Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 7.6s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69535 = x;
        double r69536 = y;
        double r69537 = r69535 * r69536;
        double r69538 = z;
        double r69539 = r69537 + r69538;
        double r69540 = r69539 * r69536;
        double r69541 = 27464.7644705;
        double r69542 = r69540 + r69541;
        double r69543 = r69542 * r69536;
        double r69544 = 230661.510616;
        double r69545 = r69543 + r69544;
        double r69546 = r69545 * r69536;
        double r69547 = t;
        double r69548 = r69546 + r69547;
        double r69549 = a;
        double r69550 = r69536 + r69549;
        double r69551 = r69550 * r69536;
        double r69552 = b;
        double r69553 = r69551 + r69552;
        double r69554 = r69553 * r69536;
        double r69555 = c;
        double r69556 = r69554 + r69555;
        double r69557 = r69556 * r69536;
        double r69558 = i;
        double r69559 = r69557 + r69558;
        double r69560 = r69548 / r69559;
        return r69560;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69561 = x;
        double r69562 = y;
        double r69563 = r69561 * r69562;
        double r69564 = z;
        double r69565 = r69563 + r69564;
        double r69566 = r69565 * r69562;
        double r69567 = cbrt(r69566);
        double r69568 = cbrt(r69567);
        double r69569 = r69568 * r69568;
        double r69570 = r69569 * r69568;
        double r69571 = r69570 * r69567;
        double r69572 = r69571 * r69567;
        double r69573 = 27464.7644705;
        double r69574 = r69572 + r69573;
        double r69575 = r69574 * r69562;
        double r69576 = 230661.510616;
        double r69577 = r69575 + r69576;
        double r69578 = r69577 * r69562;
        double r69579 = t;
        double r69580 = r69578 + r69579;
        double r69581 = a;
        double r69582 = r69562 + r69581;
        double r69583 = r69582 * r69562;
        double r69584 = b;
        double r69585 = r69583 + r69584;
        double r69586 = r69585 * r69562;
        double r69587 = c;
        double r69588 = r69586 + r69587;
        double r69589 = r69588 * r69562;
        double r69590 = i;
        double r69591 = r69589 + r69590;
        double r69592 = r69580 / r69591;
        return r69592;
}

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

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

6. Final simplification 29.2

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

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)))