Average Error: 29.3 → 29.3
Time: 14.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y}{i + y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)}\]
\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{t + \left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y}{i + y \cdot \left(\left(\left(y + a\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 r62487 = x;
        double r62488 = y;
        double r62489 = r62487 * r62488;
        double r62490 = z;
        double r62491 = r62489 + r62490;
        double r62492 = r62491 * r62488;
        double r62493 = 27464.7644705;
        double r62494 = r62492 + r62493;
        double r62495 = r62494 * r62488;
        double r62496 = 230661.510616;
        double r62497 = r62495 + r62496;
        double r62498 = r62497 * r62488;
        double r62499 = t;
        double r62500 = r62498 + r62499;
        double r62501 = a;
        double r62502 = r62488 + r62501;
        double r62503 = r62502 * r62488;
        double r62504 = b;
        double r62505 = r62503 + r62504;
        double r62506 = r62505 * r62488;
        double r62507 = c;
        double r62508 = r62506 + r62507;
        double r62509 = r62508 * r62488;
        double r62510 = i;
        double r62511 = r62509 + r62510;
        double r62512 = r62500 / r62511;
        return r62512;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62513 = t;
        double r62514 = x;
        double r62515 = y;
        double r62516 = r62514 * r62515;
        double r62517 = z;
        double r62518 = r62516 + r62517;
        double r62519 = r62518 * r62515;
        double r62520 = 27464.7644705;
        double r62521 = r62519 + r62520;
        double r62522 = r62521 * r62515;
        double r62523 = 230661.510616;
        double r62524 = r62522 + r62523;
        double r62525 = r62524 * r62515;
        double r62526 = r62513 + r62525;
        double r62527 = i;
        double r62528 = a;
        double r62529 = r62515 + r62528;
        double r62530 = r62529 * r62515;
        double r62531 = b;
        double r62532 = r62530 + r62531;
        double r62533 = r62532 * r62515;
        double r62534 = c;
        double r62535 = r62533 + r62534;
        double r62536 = r62515 * r62535;
        double r62537 = r62527 + r62536;
        double r62538 = r62526 / r62537;
        return r62538;
}

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 29.3

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

  5. Applied add-cube-cbrt29.5

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\color{blue}{\left(\sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}} + i}\]
  6. Using strategy rm

  7. Applied pow129.5

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \color{blue}{{\left(\frac{1}{\left(\sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i}\right)}^{1}}\]

  8. Applied pow129.5

    \[\leadsto \color{blue}{{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right)}^{1}} \cdot {\left(\frac{1}{\left(\sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i}\right)}^{1}\]

  9. Applied pow-prod-down29.5

    \[\leadsto \color{blue}{{\left(\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i}\right)}^{1}}\]

  10. Simplified29.3

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

  11. Final simplification29.3

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

Reproduce

herbie shell --seed 2020045 
(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)))