Average Error: 28.5 → 28.5
Time: 1.3m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \left(\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(z + x \cdot y\right)\right) \cdot \sqrt[3]{y} + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\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(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(z + x \cdot y\right)\right) \cdot \sqrt[3]{y} + 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 r7033200 = x;
        double r7033201 = y;
        double r7033202 = r7033200 * r7033201;
        double r7033203 = z;
        double r7033204 = r7033202 + r7033203;
        double r7033205 = r7033204 * r7033201;
        double r7033206 = 27464.7644705;
        double r7033207 = r7033205 + r7033206;
        double r7033208 = r7033207 * r7033201;
        double r7033209 = 230661.510616;
        double r7033210 = r7033208 + r7033209;
        double r7033211 = r7033210 * r7033201;
        double r7033212 = t;
        double r7033213 = r7033211 + r7033212;
        double r7033214 = a;
        double r7033215 = r7033201 + r7033214;
        double r7033216 = r7033215 * r7033201;
        double r7033217 = b;
        double r7033218 = r7033216 + r7033217;
        double r7033219 = r7033218 * r7033201;
        double r7033220 = c;
        double r7033221 = r7033219 + r7033220;
        double r7033222 = r7033221 * r7033201;
        double r7033223 = i;
        double r7033224 = r7033222 + r7033223;
        double r7033225 = r7033213 / r7033224;
        return r7033225;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r7033226 = y;
        double r7033227 = 230661.510616;
        double r7033228 = cbrt(r7033226);
        double r7033229 = r7033228 * r7033228;
        double r7033230 = z;
        double r7033231 = x;
        double r7033232 = r7033231 * r7033226;
        double r7033233 = r7033230 + r7033232;
        double r7033234 = r7033229 * r7033233;
        double r7033235 = r7033234 * r7033228;
        double r7033236 = 27464.7644705;
        double r7033237 = r7033235 + r7033236;
        double r7033238 = r7033237 * r7033226;
        double r7033239 = r7033227 + r7033238;
        double r7033240 = r7033226 * r7033239;
        double r7033241 = t;
        double r7033242 = r7033240 + r7033241;
        double r7033243 = c;
        double r7033244 = b;
        double r7033245 = a;
        double r7033246 = r7033226 + r7033245;
        double r7033247 = r7033226 * r7033246;
        double r7033248 = r7033244 + r7033247;
        double r7033249 = r7033248 * r7033226;
        double r7033250 = r7033243 + r7033249;
        double r7033251 = r7033226 * r7033250;
        double r7033252 = i;
        double r7033253 = r7033251 + r7033252;
        double r7033254 = r7033242 / r7033253;
        return r7033254;
}

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 28.5

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

  3. Applied add-cube-cbrt28.5

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

  4. Applied associate-*r*28.5

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

  5. Final simplification28.5

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

Reproduce

herbie shell --seed 2019112 
(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)))