Average Error: 28.8 → 28.9
Time: 27.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\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 r57482 = x;
        double r57483 = y;
        double r57484 = r57482 * r57483;
        double r57485 = z;
        double r57486 = r57484 + r57485;
        double r57487 = r57486 * r57483;
        double r57488 = 27464.7644705;
        double r57489 = r57487 + r57488;
        double r57490 = r57489 * r57483;
        double r57491 = 230661.510616;
        double r57492 = r57490 + r57491;
        double r57493 = r57492 * r57483;
        double r57494 = t;
        double r57495 = r57493 + r57494;
        double r57496 = a;
        double r57497 = r57483 + r57496;
        double r57498 = r57497 * r57483;
        double r57499 = b;
        double r57500 = r57498 + r57499;
        double r57501 = r57500 * r57483;
        double r57502 = c;
        double r57503 = r57501 + r57502;
        double r57504 = r57503 * r57483;
        double r57505 = i;
        double r57506 = r57504 + r57505;
        double r57507 = r57495 / r57506;
        return r57507;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r57508 = x;
        double r57509 = y;
        double r57510 = r57508 * r57509;
        double r57511 = z;
        double r57512 = r57510 + r57511;
        double r57513 = r57512 * r57509;
        double r57514 = 27464.7644705;
        double r57515 = r57513 + r57514;
        double r57516 = r57515 * r57509;
        double r57517 = 230661.510616;
        double r57518 = r57516 + r57517;
        double r57519 = r57518 * r57509;
        double r57520 = t;
        double r57521 = r57519 + r57520;
        double r57522 = 1.0;
        double r57523 = a;
        double r57524 = r57509 + r57523;
        double r57525 = r57524 * r57509;
        double r57526 = b;
        double r57527 = r57525 + r57526;
        double r57528 = r57527 * r57509;
        double r57529 = c;
        double r57530 = r57528 + r57529;
        double r57531 = r57530 * r57509;
        double r57532 = i;
        double r57533 = r57531 + r57532;
        double r57534 = r57522 / r57533;
        double r57535 = r57521 * r57534;
        return r57535;
}

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 28.8

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

  3. Applied div-inv28.9

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification28.9

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019303 
(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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))