Average Error: 27.9 → 28.0
Time: 1.9m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \left(\left(\sqrt[3]{y \cdot \left(z + x \cdot y\right)} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)}\right) \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)} + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\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{y \cdot \left(230661.510616 + \left(\left(\sqrt[3]{y \cdot \left(z + x \cdot y\right)} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)}\right) \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)} + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r12278200 = x;
        double r12278201 = y;
        double r12278202 = r12278200 * r12278201;
        double r12278203 = z;
        double r12278204 = r12278202 + r12278203;
        double r12278205 = r12278204 * r12278201;
        double r12278206 = 27464.7644705;
        double r12278207 = r12278205 + r12278206;
        double r12278208 = r12278207 * r12278201;
        double r12278209 = 230661.510616;
        double r12278210 = r12278208 + r12278209;
        double r12278211 = r12278210 * r12278201;
        double r12278212 = t;
        double r12278213 = r12278211 + r12278212;
        double r12278214 = a;
        double r12278215 = r12278201 + r12278214;
        double r12278216 = r12278215 * r12278201;
        double r12278217 = b;
        double r12278218 = r12278216 + r12278217;
        double r12278219 = r12278218 * r12278201;
        double r12278220 = c;
        double r12278221 = r12278219 + r12278220;
        double r12278222 = r12278221 * r12278201;
        double r12278223 = i;
        double r12278224 = r12278222 + r12278223;
        double r12278225 = r12278213 / r12278224;
        return r12278225;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r12278226 = y;
        double r12278227 = 230661.510616;
        double r12278228 = z;
        double r12278229 = x;
        double r12278230 = r12278229 * r12278226;
        double r12278231 = r12278228 + r12278230;
        double r12278232 = r12278226 * r12278231;
        double r12278233 = cbrt(r12278232);
        double r12278234 = r12278233 * r12278233;
        double r12278235 = r12278234 * r12278233;
        double r12278236 = 27464.7644705;
        double r12278237 = r12278235 + r12278236;
        double r12278238 = r12278237 * r12278226;
        double r12278239 = r12278227 + r12278238;
        double r12278240 = r12278226 * r12278239;
        double r12278241 = t;
        double r12278242 = r12278240 + r12278241;
        double r12278243 = c;
        double r12278244 = b;
        double r12278245 = a;
        double r12278246 = r12278226 + r12278245;
        double r12278247 = r12278226 * r12278246;
        double r12278248 = r12278244 + r12278247;
        double r12278249 = r12278248 * r12278226;
        double r12278250 = r12278243 + r12278249;
        double r12278251 = r12278226 * r12278250;
        double r12278252 = i;
        double r12278253 = r12278251 + r12278252;
        double r12278254 = r12278242 / r12278253;
        return r12278254;
}

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 27.9

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

  3. Applied add-cube-cbrt28.0

    \[\leadsto \frac{\left(\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Final simplification28.0

    \[\leadsto \frac{y \cdot \left(230661.510616 + \left(\left(\sqrt[3]{y \cdot \left(z + x \cdot y\right)} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)}\right) \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right)} + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]

Reproduce

herbie shell --seed 2019125 
(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)))