Average Error: 28.6 → 28.7
Time: 30.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}\right) \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}} \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot y\right) + t}{i + y \cdot \left(y \cdot \left(b + \left(a + y\right) \cdot y\right) + c\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}\right) \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}} \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot y\right) + t}{i + y \cdot \left(y \cdot \left(b + \left(a + y\right) \cdot y\right) + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5129456 = x;
        double r5129457 = y;
        double r5129458 = r5129456 * r5129457;
        double r5129459 = z;
        double r5129460 = r5129458 + r5129459;
        double r5129461 = r5129460 * r5129457;
        double r5129462 = 27464.7644705;
        double r5129463 = r5129461 + r5129462;
        double r5129464 = r5129463 * r5129457;
        double r5129465 = 230661.510616;
        double r5129466 = r5129464 + r5129465;
        double r5129467 = r5129466 * r5129457;
        double r5129468 = t;
        double r5129469 = r5129467 + r5129468;
        double r5129470 = a;
        double r5129471 = r5129457 + r5129470;
        double r5129472 = r5129471 * r5129457;
        double r5129473 = b;
        double r5129474 = r5129472 + r5129473;
        double r5129475 = r5129474 * r5129457;
        double r5129476 = c;
        double r5129477 = r5129475 + r5129476;
        double r5129478 = r5129477 * r5129457;
        double r5129479 = i;
        double r5129480 = r5129478 + r5129479;
        double r5129481 = r5129469 / r5129480;
        return r5129481;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r5129482 = y;
        double r5129483 = z;
        double r5129484 = x;
        double r5129485 = r5129484 * r5129482;
        double r5129486 = r5129483 + r5129485;
        double r5129487 = r5129482 * r5129486;
        double r5129488 = 27464.7644705;
        double r5129489 = r5129487 + r5129488;
        double r5129490 = r5129482 * r5129489;
        double r5129491 = 230661.510616;
        double r5129492 = r5129490 + r5129491;
        double r5129493 = cbrt(r5129492);
        double r5129494 = r5129493 * r5129493;
        double r5129495 = cbrt(r5129493);
        double r5129496 = r5129495 * r5129495;
        double r5129497 = r5129496 * r5129495;
        double r5129498 = r5129497 * r5129482;
        double r5129499 = r5129494 * r5129498;
        double r5129500 = t;
        double r5129501 = r5129499 + r5129500;
        double r5129502 = i;
        double r5129503 = b;
        double r5129504 = a;
        double r5129505 = r5129504 + r5129482;
        double r5129506 = r5129505 * r5129482;
        double r5129507 = r5129503 + r5129506;
        double r5129508 = r5129482 * r5129507;
        double r5129509 = c;
        double r5129510 = r5129508 + r5129509;
        double r5129511 = r5129482 * r5129510;
        double r5129512 = r5129502 + r5129511;
        double r5129513 = r5129501 / r5129512;
        return r5129513;
}

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 28.6

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt28.7

    \[\leadsto \frac{\color{blue}{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616}\right)} \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*28.7

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616}\right) \cdot \left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616} \cdot y\right)} + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt28.7

    \[\leadsto \frac{\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616}\right) \cdot \left(\color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616}} \cdot \sqrt[3]{\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616}}\right) \cdot \sqrt[3]{\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616}}\right)} \cdot y\right) + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  7. Final simplification28.7

    \[\leadsto \frac{\left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}\right) \cdot \left(\left(\left(\sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}} \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot \sqrt[3]{\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616}}\right) \cdot y\right) + t}{i + y \cdot \left(y \cdot \left(b + \left(a + y\right) \cdot y\right) + c\right)}\]

Reproduce

herbie shell --seed 2019163 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))