Average Error: 29.5 → 29.6
Time: 8.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + c\right) \cdot y + i}\]
\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(\left(\left(y + a\right) \cdot y + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{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 r74419 = x;
        double r74420 = y;
        double r74421 = r74419 * r74420;
        double r74422 = z;
        double r74423 = r74421 + r74422;
        double r74424 = r74423 * r74420;
        double r74425 = 27464.7644705;
        double r74426 = r74424 + r74425;
        double r74427 = r74426 * r74420;
        double r74428 = 230661.510616;
        double r74429 = r74427 + r74428;
        double r74430 = r74429 * r74420;
        double r74431 = t;
        double r74432 = r74430 + r74431;
        double r74433 = a;
        double r74434 = r74420 + r74433;
        double r74435 = r74434 * r74420;
        double r74436 = b;
        double r74437 = r74435 + r74436;
        double r74438 = r74437 * r74420;
        double r74439 = c;
        double r74440 = r74438 + r74439;
        double r74441 = r74440 * r74420;
        double r74442 = i;
        double r74443 = r74441 + r74442;
        double r74444 = r74432 / r74443;
        return r74444;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r74445 = x;
        double r74446 = y;
        double r74447 = r74445 * r74446;
        double r74448 = z;
        double r74449 = r74447 + r74448;
        double r74450 = r74449 * r74446;
        double r74451 = 27464.7644705;
        double r74452 = r74450 + r74451;
        double r74453 = r74452 * r74446;
        double r74454 = 230661.510616;
        double r74455 = r74453 + r74454;
        double r74456 = r74455 * r74446;
        double r74457 = t;
        double r74458 = r74456 + r74457;
        double r74459 = a;
        double r74460 = r74446 + r74459;
        double r74461 = r74460 * r74446;
        double r74462 = b;
        double r74463 = r74461 + r74462;
        double r74464 = cbrt(r74446);
        double r74465 = r74464 * r74464;
        double r74466 = r74463 * r74465;
        double r74467 = r74466 * r74464;
        double r74468 = c;
        double r74469 = r74467 + r74468;
        double r74470 = r74469 * r74446;
        double r74471 = i;
        double r74472 = r74470 + r74471;
        double r74473 = r74458 / r74472;
        return r74473;
}

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 29.5

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

  3. Applied add-cube-cbrt29.6

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

  4. Applied associate-*r*29.6

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

  5. Final simplification29.6

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

Reproduce

herbie shell --seed 2020046 
(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)))