Average Error: 28.0 → 28.1
Time: 44.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\mathsf{fma}\left(y + a, y, b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right)}\]
\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{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\mathsf{fma}\left(y + a, y, b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2454760 = x;
        double r2454761 = y;
        double r2454762 = r2454760 * r2454761;
        double r2454763 = z;
        double r2454764 = r2454762 + r2454763;
        double r2454765 = r2454764 * r2454761;
        double r2454766 = 27464.7644705;
        double r2454767 = r2454765 + r2454766;
        double r2454768 = r2454767 * r2454761;
        double r2454769 = 230661.510616;
        double r2454770 = r2454768 + r2454769;
        double r2454771 = r2454770 * r2454761;
        double r2454772 = t;
        double r2454773 = r2454771 + r2454772;
        double r2454774 = a;
        double r2454775 = r2454761 + r2454774;
        double r2454776 = r2454775 * r2454761;
        double r2454777 = b;
        double r2454778 = r2454776 + r2454777;
        double r2454779 = r2454778 * r2454761;
        double r2454780 = c;
        double r2454781 = r2454779 + r2454780;
        double r2454782 = r2454781 * r2454761;
        double r2454783 = i;
        double r2454784 = r2454782 + r2454783;
        double r2454785 = r2454773 / r2454784;
        return r2454785;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2454786 = t;
        double r2454787 = y;
        double r2454788 = z;
        double r2454789 = x;
        double r2454790 = r2454789 * r2454787;
        double r2454791 = r2454788 + r2454790;
        double r2454792 = r2454787 * r2454791;
        double r2454793 = 27464.7644705;
        double r2454794 = r2454792 + r2454793;
        double r2454795 = r2454787 * r2454794;
        double r2454796 = 230661.510616;
        double r2454797 = r2454795 + r2454796;
        double r2454798 = r2454797 * r2454787;
        double r2454799 = r2454786 + r2454798;
        double r2454800 = i;
        double r2454801 = c;
        double r2454802 = a;
        double r2454803 = r2454787 + r2454802;
        double r2454804 = b;
        double r2454805 = fma(r2454803, r2454787, r2454804);
        double r2454806 = cbrt(r2454787);
        double r2454807 = r2454806 * r2454806;
        double r2454808 = r2454805 * r2454807;
        double r2454809 = r2454808 * r2454806;
        double r2454810 = r2454801 + r2454809;
        double r2454811 = r2454787 * r2454810;
        double r2454812 = r2454800 + r2454811;
        double r2454813 = r2454799 / r2454812;
        return r2454813;
}

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

Derivation

  1. Initial program 28.0

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

  3. Applied add-cube-cbrt28.1

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

  4. Applied associate-*r*28.1

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

  5. Simplified28.1

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

  6. Final simplification28.1

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

Reproduce

herbie shell --seed 2019151 +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)))