Average Error: 29.0 → 29.1
Time: 27.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(230661.5106160000141244381666183471679688 + \left(27464.7644704999984242022037506103515625 + \left(\left(y \cdot y\right) \cdot x + z \cdot y\right)\right) \cdot y\right) \cdot y + t\right) \cdot \frac{1}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(a + y\right) + b\right)\right)}\]
\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}
↓
\left(\left(230661.5106160000141244381666183471679688 + \left(27464.7644704999984242022037506103515625 + \left(\left(y \cdot y\right) \cdot x + z \cdot y\right)\right) \cdot y\right) \cdot y + t\right) \cdot \frac{1}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(a + y\right) + b\right)\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73128 = x;
        double r73129 = y;
        double r73130 = r73128 * r73129;
        double r73131 = z;
        double r73132 = r73130 + r73131;
        double r73133 = r73132 * r73129;
        double r73134 = 27464.7644705;
        double r73135 = r73133 + r73134;
        double r73136 = r73135 * r73129;
        double r73137 = 230661.510616;
        double r73138 = r73136 + r73137;
        double r73139 = r73138 * r73129;
        double r73140 = t;
        double r73141 = r73139 + r73140;
        double r73142 = a;
        double r73143 = r73129 + r73142;
        double r73144 = r73143 * r73129;
        double r73145 = b;
        double r73146 = r73144 + r73145;
        double r73147 = r73146 * r73129;
        double r73148 = c;
        double r73149 = r73147 + r73148;
        double r73150 = r73149 * r73129;
        double r73151 = i;
        double r73152 = r73150 + r73151;
        double r73153 = r73141 / r73152;
        return r73153;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73154 = 230661.510616;
        double r73155 = 27464.7644705;
        double r73156 = y;
        double r73157 = r73156 * r73156;
        double r73158 = x;
        double r73159 = r73157 * r73158;
        double r73160 = z;
        double r73161 = r73160 * r73156;
        double r73162 = r73159 + r73161;
        double r73163 = r73155 + r73162;
        double r73164 = r73163 * r73156;
        double r73165 = r73154 + r73164;
        double r73166 = r73165 * r73156;
        double r73167 = t;
        double r73168 = r73166 + r73167;
        double r73169 = 1.0;
        double r73170 = i;
        double r73171 = c;
        double r73172 = a;
        double r73173 = r73172 + r73156;
        double r73174 = r73156 * r73173;
        double r73175 = b;
        double r73176 = r73174 + r73175;
        double r73177 = r73156 * r73176;
        double r73178 = r73171 + r73177;
        double r73179 = r73156 * r73178;
        double r73180 = r73170 + r73179;
        double r73181 = r73169 / r73180;
        double r73182 = r73168 * r73181;
        return r73182;
}

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 29.0

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

  2. Taylor expanded around 0 29.0

    \[\leadsto \frac{\left(\left(\color{blue}{\left(x \cdot {y}^{2} + z \cdot y\right)} + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  3. Simplified29.0

    \[\leadsto \frac{\left(\left(\color{blue}{\left(z \cdot y + \left(y \cdot y\right) \cdot x\right)} + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  4. Using strategy rm

  5. Applied div-inv29.1

    \[\leadsto \color{blue}{\left(\left(\left(\left(z \cdot y + \left(y \cdot y\right) \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  6. Simplified29.1

    \[\leadsto \left(\left(\left(\left(z \cdot y + \left(y \cdot y\right) \cdot x\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \color{blue}{\frac{1}{i + y \cdot \left(c + y \cdot \left(b + y \cdot \left(y + a\right)\right)\right)}}\]

  7. Final simplification29.1

    \[\leadsto \left(\left(230661.5106160000141244381666183471679688 + \left(27464.7644704999984242022037506103515625 + \left(\left(y \cdot y\right) \cdot x + z \cdot y\right)\right) \cdot y\right) \cdot y + t\right) \cdot \frac{1}{i + y \cdot \left(c + y \cdot \left(y \cdot \left(a + y\right) + b\right)\right)}\]

Reproduce

herbie shell --seed 2019196 
(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)))