Average Error: 28.7 → 28.8
Time: 8.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\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 + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \sqrt[3]{\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 r85504 = x;
        double r85505 = y;
        double r85506 = r85504 * r85505;
        double r85507 = z;
        double r85508 = r85506 + r85507;
        double r85509 = r85508 * r85505;
        double r85510 = 27464.7644705;
        double r85511 = r85509 + r85510;
        double r85512 = r85511 * r85505;
        double r85513 = 230661.510616;
        double r85514 = r85512 + r85513;
        double r85515 = r85514 * r85505;
        double r85516 = t;
        double r85517 = r85515 + r85516;
        double r85518 = a;
        double r85519 = r85505 + r85518;
        double r85520 = r85519 * r85505;
        double r85521 = b;
        double r85522 = r85520 + r85521;
        double r85523 = r85522 * r85505;
        double r85524 = c;
        double r85525 = r85523 + r85524;
        double r85526 = r85525 * r85505;
        double r85527 = i;
        double r85528 = r85526 + r85527;
        double r85529 = r85517 / r85528;
        return r85529;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r85530 = x;
        double r85531 = y;
        double r85532 = r85530 * r85531;
        double r85533 = z;
        double r85534 = r85532 + r85533;
        double r85535 = r85534 * r85531;
        double r85536 = 27464.7644705;
        double r85537 = r85535 + r85536;
        double r85538 = r85537 * r85531;
        double r85539 = 230661.510616;
        double r85540 = r85538 + r85539;
        double r85541 = r85540 * r85531;
        double r85542 = t;
        double r85543 = r85541 + r85542;
        double r85544 = a;
        double r85545 = r85531 + r85544;
        double r85546 = r85545 * r85531;
        double r85547 = b;
        double r85548 = r85546 + r85547;
        double r85549 = r85548 * r85531;
        double r85550 = cbrt(r85549);
        double r85551 = r85550 * r85550;
        double r85552 = r85551 * r85550;
        double r85553 = c;
        double r85554 = r85552 + r85553;
        double r85555 = r85554 * r85531;
        double r85556 = i;
        double r85557 = r85555 + r85556;
        double r85558 = r85543 / r85557;
        return r85558;
}

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 28.7

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}} + c\right) \cdot y + i}\]

  4. Final simplification28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020047 
(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)))