Average Error: 28.8 → 28.9
Time: 8.8s
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 r100020 = x;
        double r100021 = y;
        double r100022 = r100020 * r100021;
        double r100023 = z;
        double r100024 = r100022 + r100023;
        double r100025 = r100024 * r100021;
        double r100026 = 27464.7644705;
        double r100027 = r100025 + r100026;
        double r100028 = r100027 * r100021;
        double r100029 = 230661.510616;
        double r100030 = r100028 + r100029;
        double r100031 = r100030 * r100021;
        double r100032 = t;
        double r100033 = r100031 + r100032;
        double r100034 = a;
        double r100035 = r100021 + r100034;
        double r100036 = r100035 * r100021;
        double r100037 = b;
        double r100038 = r100036 + r100037;
        double r100039 = r100038 * r100021;
        double r100040 = c;
        double r100041 = r100039 + r100040;
        double r100042 = r100041 * r100021;
        double r100043 = i;
        double r100044 = r100042 + r100043;
        double r100045 = r100033 / r100044;
        return r100045;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r100046 = x;
        double r100047 = y;
        double r100048 = r100046 * r100047;
        double r100049 = z;
        double r100050 = r100048 + r100049;
        double r100051 = r100050 * r100047;
        double r100052 = 27464.7644705;
        double r100053 = r100051 + r100052;
        double r100054 = r100053 * r100047;
        double r100055 = cbrt(r100054);
        double r100056 = r100055 * r100055;
        double r100057 = r100056 * r100055;
        double r100058 = 230661.510616;
        double r100059 = r100057 + r100058;
        double r100060 = r100059 * r100047;
        double r100061 = t;
        double r100062 = r100060 + r100061;
        double r100063 = a;
        double r100064 = r100047 + r100063;
        double r100065 = r100064 * r100047;
        double r100066 = b;
        double r100067 = r100065 + r100066;
        double r100068 = r100067 * r100047;
        double r100069 = c;
        double r100070 = r100068 + r100069;
        double r100071 = r100070 * r100047;
        double r100072 = i;
        double r100073 = r100071 + r100072;
        double r100074 = r100062 / r100073;
        return r100074;
}

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

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

  3. Applied add-cube-cbrt28.9

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

  4. Final simplification28.9

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

Reproduce

herbie shell --seed 2020018 +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)))