Average Error: 28.8 → 28.9
Time: 1.9m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{y \cdot \left(c + \sqrt[3]{y \cdot \left(b + \left(y + a\right) \cdot y\right)} \cdot \left(\sqrt[3]{y \cdot \left(b + \left(y + a\right) \cdot y\right)} \cdot \sqrt[3]{y \cdot \left(b + \left(y + a\right) \cdot y\right)}\right)\right) + i}\]
\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{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{y \cdot \left(c + \sqrt[3]{y \cdot \left(b + \left(y + a\right) \cdot y\right)} \cdot \left(\sqrt[3]{y \cdot \left(b + \left(y + a\right) \cdot y\right)} \cdot \sqrt[3]{y \cdot \left(b + \left(y + a\right) \cdot y\right)}\right)\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r11204654 = x;
        double r11204655 = y;
        double r11204656 = r11204654 * r11204655;
        double r11204657 = z;
        double r11204658 = r11204656 + r11204657;
        double r11204659 = r11204658 * r11204655;
        double r11204660 = 27464.7644705;
        double r11204661 = r11204659 + r11204660;
        double r11204662 = r11204661 * r11204655;
        double r11204663 = 230661.510616;
        double r11204664 = r11204662 + r11204663;
        double r11204665 = r11204664 * r11204655;
        double r11204666 = t;
        double r11204667 = r11204665 + r11204666;
        double r11204668 = a;
        double r11204669 = r11204655 + r11204668;
        double r11204670 = r11204669 * r11204655;
        double r11204671 = b;
        double r11204672 = r11204670 + r11204671;
        double r11204673 = r11204672 * r11204655;
        double r11204674 = c;
        double r11204675 = r11204673 + r11204674;
        double r11204676 = r11204675 * r11204655;
        double r11204677 = i;
        double r11204678 = r11204676 + r11204677;
        double r11204679 = r11204667 / r11204678;
        return r11204679;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r11204680 = t;
        double r11204681 = y;
        double r11204682 = z;
        double r11204683 = x;
        double r11204684 = r11204683 * r11204681;
        double r11204685 = r11204682 + r11204684;
        double r11204686 = r11204681 * r11204685;
        double r11204687 = 27464.7644705;
        double r11204688 = r11204686 + r11204687;
        double r11204689 = r11204681 * r11204688;
        double r11204690 = 230661.510616;
        double r11204691 = r11204689 + r11204690;
        double r11204692 = r11204691 * r11204681;
        double r11204693 = r11204680 + r11204692;
        double r11204694 = c;
        double r11204695 = b;
        double r11204696 = a;
        double r11204697 = r11204681 + r11204696;
        double r11204698 = r11204697 * r11204681;
        double r11204699 = r11204695 + r11204698;
        double r11204700 = r11204681 * r11204699;
        double r11204701 = cbrt(r11204700);
        double r11204702 = r11204701 * r11204701;
        double r11204703 = r11204701 * r11204702;
        double r11204704 = r11204694 + r11204703;
        double r11204705 = r11204681 * r11204704;
        double r11204706 = i;
        double r11204707 = r11204705 + r11204706;
        double r11204708 = r11204693 / r11204707;
        return r11204708;
}

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 28.8

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

  3. Applied add-cube-cbrt28.9

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

  4. Final simplification28.9

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

Reproduce

herbie shell --seed 2019121 
(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)))