Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.4 → 28.6

Time: 17.7s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 2.1539959223483919 \cdot 10^{306}:\\ \;\;\;\;\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65639 = x;
        double r65640 = y;
        double r65641 = r65639 * r65640;
        double r65642 = z;
        double r65643 = r65641 + r65642;
        double r65644 = r65643 * r65640;
        double r65645 = 27464.7644705;
        double r65646 = r65644 + r65645;
        double r65647 = r65646 * r65640;
        double r65648 = 230661.510616;
        double r65649 = r65647 + r65648;
        double r65650 = r65649 * r65640;
        double r65651 = t;
        double r65652 = r65650 + r65651;
        double r65653 = a;
        double r65654 = r65640 + r65653;
        double r65655 = r65654 * r65640;
        double r65656 = b;
        double r65657 = r65655 + r65656;
        double r65658 = r65657 * r65640;
        double r65659 = c;
        double r65660 = r65658 + r65659;
        double r65661 = r65660 * r65640;
        double r65662 = i;
        double r65663 = r65661 + r65662;
        double r65664 = r65652 / r65663;
        return r65664;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65665 = x;
        double r65666 = y;
        double r65667 = r65665 * r65666;
        double r65668 = z;
        double r65669 = r65667 + r65668;
        double r65670 = r65669 * r65666;
        double r65671 = 27464.7644705;
        double r65672 = r65670 + r65671;
        double r65673 = r65672 * r65666;
        double r65674 = 230661.510616;
        double r65675 = r65673 + r65674;
        double r65676 = r65675 * r65666;
        double r65677 = t;
        double r65678 = r65676 + r65677;
        double r65679 = a;
        double r65680 = r65666 + r65679;
        double r65681 = r65680 * r65666;
        double r65682 = b;
        double r65683 = r65681 + r65682;
        double r65684 = r65683 * r65666;
        double r65685 = c;
        double r65686 = r65684 + r65685;
        double r65687 = r65686 * r65666;
        double r65688 = i;
        double r65689 = r65687 + r65688;
        double r65690 = r65678 / r65689;
        double r65691 = 2.153995922348392e+306;
        bool r65692 = r65690 <= r65691;
        double r65693 = cbrt(r65673);
        double r65694 = r65693 * r65693;
        double r65695 = r65694 * r65693;
        double r65696 = r65695 + r65674;
        double r65697 = r65696 * r65666;
        double r65698 = r65697 + r65677;
        double r65699 = r65698 / r65689;
        double r65700 = 0.0;
        double r65701 = r65692 ? r65699 : r65700;
        return r65701;
}

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

Derivation

1. Split input into 2 regimes

2. if (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)) < 2.153995922348392e+306

   1. Initial program 5.8

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

   3. Applied add-cube-cbrt 6.0

      \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

   if 2.153995922348392e+306 < (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))

   1. Initial program 64.0

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

   2. Taylor expanded around 0 61.8

      \[\leadsto \color{blue}{0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 28.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 2.1539959223483919 \cdot 10^{306}:\\ \;\;\;\;\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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)))