Average Error: 29.6 → 29.6
Time: 18.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{471841060772561}{17179869184}\right) \cdot y + \frac{7925469156333415}{34359738368}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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(\left(x \cdot y + z\right) \cdot y + \frac{471841060772561}{17179869184}\right) \cdot y + \frac{7925469156333415}{34359738368}\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 r69061 = x;
        double r69062 = y;
        double r69063 = r69061 * r69062;
        double r69064 = z;
        double r69065 = r69063 + r69064;
        double r69066 = r69065 * r69062;
        double r69067 = 27464.7644705;
        double r69068 = r69066 + r69067;
        double r69069 = r69068 * r69062;
        double r69070 = 230661.510616;
        double r69071 = r69069 + r69070;
        double r69072 = r69071 * r69062;
        double r69073 = t;
        double r69074 = r69072 + r69073;
        double r69075 = a;
        double r69076 = r69062 + r69075;
        double r69077 = r69076 * r69062;
        double r69078 = b;
        double r69079 = r69077 + r69078;
        double r69080 = r69079 * r69062;
        double r69081 = c;
        double r69082 = r69080 + r69081;
        double r69083 = r69082 * r69062;
        double r69084 = i;
        double r69085 = r69083 + r69084;
        double r69086 = r69074 / r69085;
        return r69086;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69087 = x;
        double r69088 = y;
        double r69089 = r69087 * r69088;
        double r69090 = z;
        double r69091 = r69089 + r69090;
        double r69092 = r69091 * r69088;
        double r69093 = 471841060772561.0;
        double r69094 = 17179869184.0;
        double r69095 = r69093 / r69094;
        double r69096 = r69092 + r69095;
        double r69097 = r69096 * r69088;
        double r69098 = 7925469156333415.0;
        double r69099 = 34359738368.0;
        double r69100 = r69098 / r69099;
        double r69101 = r69097 + r69100;
        double r69102 = r69101 * r69088;
        double r69103 = t;
        double r69104 = r69102 + r69103;
        double r69105 = a;
        double r69106 = r69088 + r69105;
        double r69107 = r69106 * r69088;
        double r69108 = b;
        double r69109 = r69107 + r69108;
        double r69110 = r69109 * r69088;
        double r69111 = c;
        double r69112 = r69110 + r69111;
        double r69113 = r69112 * r69088;
        double r69114 = i;
        double r69115 = r69113 + r69114;
        double r69116 = r69104 / r69115;
        return r69116;
}

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 29.6

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

  2. Final simplification29.6

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + \frac{471841060772561}{17179869184}\right) \cdot y + \frac{7925469156333415}{34359738368}\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019304 
(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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))