Average Error: 28.7 → 28.8
Time: 14.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right) \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} + c\right) \cdot y + i}\]
\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(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right) \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71047 = x;
        double r71048 = y;
        double r71049 = r71047 * r71048;
        double r71050 = z;
        double r71051 = r71049 + r71050;
        double r71052 = r71051 * r71048;
        double r71053 = 27464.7644705;
        double r71054 = r71052 + r71053;
        double r71055 = r71054 * r71048;
        double r71056 = 230661.510616;
        double r71057 = r71055 + r71056;
        double r71058 = r71057 * r71048;
        double r71059 = t;
        double r71060 = r71058 + r71059;
        double r71061 = a;
        double r71062 = r71048 + r71061;
        double r71063 = r71062 * r71048;
        double r71064 = b;
        double r71065 = r71063 + r71064;
        double r71066 = r71065 * r71048;
        double r71067 = c;
        double r71068 = r71066 + r71067;
        double r71069 = r71068 * r71048;
        double r71070 = i;
        double r71071 = r71069 + r71070;
        double r71072 = r71060 / r71071;
        return r71072;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71073 = x;
        double r71074 = y;
        double r71075 = r71073 * r71074;
        double r71076 = z;
        double r71077 = r71075 + r71076;
        double r71078 = r71077 * r71074;
        double r71079 = 27464.7644705;
        double r71080 = r71078 + r71079;
        double r71081 = r71080 * r71074;
        double r71082 = 230661.510616;
        double r71083 = r71081 + r71082;
        double r71084 = r71083 * r71074;
        double r71085 = t;
        double r71086 = r71084 + r71085;
        double r71087 = 2.0;
        double r71088 = pow(r71074, r71087);
        double r71089 = a;
        double r71090 = r71074 + r71089;
        double r71091 = r71088 * r71090;
        double r71092 = b;
        double r71093 = r71074 * r71092;
        double r71094 = r71091 + r71093;
        double r71095 = cbrt(r71094);
        double r71096 = r71095 * r71095;
        double r71097 = r71096 * r71095;
        double r71098 = c;
        double r71099 = r71097 + r71098;
        double r71100 = r71099 * r71074;
        double r71101 = i;
        double r71102 = r71100 + r71101;
        double r71103 = r71086 / r71102;
        return r71103;
}

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. Taylor expanded around inf 28.7

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right)} + c\right) \cdot y + i}\]
  3. Using strategy rm

  4. Applied add-cube-cbrt28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)} \cdot \sqrt[3]{y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)}\right) \cdot \sqrt[3]{y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)}} + c\right) \cdot y + i}\]

  5. Simplified28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right)} \cdot \sqrt[3]{y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)} + c\right) \cdot y + i}\]

  6. Simplified28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right) \cdot \color{blue}{\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}} + c\right) \cdot y + i}\]

  7. Final simplification28.8

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b}\right) \cdot \sqrt[3]{{y}^{2} \cdot \left(y + a\right) + y \cdot b} + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020047 
(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)))