Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 9.1s

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 r59595 = x;
        double r59596 = y;
        double r59597 = r59595 * r59596;
        double r59598 = z;
        double r59599 = r59597 + r59598;
        double r59600 = r59599 * r59596;
        double r59601 = 27464.7644705;
        double r59602 = r59600 + r59601;
        double r59603 = r59602 * r59596;
        double r59604 = 230661.510616;
        double r59605 = r59603 + r59604;
        double r59606 = r59605 * r59596;
        double r59607 = t;
        double r59608 = r59606 + r59607;
        double r59609 = a;
        double r59610 = r59596 + r59609;
        double r59611 = r59610 * r59596;
        double r59612 = b;
        double r59613 = r59611 + r59612;
        double r59614 = r59613 * r59596;
        double r59615 = c;
        double r59616 = r59614 + r59615;
        double r59617 = r59616 * r59596;
        double r59618 = i;
        double r59619 = r59617 + r59618;
        double r59620 = r59608 / r59619;
        return r59620;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59621 = x;
        double r59622 = y;
        double r59623 = r59621 * r59622;
        double r59624 = z;
        double r59625 = r59623 + r59624;
        double r59626 = r59625 * r59622;
        double r59627 = 27464.7644705;
        double r59628 = r59626 + r59627;
        double r59629 = cbrt(r59628);
        double r59630 = r59629 * r59629;
        double r59631 = r59629 * r59622;
        double r59632 = r59630 * r59631;
        double r59633 = 230661.510616;
        double r59634 = r59632 + r59633;
        double r59635 = r59634 * r59622;
        double r59636 = t;
        double r59637 = r59635 + r59636;
        double r59638 = a;
        double r59639 = r59622 + r59638;
        double r59640 = r59639 * r59622;
        double r59641 = b;
        double r59642 = r59640 + r59641;
        double r59643 = r59642 * r59622;
        double r59644 = c;
        double r59645 = r59643 + r59644;
        double r59646 = r59645 * r59622;
        double r59647 = i;
        double r59648 = r59646 + r59647;
        double r59649 = r59637 / r59648;
        return r59649;
}

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 2020002 
(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)))