Average Error: 29.6 → 29.6
Time: 16.2s
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 r70097 = x;
        double r70098 = y;
        double r70099 = r70097 * r70098;
        double r70100 = z;
        double r70101 = r70099 + r70100;
        double r70102 = r70101 * r70098;
        double r70103 = 27464.7644705;
        double r70104 = r70102 + r70103;
        double r70105 = r70104 * r70098;
        double r70106 = 230661.510616;
        double r70107 = r70105 + r70106;
        double r70108 = r70107 * r70098;
        double r70109 = t;
        double r70110 = r70108 + r70109;
        double r70111 = a;
        double r70112 = r70098 + r70111;
        double r70113 = r70112 * r70098;
        double r70114 = b;
        double r70115 = r70113 + r70114;
        double r70116 = r70115 * r70098;
        double r70117 = c;
        double r70118 = r70116 + r70117;
        double r70119 = r70118 * r70098;
        double r70120 = i;
        double r70121 = r70119 + r70120;
        double r70122 = r70110 / r70121;
        return r70122;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70123 = x;
        double r70124 = y;
        double r70125 = r70123 * r70124;
        double r70126 = z;
        double r70127 = r70125 + r70126;
        double r70128 = r70127 * r70124;
        double r70129 = 471841060772561.0;
        double r70130 = 17179869184.0;
        double r70131 = r70129 / r70130;
        double r70132 = r70128 + r70131;
        double r70133 = r70132 * r70124;
        double r70134 = 7925469156333415.0;
        double r70135 = 34359738368.0;
        double r70136 = r70134 / r70135;
        double r70137 = r70133 + r70136;
        double r70138 = r70137 * r70124;
        double r70139 = t;
        double r70140 = r70138 + r70139;
        double r70141 = a;
        double r70142 = r70124 + r70141;
        double r70143 = r70142 * r70124;
        double r70144 = b;
        double r70145 = r70143 + r70144;
        double r70146 = r70145 * r70124;
        double r70147 = c;
        double r70148 = r70146 + r70147;
        double r70149 = r70148 * r70124;
        double r70150 = i;
        double r70151 = r70149 + r70150;
        double r70152 = r70140 / r70151;
        return r70152;
}

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. Simplified29.6

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

  3. 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)))