Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.2 → 29.3

Time: 28.9s

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 r57538 = x;
        double r57539 = y;
        double r57540 = r57538 * r57539;
        double r57541 = z;
        double r57542 = r57540 + r57541;
        double r57543 = r57542 * r57539;
        double r57544 = 27464.7644705;
        double r57545 = r57543 + r57544;
        double r57546 = r57545 * r57539;
        double r57547 = 230661.510616;
        double r57548 = r57546 + r57547;
        double r57549 = r57548 * r57539;
        double r57550 = t;
        double r57551 = r57549 + r57550;
        double r57552 = a;
        double r57553 = r57539 + r57552;
        double r57554 = r57553 * r57539;
        double r57555 = b;
        double r57556 = r57554 + r57555;
        double r57557 = r57556 * r57539;
        double r57558 = c;
        double r57559 = r57557 + r57558;
        double r57560 = r57559 * r57539;
        double r57561 = i;
        double r57562 = r57560 + r57561;
        double r57563 = r57551 / r57562;
        return r57563;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r57564 = x;
        double r57565 = y;
        double r57566 = r57564 * r57565;
        double r57567 = z;
        double r57568 = r57566 + r57567;
        double r57569 = r57568 * r57565;
        double r57570 = 27464.7644705;
        double r57571 = r57569 + r57570;
        double r57572 = cbrt(r57571);
        double r57573 = r57572 * r57572;
        double r57574 = r57572 * r57565;
        double r57575 = r57573 * r57574;
        double r57576 = 230661.510616;
        double r57577 = r57575 + r57576;
        double r57578 = r57577 * r57565;
        double r57579 = t;
        double r57580 = r57578 + r57579;
        double r57581 = a;
        double r57582 = r57565 + r57581;
        double r57583 = r57582 * r57565;
        double r57584 = b;
        double r57585 = r57583 + r57584;
        double r57586 = r57585 * r57565;
        double r57587 = c;
        double r57588 = r57586 + r57587;
        double r57589 = r57588 * r57565;
        double r57590 = i;
        double r57591 = r57589 + r57590;
        double r57592 = r57580 / r57591;
        return r57592;
}

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 29.2

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

3. Applied add-cube-cbrt 29.3

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

4. Applied associate-*l* 29.3

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

5. Final simplification 29.3

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

Reproduce

herbie shell --seed 2019326 
(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)))