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 r70434 = x;
        double r70435 = y;
        double r70436 = r70434 * r70435;
        double r70437 = z;
        double r70438 = r70436 + r70437;
        double r70439 = r70438 * r70435;
        double r70440 = 27464.7644705;
        double r70441 = r70439 + r70440;
        double r70442 = r70441 * r70435;
        double r70443 = 230661.510616;
        double r70444 = r70442 + r70443;
        double r70445 = r70444 * r70435;
        double r70446 = t;
        double r70447 = r70445 + r70446;
        double r70448 = a;
        double r70449 = r70435 + r70448;
        double r70450 = r70449 * r70435;
        double r70451 = b;
        double r70452 = r70450 + r70451;
        double r70453 = r70452 * r70435;
        double r70454 = c;
        double r70455 = r70453 + r70454;
        double r70456 = r70455 * r70435;
        double r70457 = i;
        double r70458 = r70456 + r70457;
        double r70459 = r70447 / r70458;
        return r70459;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70460 = x;
        double r70461 = y;
        double r70462 = r70460 * r70461;
        double r70463 = z;
        double r70464 = r70462 + r70463;
        double r70465 = r70464 * r70461;
        double r70466 = cbrt(r70465);
        double r70467 = cbrt(r70466);
        double r70468 = r70467 * r70467;
        double r70469 = r70468 * r70467;
        double r70470 = r70466 * r70469;
        double r70471 = r70470 * r70466;
        double r70472 = 27464.7644705;
        double r70473 = r70471 + r70472;
        double r70474 = r70473 * r70461;
        double r70475 = 230661.510616;
        double r70476 = r70474 + r70475;
        double r70477 = r70476 * r70461;
        double r70478 = t;
        double r70479 = r70477 + r70478;
        double r70480 = a;
        double r70481 = r70461 + r70480;
        double r70482 = r70481 * r70461;
        double r70483 = b;
        double r70484 = r70482 + r70483;
        double r70485 = r70484 * r70461;
        double r70486 = c;
        double r70487 = r70485 + r70486;
        double r70488 = r70487 * r70461;
        double r70489 = i;
        double r70490 = r70488 + r70489;
        double r70491 = r70479 / r70490;
        return r70491;
}

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)))