Average Error: 29.2 → 29.3
Time: 8.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r57503 = x;
        double r57504 = y;
        double r57505 = r57503 * r57504;
        double r57506 = z;
        double r57507 = r57505 + r57506;
        double r57508 = r57507 * r57504;
        double r57509 = 27464.7644705;
        double r57510 = r57508 + r57509;
        double r57511 = r57510 * r57504;
        double r57512 = 230661.510616;
        double r57513 = r57511 + r57512;
        double r57514 = r57513 * r57504;
        double r57515 = t;
        double r57516 = r57514 + r57515;
        double r57517 = a;
        double r57518 = r57504 + r57517;
        double r57519 = r57518 * r57504;
        double r57520 = b;
        double r57521 = r57519 + r57520;
        double r57522 = r57521 * r57504;
        double r57523 = c;
        double r57524 = r57522 + r57523;
        double r57525 = r57524 * r57504;
        double r57526 = i;
        double r57527 = r57525 + r57526;
        double r57528 = r57516 / r57527;
        return r57528;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r57529 = x;
        double r57530 = y;
        double r57531 = r57529 * r57530;
        double r57532 = z;
        double r57533 = r57531 + r57532;
        double r57534 = r57533 * r57530;
        double r57535 = 27464.7644705;
        double r57536 = r57534 + r57535;
        double r57537 = r57536 * r57530;
        double r57538 = cbrt(r57537);
        double r57539 = r57538 * r57538;
        double r57540 = r57539 * r57538;
        double r57541 = 230661.510616;
        double r57542 = r57540 + r57541;
        double r57543 = r57542 * r57530;
        double r57544 = t;
        double r57545 = r57543 + r57544;
        double r57546 = a;
        double r57547 = r57530 + r57546;
        double r57548 = r57547 * r57530;
        double r57549 = b;
        double r57550 = r57548 + r57549;
        double r57551 = r57550 * r57530;
        double r57552 = c;
        double r57553 = r57551 + r57552;
        double r57554 = r57553 * r57530;
        double r57555 = i;
        double r57556 = r57554 + r57555;
        double r57557 = r57545 / r57556;
        return r57557;
}

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 add-cube-cbrt29.3

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

  4. Final simplification29.3

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(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)))