Average Error: 28.3 → 28.3
Time: 32.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(230661.510616 + \left(27464.7644705 + \left(x \cdot \left(y \cdot y\right) + y \cdot z\right)\right) \cdot y\right) \cdot y + t}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\left(230661.510616 + \left(27464.7644705 + \left(x \cdot \left(y \cdot y\right) + y \cdot z\right)\right) \cdot y\right) \cdot y + t}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1257048 = x;
        double r1257049 = y;
        double r1257050 = r1257048 * r1257049;
        double r1257051 = z;
        double r1257052 = r1257050 + r1257051;
        double r1257053 = r1257052 * r1257049;
        double r1257054 = 27464.7644705;
        double r1257055 = r1257053 + r1257054;
        double r1257056 = r1257055 * r1257049;
        double r1257057 = 230661.510616;
        double r1257058 = r1257056 + r1257057;
        double r1257059 = r1257058 * r1257049;
        double r1257060 = t;
        double r1257061 = r1257059 + r1257060;
        double r1257062 = a;
        double r1257063 = r1257049 + r1257062;
        double r1257064 = r1257063 * r1257049;
        double r1257065 = b;
        double r1257066 = r1257064 + r1257065;
        double r1257067 = r1257066 * r1257049;
        double r1257068 = c;
        double r1257069 = r1257067 + r1257068;
        double r1257070 = r1257069 * r1257049;
        double r1257071 = i;
        double r1257072 = r1257070 + r1257071;
        double r1257073 = r1257061 / r1257072;
        return r1257073;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1257074 = 230661.510616;
        double r1257075 = 27464.7644705;
        double r1257076 = x;
        double r1257077 = y;
        double r1257078 = r1257077 * r1257077;
        double r1257079 = r1257076 * r1257078;
        double r1257080 = z;
        double r1257081 = r1257077 * r1257080;
        double r1257082 = r1257079 + r1257081;
        double r1257083 = r1257075 + r1257082;
        double r1257084 = r1257083 * r1257077;
        double r1257085 = r1257074 + r1257084;
        double r1257086 = r1257085 * r1257077;
        double r1257087 = t;
        double r1257088 = r1257086 + r1257087;
        double r1257089 = i;
        double r1257090 = a;
        double r1257091 = r1257090 + r1257077;
        double r1257092 = r1257091 * r1257077;
        double r1257093 = b;
        double r1257094 = r1257092 + r1257093;
        double r1257095 = r1257094 * r1257077;
        double r1257096 = c;
        double r1257097 = r1257095 + r1257096;
        double r1257098 = r1257077 * r1257097;
        double r1257099 = r1257089 + r1257098;
        double r1257100 = r1257088 / r1257099;
        return r1257100;
}

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 28.3

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Taylor expanded around -inf 28.3

    \[\leadsto \frac{\left(\left(\color{blue}{\left(z \cdot y + x \cdot {y}^{2}\right)} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  3. Simplified28.3

    \[\leadsto \frac{\left(\left(\color{blue}{\left(x \cdot \left(y \cdot y\right) + z \cdot y\right)} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Final simplification28.3

    \[\leadsto \frac{\left(230661.510616 + \left(27464.7644705 + \left(x \cdot \left(y \cdot y\right) + y \cdot z\right)\right) \cdot y\right) \cdot y + t}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]

Reproduce

herbie shell --seed 2019153 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))