Average Error: 28.7 → 28.8
Time: 7.8s
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 r65014 = x;
        double r65015 = y;
        double r65016 = r65014 * r65015;
        double r65017 = z;
        double r65018 = r65016 + r65017;
        double r65019 = r65018 * r65015;
        double r65020 = 27464.7644705;
        double r65021 = r65019 + r65020;
        double r65022 = r65021 * r65015;
        double r65023 = 230661.510616;
        double r65024 = r65022 + r65023;
        double r65025 = r65024 * r65015;
        double r65026 = t;
        double r65027 = r65025 + r65026;
        double r65028 = a;
        double r65029 = r65015 + r65028;
        double r65030 = r65029 * r65015;
        double r65031 = b;
        double r65032 = r65030 + r65031;
        double r65033 = r65032 * r65015;
        double r65034 = c;
        double r65035 = r65033 + r65034;
        double r65036 = r65035 * r65015;
        double r65037 = i;
        double r65038 = r65036 + r65037;
        double r65039 = r65027 / r65038;
        return r65039;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r65040 = x;
        double r65041 = y;
        double r65042 = r65040 * r65041;
        double r65043 = z;
        double r65044 = r65042 + r65043;
        double r65045 = r65044 * r65041;
        double r65046 = 27464.7644705;
        double r65047 = r65045 + r65046;
        double r65048 = r65047 * r65041;
        double r65049 = cbrt(r65048);
        double r65050 = r65049 * r65049;
        double r65051 = r65050 * r65049;
        double r65052 = 230661.510616;
        double r65053 = r65051 + r65052;
        double r65054 = r65053 * r65041;
        double r65055 = t;
        double r65056 = r65054 + r65055;
        double r65057 = a;
        double r65058 = r65041 + r65057;
        double r65059 = r65058 * r65041;
        double r65060 = b;
        double r65061 = r65059 + r65060;
        double r65062 = r65061 * r65041;
        double r65063 = c;
        double r65064 = r65062 + r65063;
        double r65065 = r65064 * r65041;
        double r65066 = i;
        double r65067 = r65065 + r65066;
        double r65068 = r65056 / r65067;
        return r65068;
}

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 28.7

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

  3. Applied add-cube-cbrt28.8

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

  4. Final simplification28.8

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

Reproduce

herbie shell --seed 2020065 
(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)))