Average Error: 28.7 → 28.8
Time: 16.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r88182 = x;
        double r88183 = y;
        double r88184 = r88182 * r88183;
        double r88185 = z;
        double r88186 = r88184 + r88185;
        double r88187 = r88186 * r88183;
        double r88188 = 27464.7644705;
        double r88189 = r88187 + r88188;
        double r88190 = r88189 * r88183;
        double r88191 = 230661.510616;
        double r88192 = r88190 + r88191;
        double r88193 = r88192 * r88183;
        double r88194 = t;
        double r88195 = r88193 + r88194;
        double r88196 = a;
        double r88197 = r88183 + r88196;
        double r88198 = r88197 * r88183;
        double r88199 = b;
        double r88200 = r88198 + r88199;
        double r88201 = r88200 * r88183;
        double r88202 = c;
        double r88203 = r88201 + r88202;
        double r88204 = r88203 * r88183;
        double r88205 = i;
        double r88206 = r88204 + r88205;
        double r88207 = r88195 / r88206;
        return r88207;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r88208 = x;
        double r88209 = y;
        double r88210 = r88208 * r88209;
        double r88211 = z;
        double r88212 = r88210 + r88211;
        double r88213 = r88212 * r88209;
        double r88214 = 27464.7644705;
        double r88215 = r88213 + r88214;
        double r88216 = r88215 * r88209;
        double r88217 = 230661.510616;
        double r88218 = r88216 + r88217;
        double r88219 = r88218 * r88209;
        double r88220 = t;
        double r88221 = r88219 + r88220;
        double r88222 = 1.0;
        double r88223 = b;
        double r88224 = r88209 * r88223;
        double r88225 = 3.0;
        double r88226 = pow(r88209, r88225);
        double r88227 = a;
        double r88228 = 2.0;
        double r88229 = pow(r88209, r88228);
        double r88230 = r88227 * r88229;
        double r88231 = r88226 + r88230;
        double r88232 = r88224 + r88231;
        double r88233 = c;
        double r88234 = r88232 + r88233;
        double r88235 = r88234 * r88209;
        double r88236 = i;
        double r88237 = r88235 + r88236;
        double r88238 = r88222 / r88237;
        double r88239 = r88221 * r88238;
        return r88239;
}

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 div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}}\]

  5. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]

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)))