Average Error: 28.7 → 28.8
Time: 14.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right) \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} + c\right) \cdot y + i}\]
\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]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right) \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r81389 = x;
        double r81390 = y;
        double r81391 = r81389 * r81390;
        double r81392 = z;
        double r81393 = r81391 + r81392;
        double r81394 = r81393 * r81390;
        double r81395 = 27464.7644705;
        double r81396 = r81394 + r81395;
        double r81397 = r81396 * r81390;
        double r81398 = 230661.510616;
        double r81399 = r81397 + r81398;
        double r81400 = r81399 * r81390;
        double r81401 = t;
        double r81402 = r81400 + r81401;
        double r81403 = a;
        double r81404 = r81390 + r81403;
        double r81405 = r81404 * r81390;
        double r81406 = b;
        double r81407 = r81405 + r81406;
        double r81408 = r81407 * r81390;
        double r81409 = c;
        double r81410 = r81408 + r81409;
        double r81411 = r81410 * r81390;
        double r81412 = i;
        double r81413 = r81411 + r81412;
        double r81414 = r81402 / r81413;
        return r81414;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r81415 = x;
        double r81416 = y;
        double r81417 = r81415 * r81416;
        double r81418 = z;
        double r81419 = r81417 + r81418;
        double r81420 = r81419 * r81416;
        double r81421 = 27464.7644705;
        double r81422 = r81420 + r81421;
        double r81423 = r81422 * r81416;
        double r81424 = 230661.510616;
        double r81425 = r81423 + r81424;
        double r81426 = r81425 * r81416;
        double r81427 = t;
        double r81428 = r81426 + r81427;
        double r81429 = 2.0;
        double r81430 = pow(r81416, r81429);
        double r81431 = a;
        double r81432 = r81416 + r81431;
        double r81433 = r81430 * r81432;
        double r81434 = b;
        double r81435 = r81416 * r81434;
        double r81436 = r81433 + r81435;
        double r81437 = cbrt(r81436);
        double r81438 = r81437 * r81437;
        double r81439 = r81438 * r81437;
        double r81440 = c;
        double r81441 = r81439 + r81440;
        double r81442 = r81441 * r81416;
        double r81443 = i;
        double r81444 = r81442 + r81443;
        double r81445 = r81428 / r81444;
        return r81445;
}

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. Taylor expanded around inf 28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right)} + c\right) \cdot y + i}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)} \cdot \sqrt[3]{y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)}\right) \cdot \sqrt[3]{y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)}} + c\right) \cdot y + i}\]

  5. Simplified28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right)} \cdot \sqrt[3]{y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)} + c\right) \cdot y + i}\]

  6. Simplified28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right) \cdot \color{blue}{\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}} + c\right) \cdot y + i}\]

  7. Final simplification28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right) \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} + c\right) \cdot y + i}\]

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)))