Average Error: 28.5 → 28.7
Time: 5.0m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)}{t + y \cdot \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right)}}\]
\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{1}{\frac{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)}{t + y \cdot \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right)}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r36625718 = x;
        double r36625719 = y;
        double r36625720 = r36625718 * r36625719;
        double r36625721 = z;
        double r36625722 = r36625720 + r36625721;
        double r36625723 = r36625722 * r36625719;
        double r36625724 = 27464.7644705;
        double r36625725 = r36625723 + r36625724;
        double r36625726 = r36625725 * r36625719;
        double r36625727 = 230661.510616;
        double r36625728 = r36625726 + r36625727;
        double r36625729 = r36625728 * r36625719;
        double r36625730 = t;
        double r36625731 = r36625729 + r36625730;
        double r36625732 = a;
        double r36625733 = r36625719 + r36625732;
        double r36625734 = r36625733 * r36625719;
        double r36625735 = b;
        double r36625736 = r36625734 + r36625735;
        double r36625737 = r36625736 * r36625719;
        double r36625738 = c;
        double r36625739 = r36625737 + r36625738;
        double r36625740 = r36625739 * r36625719;
        double r36625741 = i;
        double r36625742 = r36625740 + r36625741;
        double r36625743 = r36625731 / r36625742;
        return r36625743;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r36625744 = 1.0;
        double r36625745 = i;
        double r36625746 = y;
        double r36625747 = b;
        double r36625748 = a;
        double r36625749 = r36625746 + r36625748;
        double r36625750 = r36625749 * r36625746;
        double r36625751 = r36625747 + r36625750;
        double r36625752 = r36625751 * r36625746;
        double r36625753 = c;
        double r36625754 = r36625752 + r36625753;
        double r36625755 = r36625746 * r36625754;
        double r36625756 = r36625745 + r36625755;
        double r36625757 = t;
        double r36625758 = x;
        double r36625759 = r36625746 * r36625758;
        double r36625760 = z;
        double r36625761 = r36625759 + r36625760;
        double r36625762 = r36625761 * r36625746;
        double r36625763 = 27464.7644705;
        double r36625764 = r36625762 + r36625763;
        double r36625765 = r36625764 * r36625746;
        double r36625766 = 230661.510616;
        double r36625767 = r36625765 + r36625766;
        double r36625768 = r36625746 * r36625767;
        double r36625769 = r36625757 + r36625768;
        double r36625770 = r36625756 / r36625769;
        double r36625771 = r36625744 / r36625770;
        return r36625771;
}

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 28.5

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

  3. Applied clear-num28.7

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

  4. Final simplification28.7

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

Reproduce

herbie shell --seed 2019107 
(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)))