Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 9.6s

Precision: 64

Math

\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

↓

\[\frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r63605 = x;
        double r63606 = y;
        double r63607 = r63605 * r63606;
        double r63608 = z;
        double r63609 = r63607 + r63608;
        double r63610 = r63609 * r63606;
        double r63611 = 27464.7644705;
        double r63612 = r63610 + r63611;
        double r63613 = r63612 * r63606;
        double r63614 = 230661.510616;
        double r63615 = r63613 + r63614;
        double r63616 = r63615 * r63606;
        double r63617 = t;
        double r63618 = r63616 + r63617;
        double r63619 = a;
        double r63620 = r63606 + r63619;
        double r63621 = r63620 * r63606;
        double r63622 = b;
        double r63623 = r63621 + r63622;
        double r63624 = r63623 * r63606;
        double r63625 = c;
        double r63626 = r63624 + r63625;
        double r63627 = r63626 * r63606;
        double r63628 = i;
        double r63629 = r63627 + r63628;
        double r63630 = r63618 / r63629;
        return r63630;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r63631 = x;
        double r63632 = y;
        double r63633 = r63631 * r63632;
        double r63634 = z;
        double r63635 = r63633 + r63634;
        double r63636 = r63635 * r63632;
        double r63637 = 27464.7644705;
        double r63638 = r63636 + r63637;
        double r63639 = cbrt(r63638);
        double r63640 = r63639 * r63639;
        double r63641 = r63639 * r63632;
        double r63642 = r63640 * r63641;
        double r63643 = 230661.510616;
        double r63644 = r63642 + r63643;
        double r63645 = r63644 * r63632;
        double r63646 = t;
        double r63647 = r63645 + r63646;
        double r63648 = a;
        double r63649 = r63632 + r63648;
        double r63650 = r63649 * r63632;
        double r63651 = b;
        double r63652 = r63650 + r63651;
        double r63653 = r63652 * r63632;
        double r63654 = c;
        double r63655 = r63653 + r63654;
        double r63656 = r63655 * r63632;
        double r63657 = i;
        double r63658 = r63656 + r63657;
        double r63659 = r63647 / r63658;
        return r63659;
}

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. Initial program 29.1

   \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
2. Using strategy rm

3. Applied add-cube-cbrt 29.2

   \[\leadsto \frac{\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right)} \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

4. Applied associate-*l* 29.2

   \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right)} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

5. Final simplification 29.2

   \[\leadsto \frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(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)))