Average Error: 28.1 → 28.2
Time: 1.8m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \left(\left(\sqrt[3]{y \cdot \left(z + x \cdot y\right)} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)}\right) \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)} + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\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{y \cdot \left(230661.510616 + \left(\left(\sqrt[3]{y \cdot \left(z + x \cdot y\right)} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)}\right) \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)} + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r9615605 = x;
        double r9615606 = y;
        double r9615607 = r9615605 * r9615606;
        double r9615608 = z;
        double r9615609 = r9615607 + r9615608;
        double r9615610 = r9615609 * r9615606;
        double r9615611 = 27464.7644705;
        double r9615612 = r9615610 + r9615611;
        double r9615613 = r9615612 * r9615606;
        double r9615614 = 230661.510616;
        double r9615615 = r9615613 + r9615614;
        double r9615616 = r9615615 * r9615606;
        double r9615617 = t;
        double r9615618 = r9615616 + r9615617;
        double r9615619 = a;
        double r9615620 = r9615606 + r9615619;
        double r9615621 = r9615620 * r9615606;
        double r9615622 = b;
        double r9615623 = r9615621 + r9615622;
        double r9615624 = r9615623 * r9615606;
        double r9615625 = c;
        double r9615626 = r9615624 + r9615625;
        double r9615627 = r9615626 * r9615606;
        double r9615628 = i;
        double r9615629 = r9615627 + r9615628;
        double r9615630 = r9615618 / r9615629;
        return r9615630;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r9615631 = y;
        double r9615632 = 230661.510616;
        double r9615633 = z;
        double r9615634 = x;
        double r9615635 = r9615634 * r9615631;
        double r9615636 = r9615633 + r9615635;
        double r9615637 = r9615631 * r9615636;
        double r9615638 = cbrt(r9615637);
        double r9615639 = r9615638 * r9615638;
        double r9615640 = r9615639 * r9615638;
        double r9615641 = 27464.7644705;
        double r9615642 = r9615640 + r9615641;
        double r9615643 = r9615642 * r9615631;
        double r9615644 = r9615632 + r9615643;
        double r9615645 = r9615631 * r9615644;
        double r9615646 = t;
        double r9615647 = r9615645 + r9615646;
        double r9615648 = c;
        double r9615649 = b;
        double r9615650 = a;
        double r9615651 = r9615631 + r9615650;
        double r9615652 = r9615631 * r9615651;
        double r9615653 = r9615649 + r9615652;
        double r9615654 = r9615653 * r9615631;
        double r9615655 = r9615648 + r9615654;
        double r9615656 = r9615631 * r9615655;
        double r9615657 = i;
        double r9615658 = r9615656 + r9615657;
        double r9615659 = r9615647 / r9615658;
        return r9615659;
}

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 28.1

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

  3. Applied add-cube-cbrt28.2

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

  4. Final simplification28.2

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

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(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)))