Average Error: 28.6 → 28.7
Time: 32.0s
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 r3611611 = x;
        double r3611612 = y;
        double r3611613 = r3611611 * r3611612;
        double r3611614 = z;
        double r3611615 = r3611613 + r3611614;
        double r3611616 = r3611615 * r3611612;
        double r3611617 = 27464.7644705;
        double r3611618 = r3611616 + r3611617;
        double r3611619 = r3611618 * r3611612;
        double r3611620 = 230661.510616;
        double r3611621 = r3611619 + r3611620;
        double r3611622 = r3611621 * r3611612;
        double r3611623 = t;
        double r3611624 = r3611622 + r3611623;
        double r3611625 = a;
        double r3611626 = r3611612 + r3611625;
        double r3611627 = r3611626 * r3611612;
        double r3611628 = b;
        double r3611629 = r3611627 + r3611628;
        double r3611630 = r3611629 * r3611612;
        double r3611631 = c;
        double r3611632 = r3611630 + r3611631;
        double r3611633 = r3611632 * r3611612;
        double r3611634 = i;
        double r3611635 = r3611633 + r3611634;
        double r3611636 = r3611624 / r3611635;
        return r3611636;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3611637 = y;
        double r3611638 = z;
        double r3611639 = x;
        double r3611640 = r3611639 * r3611637;
        double r3611641 = r3611638 + r3611640;
        double r3611642 = r3611637 * r3611641;
        double r3611643 = 27464.7644705;
        double r3611644 = r3611642 + r3611643;
        double r3611645 = r3611637 * r3611644;
        double r3611646 = 230661.510616;
        double r3611647 = r3611645 + r3611646;
        double r3611648 = cbrt(r3611647);
        double r3611649 = r3611648 * r3611648;
        double r3611650 = cbrt(r3611648);
        double r3611651 = r3611650 * r3611650;
        double r3611652 = r3611651 * r3611650;
        double r3611653 = r3611652 * r3611637;
        double r3611654 = r3611649 * r3611653;
        double r3611655 = t;
        double r3611656 = r3611654 + r3611655;
        double r3611657 = i;
        double r3611658 = b;
        double r3611659 = a;
        double r3611660 = r3611659 + r3611637;
        double r3611661 = r3611660 * r3611637;
        double r3611662 = r3611658 + r3611661;
        double r3611663 = r3611637 * r3611662;
        double r3611664 = c;
        double r3611665 = r3611663 + r3611664;
        double r3611666 = r3611637 * r3611665;
        double r3611667 = r3611657 + r3611666;
        double r3611668 = r3611656 / r3611667;
        return r3611668;
}

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)))