Average Error: 29.2 → 29.3
Time: 8.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r55529 = x;
        double r55530 = y;
        double r55531 = r55529 * r55530;
        double r55532 = z;
        double r55533 = r55531 + r55532;
        double r55534 = r55533 * r55530;
        double r55535 = 27464.7644705;
        double r55536 = r55534 + r55535;
        double r55537 = r55536 * r55530;
        double r55538 = 230661.510616;
        double r55539 = r55537 + r55538;
        double r55540 = r55539 * r55530;
        double r55541 = t;
        double r55542 = r55540 + r55541;
        double r55543 = a;
        double r55544 = r55530 + r55543;
        double r55545 = r55544 * r55530;
        double r55546 = b;
        double r55547 = r55545 + r55546;
        double r55548 = r55547 * r55530;
        double r55549 = c;
        double r55550 = r55548 + r55549;
        double r55551 = r55550 * r55530;
        double r55552 = i;
        double r55553 = r55551 + r55552;
        double r55554 = r55542 / r55553;
        return r55554;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r55555 = x;
        double r55556 = y;
        double r55557 = r55555 * r55556;
        double r55558 = z;
        double r55559 = r55557 + r55558;
        double r55560 = r55559 * r55556;
        double r55561 = 27464.7644705;
        double r55562 = r55560 + r55561;
        double r55563 = r55562 * r55556;
        double r55564 = 230661.510616;
        double r55565 = r55563 + r55564;
        double r55566 = r55565 * r55556;
        double r55567 = t;
        double r55568 = r55566 + r55567;
        double r55569 = 1.0;
        double r55570 = a;
        double r55571 = r55556 + r55570;
        double r55572 = r55571 * r55556;
        double r55573 = b;
        double r55574 = r55572 + r55573;
        double r55575 = r55574 * r55556;
        double r55576 = c;
        double r55577 = r55575 + r55576;
        double r55578 = r55577 * r55556;
        double r55579 = i;
        double r55580 = r55578 + r55579;
        double r55581 = r55569 / r55580;
        double r55582 = r55568 * r55581;
        return r55582;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.2

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

  3. Applied div-inv29.3

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification29.3

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020003 
(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)))