Average Error: 28.6 → 28.6
Time: 32.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + y \cdot \left(\left(z + y \cdot x\right) \cdot y + 27464.7644705\right)\right) + t}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot y + i}\]
\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 + y \cdot \left(\left(z + y \cdot x\right) \cdot y + 27464.7644705\right)\right) + t}{\left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2081732 = x;
        double r2081733 = y;
        double r2081734 = r2081732 * r2081733;
        double r2081735 = z;
        double r2081736 = r2081734 + r2081735;
        double r2081737 = r2081736 * r2081733;
        double r2081738 = 27464.7644705;
        double r2081739 = r2081737 + r2081738;
        double r2081740 = r2081739 * r2081733;
        double r2081741 = 230661.510616;
        double r2081742 = r2081740 + r2081741;
        double r2081743 = r2081742 * r2081733;
        double r2081744 = t;
        double r2081745 = r2081743 + r2081744;
        double r2081746 = a;
        double r2081747 = r2081733 + r2081746;
        double r2081748 = r2081747 * r2081733;
        double r2081749 = b;
        double r2081750 = r2081748 + r2081749;
        double r2081751 = r2081750 * r2081733;
        double r2081752 = c;
        double r2081753 = r2081751 + r2081752;
        double r2081754 = r2081753 * r2081733;
        double r2081755 = i;
        double r2081756 = r2081754 + r2081755;
        double r2081757 = r2081745 / r2081756;
        return r2081757;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2081758 = y;
        double r2081759 = 230661.510616;
        double r2081760 = z;
        double r2081761 = x;
        double r2081762 = r2081758 * r2081761;
        double r2081763 = r2081760 + r2081762;
        double r2081764 = r2081763 * r2081758;
        double r2081765 = 27464.7644705;
        double r2081766 = r2081764 + r2081765;
        double r2081767 = r2081758 * r2081766;
        double r2081768 = r2081759 + r2081767;
        double r2081769 = r2081758 * r2081768;
        double r2081770 = t;
        double r2081771 = r2081769 + r2081770;
        double r2081772 = c;
        double r2081773 = b;
        double r2081774 = a;
        double r2081775 = r2081758 + r2081774;
        double r2081776 = r2081758 * r2081775;
        double r2081777 = r2081773 + r2081776;
        double r2081778 = r2081758 * r2081777;
        double r2081779 = r2081772 + r2081778;
        double r2081780 = r2081779 * r2081758;
        double r2081781 = i;
        double r2081782 = r2081780 + r2081781;
        double r2081783 = r2081771 / r2081782;
        return r2081783;
}

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 *-un-lft-identity28.6

    \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-/l*28.8

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]
  5. Using strategy rm

  6. Applied div-inv28.9

    \[\leadsto \frac{1}{\color{blue}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]
  7. Using strategy rm

  8. Applied div-inv28.9

    \[\leadsto \color{blue}{1 \cdot \frac{1}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]

  9. Simplified28.6

    \[\leadsto 1 \cdot \color{blue}{\frac{t + y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right)}{i + y \cdot \left(c + \left(y \cdot \left(a + y\right) + b\right) \cdot y\right)}}\]

  10. Final simplification28.6

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

Reproduce

herbie shell --seed 2019129 
(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)))