Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 7.5s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r55578 = x;
        double r55579 = y;
        double r55580 = r55578 * r55579;
        double r55581 = z;
        double r55582 = r55580 + r55581;
        double r55583 = r55582 * r55579;
        double r55584 = 27464.7644705;
        double r55585 = r55583 + r55584;
        double r55586 = r55585 * r55579;
        double r55587 = 230661.510616;
        double r55588 = r55586 + r55587;
        double r55589 = r55588 * r55579;
        double r55590 = t;
        double r55591 = r55589 + r55590;
        double r55592 = a;
        double r55593 = r55579 + r55592;
        double r55594 = r55593 * r55579;
        double r55595 = b;
        double r55596 = r55594 + r55595;
        double r55597 = r55596 * r55579;
        double r55598 = c;
        double r55599 = r55597 + r55598;
        double r55600 = r55599 * r55579;
        double r55601 = i;
        double r55602 = r55600 + r55601;
        double r55603 = r55591 / r55602;
        return r55603;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r55604 = x;
        double r55605 = y;
        double r55606 = r55604 * r55605;
        double r55607 = z;
        double r55608 = r55606 + r55607;
        double r55609 = r55608 * r55605;
        double r55610 = cbrt(r55609);
        double r55611 = cbrt(r55610);
        double r55612 = r55611 * r55611;
        double r55613 = r55612 * r55611;
        double r55614 = r55610 * r55613;
        double r55615 = r55614 * r55610;
        double r55616 = 27464.7644705;
        double r55617 = r55615 + r55616;
        double r55618 = r55617 * r55605;
        double r55619 = 230661.510616;
        double r55620 = r55618 + r55619;
        double r55621 = r55620 * r55605;
        double r55622 = t;
        double r55623 = r55621 + r55622;
        double r55624 = a;
        double r55625 = r55605 + r55624;
        double r55626 = r55625 * r55605;
        double r55627 = b;
        double r55628 = r55626 + r55627;
        double r55629 = r55628 * r55605;
        double r55630 = c;
        double r55631 = r55629 + r55630;
        double r55632 = r55631 * r55605;
        double r55633 = i;
        double r55634 = r55632 + r55633;
        double r55635 = r55623 / r55634;
        return r55635;
}

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

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

3. Applied add-cube-cbrt 29.2

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

5. Applied add-cube-cbrt 29.2

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

6. Final simplification 29.2

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

Reproduce

herbie shell --seed 2020062 
(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)))