Average Error: 28.8 → 28.9
Time: 2.4m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)}\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\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(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \left(\sqrt[3]{y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right)} \cdot \sqrt[3]{y \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 r3447298 = x;
        double r3447299 = y;
        double r3447300 = r3447298 * r3447299;
        double r3447301 = z;
        double r3447302 = r3447300 + r3447301;
        double r3447303 = r3447302 * r3447299;
        double r3447304 = 27464.7644705;
        double r3447305 = r3447303 + r3447304;
        double r3447306 = r3447305 * r3447299;
        double r3447307 = 230661.510616;
        double r3447308 = r3447306 + r3447307;
        double r3447309 = r3447308 * r3447299;
        double r3447310 = t;
        double r3447311 = r3447309 + r3447310;
        double r3447312 = a;
        double r3447313 = r3447299 + r3447312;
        double r3447314 = r3447313 * r3447299;
        double r3447315 = b;
        double r3447316 = r3447314 + r3447315;
        double r3447317 = r3447316 * r3447299;
        double r3447318 = c;
        double r3447319 = r3447317 + r3447318;
        double r3447320 = r3447319 * r3447299;
        double r3447321 = i;
        double r3447322 = r3447320 + r3447321;
        double r3447323 = r3447311 / r3447322;
        return r3447323;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3447324 = y;
        double r3447325 = 230661.510616;
        double r3447326 = z;
        double r3447327 = x;
        double r3447328 = r3447327 * r3447324;
        double r3447329 = r3447326 + r3447328;
        double r3447330 = r3447324 * r3447329;
        double r3447331 = 27464.7644705;
        double r3447332 = r3447330 + r3447331;
        double r3447333 = r3447324 * r3447332;
        double r3447334 = cbrt(r3447333);
        double r3447335 = r3447334 * r3447334;
        double r3447336 = r3447334 * r3447335;
        double r3447337 = r3447325 + r3447336;
        double r3447338 = r3447324 * r3447337;
        double r3447339 = t;
        double r3447340 = r3447338 + r3447339;
        double r3447341 = c;
        double r3447342 = b;
        double r3447343 = a;
        double r3447344 = r3447324 + r3447343;
        double r3447345 = r3447324 * r3447344;
        double r3447346 = r3447342 + r3447345;
        double r3447347 = r3447346 * r3447324;
        double r3447348 = r3447341 + r3447347;
        double r3447349 = r3447324 * r3447348;
        double r3447350 = i;
        double r3447351 = r3447349 + r3447350;
        double r3447352 = r3447340 / r3447351;
        return r3447352;
}

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 28.8

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

  3. Applied add-cube-cbrt28.9

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

  4. Final simplification28.9

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

Reproduce

herbie shell --seed 2019142 
(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)))