Average Error: 28.2 → 28.3
Time: 4.1m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \sqrt[3]{y} \cdot \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\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 + \sqrt[3]{y} \cdot \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)\right)\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 r3895199 = x;
        double r3895200 = y;
        double r3895201 = r3895199 * r3895200;
        double r3895202 = z;
        double r3895203 = r3895201 + r3895202;
        double r3895204 = r3895203 * r3895200;
        double r3895205 = 27464.7644705;
        double r3895206 = r3895204 + r3895205;
        double r3895207 = r3895206 * r3895200;
        double r3895208 = 230661.510616;
        double r3895209 = r3895207 + r3895208;
        double r3895210 = r3895209 * r3895200;
        double r3895211 = t;
        double r3895212 = r3895210 + r3895211;
        double r3895213 = a;
        double r3895214 = r3895200 + r3895213;
        double r3895215 = r3895214 * r3895200;
        double r3895216 = b;
        double r3895217 = r3895215 + r3895216;
        double r3895218 = r3895217 * r3895200;
        double r3895219 = c;
        double r3895220 = r3895218 + r3895219;
        double r3895221 = r3895220 * r3895200;
        double r3895222 = i;
        double r3895223 = r3895221 + r3895222;
        double r3895224 = r3895212 / r3895223;
        return r3895224;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3895225 = y;
        double r3895226 = 230661.510616;
        double r3895227 = cbrt(r3895225);
        double r3895228 = r3895227 * r3895227;
        double r3895229 = z;
        double r3895230 = x;
        double r3895231 = r3895230 * r3895225;
        double r3895232 = r3895229 + r3895231;
        double r3895233 = r3895225 * r3895232;
        double r3895234 = 27464.7644705;
        double r3895235 = r3895233 + r3895234;
        double r3895236 = r3895228 * r3895235;
        double r3895237 = r3895227 * r3895236;
        double r3895238 = r3895226 + r3895237;
        double r3895239 = r3895225 * r3895238;
        double r3895240 = t;
        double r3895241 = r3895239 + r3895240;
        double r3895242 = c;
        double r3895243 = b;
        double r3895244 = a;
        double r3895245 = r3895225 + r3895244;
        double r3895246 = r3895225 * r3895245;
        double r3895247 = r3895243 + r3895246;
        double r3895248 = r3895247 * r3895225;
        double r3895249 = r3895242 + r3895248;
        double r3895250 = r3895225 * r3895249;
        double r3895251 = i;
        double r3895252 = r3895250 + r3895251;
        double r3895253 = r3895241 / r3895252;
        return r3895253;
}

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 28.2

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

  3. Applied add-cube-cbrt28.3

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

  4. Applied associate-*r*28.3

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

  5. Final simplification28.3

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

Reproduce

herbie shell --seed 2019144 
(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)))