Average Error: 28.8 → 29.1
Time: 8.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}\]
\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{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 + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r79623 = x;
        double r79624 = y;
        double r79625 = r79623 * r79624;
        double r79626 = z;
        double r79627 = r79625 + r79626;
        double r79628 = r79627 * r79624;
        double r79629 = 27464.7644705;
        double r79630 = r79628 + r79629;
        double r79631 = r79630 * r79624;
        double r79632 = 230661.510616;
        double r79633 = r79631 + r79632;
        double r79634 = r79633 * r79624;
        double r79635 = t;
        double r79636 = r79634 + r79635;
        double r79637 = a;
        double r79638 = r79624 + r79637;
        double r79639 = r79638 * r79624;
        double r79640 = b;
        double r79641 = r79639 + r79640;
        double r79642 = r79641 * r79624;
        double r79643 = c;
        double r79644 = r79642 + r79643;
        double r79645 = r79644 * r79624;
        double r79646 = i;
        double r79647 = r79645 + r79646;
        double r79648 = r79636 / r79647;
        return r79648;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r79649 = 1.0;
        double r79650 = y;
        double r79651 = a;
        double r79652 = r79650 + r79651;
        double r79653 = r79652 * r79650;
        double r79654 = b;
        double r79655 = r79653 + r79654;
        double r79656 = r79655 * r79650;
        double r79657 = c;
        double r79658 = r79656 + r79657;
        double r79659 = r79658 * r79650;
        double r79660 = i;
        double r79661 = r79659 + r79660;
        double r79662 = x;
        double r79663 = r79662 * r79650;
        double r79664 = z;
        double r79665 = r79663 + r79664;
        double r79666 = r79665 * r79650;
        double r79667 = 27464.7644705;
        double r79668 = r79666 + r79667;
        double r79669 = r79668 * r79650;
        double r79670 = 230661.510616;
        double r79671 = r79669 + r79670;
        double r79672 = r79671 * r79650;
        double r79673 = t;
        double r79674 = r79672 + r79673;
        double r79675 = r79649 / r79674;
        double r79676 = r79661 * r79675;
        double r79677 = r79649 / r79676;
        return r79677;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied clear-num29.1

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]
  4. Using strategy rm

  5. Applied div-inv29.1

    \[\leadsto \frac{1}{\color{blue}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}}\]

  6. Final simplification29.1

    \[\leadsto \frac{1}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}\]

Reproduce

herbie shell --seed 2020018 
(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)))