Average Error: 29.5 → 29.6
Time: 8.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]
\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]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77692 = x;
        double r77693 = y;
        double r77694 = r77692 * r77693;
        double r77695 = z;
        double r77696 = r77694 + r77695;
        double r77697 = r77696 * r77693;
        double r77698 = 27464.7644705;
        double r77699 = r77697 + r77698;
        double r77700 = r77699 * r77693;
        double r77701 = 230661.510616;
        double r77702 = r77700 + r77701;
        double r77703 = r77702 * r77693;
        double r77704 = t;
        double r77705 = r77703 + r77704;
        double r77706 = a;
        double r77707 = r77693 + r77706;
        double r77708 = r77707 * r77693;
        double r77709 = b;
        double r77710 = r77708 + r77709;
        double r77711 = r77710 * r77693;
        double r77712 = c;
        double r77713 = r77711 + r77712;
        double r77714 = r77713 * r77693;
        double r77715 = i;
        double r77716 = r77714 + r77715;
        double r77717 = r77705 / r77716;
        return r77717;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77718 = x;
        double r77719 = y;
        double r77720 = r77718 * r77719;
        double r77721 = z;
        double r77722 = r77720 + r77721;
        double r77723 = r77722 * r77719;
        double r77724 = 27464.7644705;
        double r77725 = r77723 + r77724;
        double r77726 = r77725 * r77719;
        double r77727 = 230661.510616;
        double r77728 = r77726 + r77727;
        double r77729 = r77728 * r77719;
        double r77730 = t;
        double r77731 = r77729 + r77730;
        double r77732 = a;
        double r77733 = r77719 + r77732;
        double r77734 = r77733 * r77719;
        double r77735 = b;
        double r77736 = r77734 + r77735;
        double r77737 = cbrt(r77736);
        double r77738 = r77737 * r77737;
        double r77739 = r77737 * r77719;
        double r77740 = r77738 * r77739;
        double r77741 = c;
        double r77742 = r77740 + r77741;
        double r77743 = r77742 * r77719;
        double r77744 = i;
        double r77745 = r77743 + r77744;
        double r77746 = r77731 / r77745;
        return r77746;
}

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

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

  4. Applied associate-*l*29.6

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

  5. Final simplification29.6

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))