Average Error: 29.1 → 29.2
Time: 1.3m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]
\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}
↓
\left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y\right) \cdot \frac{1}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3213642 = x;
        double r3213643 = y;
        double r3213644 = r3213642 * r3213643;
        double r3213645 = z;
        double r3213646 = r3213644 + r3213645;
        double r3213647 = r3213646 * r3213643;
        double r3213648 = 27464.7644705;
        double r3213649 = r3213647 + r3213648;
        double r3213650 = r3213649 * r3213643;
        double r3213651 = 230661.510616;
        double r3213652 = r3213650 + r3213651;
        double r3213653 = r3213652 * r3213643;
        double r3213654 = t;
        double r3213655 = r3213653 + r3213654;
        double r3213656 = a;
        double r3213657 = r3213643 + r3213656;
        double r3213658 = r3213657 * r3213643;
        double r3213659 = b;
        double r3213660 = r3213658 + r3213659;
        double r3213661 = r3213660 * r3213643;
        double r3213662 = c;
        double r3213663 = r3213661 + r3213662;
        double r3213664 = r3213663 * r3213643;
        double r3213665 = i;
        double r3213666 = r3213664 + r3213665;
        double r3213667 = r3213655 / r3213666;
        return r3213667;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3213668 = t;
        double r3213669 = y;
        double r3213670 = z;
        double r3213671 = x;
        double r3213672 = r3213671 * r3213669;
        double r3213673 = r3213670 + r3213672;
        double r3213674 = r3213669 * r3213673;
        double r3213675 = 27464.7644705;
        double r3213676 = r3213674 + r3213675;
        double r3213677 = r3213669 * r3213676;
        double r3213678 = 230661.510616;
        double r3213679 = r3213677 + r3213678;
        double r3213680 = r3213679 * r3213669;
        double r3213681 = r3213668 + r3213680;
        double r3213682 = 1.0;
        double r3213683 = i;
        double r3213684 = a;
        double r3213685 = r3213684 + r3213669;
        double r3213686 = r3213685 * r3213669;
        double r3213687 = b;
        double r3213688 = r3213686 + r3213687;
        double r3213689 = r3213688 * r3213669;
        double r3213690 = c;
        double r3213691 = r3213689 + r3213690;
        double r3213692 = r3213669 * r3213691;
        double r3213693 = r3213683 + r3213692;
        double r3213694 = r3213682 / r3213693;
        double r3213695 = r3213681 * r3213694;
        return r3213695;
}

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 29.1

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

  3. Applied div-inv29.2

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

  4. Final simplification29.2

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

Reproduce

herbie shell --seed 2019165 
(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)))