501 = r69500 * r69480;
        double r69502 = i;
        double r69503 = r69501 + r69502;
        double r69504 = r69492 / r69503;
        return r69504;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69505 = x;
        double r69506 = y;
        double r69507 = r69505 * r69506;
        double r69508 = z;
        double r69509 = r69507 + r69508;
        double r69510 = r69509 * r69506;
        double r69511 = 27464.7644705;
        double r69512 = r69510 + r69511;
        double r69513 = cbrt(r69506);
        double r69514 = r69513 * r69513;
        double r69515 = r69512 * r69514;
        double r69516 = r69515 * r69513;
        double r69517 = 230661.510616;
        double r69518 = r69516 + r69517;
        double r69519 = r69518 * r69506;
        double r69520 = t;
        double r69521 = r69519 + r69520;
        double r69522 = a;
        double r69523 = r69506 + r69522;
        double r69524 = r69523 * r69506;
        double r69525 = b;
        double r69526 = r69524 + r69525;
        double r69527 = r69526 * r69506;
        double r69528 = c;
        double r69529 = r69527 + r69528;
        double r69530 = r69529 * r69506;
        double r69531 = i;
        double r69532 = r69530 + r69531;
        double r69533 = r69521 / r69532;
        return r69533;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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-cbrt29.3

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

  4. Applied associate-*r*29.3

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

  5. Final simplification29.3

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

Reproduce

herbie shell --seed 2019354 
(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)))