Average Error: 29.0 → 29.0
Time: 44.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left(y \cdot y\right) \cdot \left(a + y\right)\right) + c\right) \cdot y + i}\]
\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}
↓
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left(y \cdot y\right) \cdot \left(a + y\right)\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71570 = x;
        double r71571 = y;
        double r71572 = r71570 * r71571;
        double r71573 = z;
        double r71574 = r71572 + r71573;
        double r71575 = r71574 * r71571;
        double r71576 = 27464.7644705;
        double r71577 = r71575 + r71576;
        double r71578 = r71577 * r71571;
        double r71579 = 230661.510616;
        double r71580 = r71578 + r71579;
        double r71581 = r71580 * r71571;
        double r71582 = t;
        double r71583 = r71581 + r71582;
        double r71584 = a;
        double r71585 = r71571 + r71584;
        double r71586 = r71585 * r71571;
        double r71587 = b;
        double r71588 = r71586 + r71587;
        double r71589 = r71588 * r71571;
        double r71590 = c;
        double r71591 = r71589 + r71590;
        double r71592 = r71591 * r71571;
        double r71593 = i;
        double r71594 = r71592 + r71593;
        double r71595 = r71583 / r71594;
        return r71595;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71596 = x;
        double r71597 = y;
        double r71598 = r71596 * r71597;
        double r71599 = z;
        double r71600 = r71598 + r71599;
        double r71601 = r71600 * r71597;
        double r71602 = 27464.7644705;
        double r71603 = r71601 + r71602;
        double r71604 = r71603 * r71597;
        double r71605 = 230661.510616;
        double r71606 = r71604 + r71605;
        double r71607 = r71606 * r71597;
        double r71608 = t;
        double r71609 = r71607 + r71608;
        double r71610 = b;
        double r71611 = r71597 * r71610;
        double r71612 = r71597 * r71597;
        double r71613 = a;
        double r71614 = r71613 + r71597;
        double r71615 = r71612 * r71614;
        double r71616 = r71611 + r71615;
        double r71617 = c;
        double r71618 = r71616 + r71617;
        double r71619 = r71618 * r71597;
        double r71620 = i;
        double r71621 = r71619 + r71620;
        double r71622 = r71609 / r71621;
        return r71622;
}

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 29.0

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

  2. Taylor expanded around inf 29.0

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right)} + c\right) \cdot y + i}\]

  3. Simplified29.0

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

  4. Final simplification29.0

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

Reproduce

herbie shell --seed 2019199 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))