Average Error: 28.9 → 28.9
Time: 31.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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}
↓
\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r74026 = x;
        double r74027 = y;
        double r74028 = r74026 * r74027;
        double r74029 = z;
        double r74030 = r74028 + r74029;
        double r74031 = r74030 * r74027;
        double r74032 = 27464.7644705;
        double r74033 = r74031 + r74032;
        double r74034 = r74033 * r74027;
        double r74035 = 230661.510616;
        double r74036 = r74034 + r74035;
        double r74037 = r74036 * r74027;
        double r74038 = t;
        double r74039 = r74037 + r74038;
        double r74040 = a;
        double r74041 = r74027 + r74040;
        double r74042 = r74041 * r74027;
        double r74043 = b;
        double r74044 = r74042 + r74043;
        double r74045 = r74044 * r74027;
        double r74046 = c;
        double r74047 = r74045 + r74046;
        double r74048 = r74047 * r74027;
        double r74049 = i;
        double r74050 = r74048 + r74049;
        double r74051 = r74039 / r74050;
        return r74051;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r74052 = x;
        double r74053 = y;
        double r74054 = r74052 * r74053;
        double r74055 = z;
        double r74056 = r74054 + r74055;
        double r74057 = r74056 * r74053;
        double r74058 = 27464.7644705;
        double r74059 = r74057 + r74058;
        double r74060 = r74059 * r74053;
        double r74061 = cbrt(r74060);
        double r74062 = r74061 * r74061;
        double r74063 = r74062 * r74061;
        double r74064 = 230661.510616;
        double r74065 = r74063 + r74064;
        double r74066 = r74065 * r74053;
        double r74067 = t;
        double r74068 = r74066 + r74067;
        double r74069 = a;
        double r74070 = r74053 + r74069;
        double r74071 = r74070 * r74053;
        double r74072 = b;
        double r74073 = r74071 + r74072;
        double r74074 = r74073 * r74053;
        double r74075 = c;
        double r74076 = r74074 + r74075;
        double r74077 = r74076 * r74053;
        double r74078 = i;
        double r74079 = r74077 + r74078;
        double r74080 = r74068 / r74079;
        return r74080;
}

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 28.9

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

  3. Applied add-cube-cbrt28.9

    \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Final simplification28.9

    \[\leadsto \frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019322 
(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)))