Average Error: 28.3 → 28.3
Time: 25.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(230661.510616 + \left(27464.7644705 + \left(x \cdot \left(y \cdot y\right) + y \cdot z\right)\right) \cdot y\right) \cdot y + t}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\left(230661.510616 + \left(27464.7644705 + \left(x \cdot \left(y \cdot y\right) + y \cdot z\right)\right) \cdot y\right) \cdot y + t}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1240448 = x;
        double r1240449 = y;
        double r1240450 = r1240448 * r1240449;
        double r1240451 = z;
        double r1240452 = r1240450 + r1240451;
        double r1240453 = r1240452 * r1240449;
        double r1240454 = 27464.7644705;
        double r1240455 = r1240453 + r1240454;
        double r1240456 = r1240455 * r1240449;
        double r1240457 = 230661.510616;
        double r1240458 = r1240456 + r1240457;
        double r1240459 = r1240458 * r1240449;
        double r1240460 = t;
        double r1240461 = r1240459 + r1240460;
        double r1240462 = a;
        double r1240463 = r1240449 + r1240462;
        double r1240464 = r1240463 * r1240449;
        double r1240465 = b;
        double r1240466 = r1240464 + r1240465;
        double r1240467 = r1240466 * r1240449;
        double r1240468 = c;
        double r1240469 = r1240467 + r1240468;
        double r1240470 = r1240469 * r1240449;
        double r1240471 = i;
        double r1240472 = r1240470 + r1240471;
        double r1240473 = r1240461 / r1240472;
        return r1240473;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1240474 = 230661.510616;
        double r1240475 = 27464.7644705;
        double r1240476 = x;
        double r1240477 = y;
        double r1240478 = r1240477 * r1240477;
        double r1240479 = r1240476 * r1240478;
        double r1240480 = z;
        double r1240481 = r1240477 * r1240480;
        double r1240482 = r1240479 + r1240481;
        double r1240483 = r1240475 + r1240482;
        double r1240484 = r1240483 * r1240477;
        double r1240485 = r1240474 + r1240484;
        double r1240486 = r1240485 * r1240477;
        double r1240487 = t;
        double r1240488 = r1240486 + r1240487;
        double r1240489 = i;
        double r1240490 = a;
        double r1240491 = r1240490 + r1240477;
        double r1240492 = r1240491 * r1240477;
        double r1240493 = b;
        double r1240494 = r1240492 + r1240493;
        double r1240495 = r1240494 * r1240477;
        double r1240496 = c;
        double r1240497 = r1240495 + r1240496;
        double r1240498 = r1240477 * r1240497;
        double r1240499 = r1240489 + r1240498;
        double r1240500 = r1240488 / r1240499;
        return r1240500;
}

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 28.3

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Taylor expanded around 0 28.3

    \[\leadsto \frac{\left(\left(\color{blue}{\left(x \cdot {y}^{2} + z \cdot y\right)} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  3. Simplified28.3

    \[\leadsto \frac{\left(\left(\color{blue}{\left(x \cdot \left(y \cdot y\right) + z \cdot y\right)} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Final simplification28.3

    \[\leadsto \frac{\left(230661.510616 + \left(27464.7644705 + \left(x \cdot \left(y \cdot y\right) + y \cdot z\right)\right) \cdot y\right) \cdot y + t}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]

Reproduce

herbie shell --seed 2019153 
(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)))