Average Error: 28.6 → 28.7
Time: 33.5s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \mathsf{fma}\left(y + a, y, b\right)\right) \cdot \sqrt[3]{y}\right)}\]
\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{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644705\right) + 230661.510616\right) \cdot y}{i + y \cdot \left(c + \left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \mathsf{fma}\left(y + a, y, b\right)\right) \cdot \sqrt[3]{y}\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3986259 = x;
        double r3986260 = y;
        double r3986261 = r3986259 * r3986260;
        double r3986262 = z;
        double r3986263 = r3986261 + r3986262;
        double r3986264 = r3986263 * r3986260;
        double r3986265 = 27464.7644705;
        double r3986266 = r3986264 + r3986265;
        double r3986267 = r3986266 * r3986260;
        double r3986268 = 230661.510616;
        double r3986269 = r3986267 + r3986268;
        double r3986270 = r3986269 * r3986260;
        double r3986271 = t;
        double r3986272 = r3986270 + r3986271;
        double r3986273 = a;
        double r3986274 = r3986260 + r3986273;
        double r3986275 = r3986274 * r3986260;
        double r3986276 = b;
        double r3986277 = r3986275 + r3986276;
        double r3986278 = r3986277 * r3986260;
        double r3986279 = c;
        double r3986280 = r3986278 + r3986279;
        double r3986281 = r3986280 * r3986260;
        double r3986282 = i;
        double r3986283 = r3986281 + r3986282;
        double r3986284 = r3986272 / r3986283;
        return r3986284;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3986285 = t;
        double r3986286 = y;
        double r3986287 = z;
        double r3986288 = x;
        double r3986289 = r3986288 * r3986286;
        double r3986290 = r3986287 + r3986289;
        double r3986291 = r3986286 * r3986290;
        double r3986292 = 27464.7644705;
        double r3986293 = r3986291 + r3986292;
        double r3986294 = r3986286 * r3986293;
        double r3986295 = 230661.510616;
        double r3986296 = r3986294 + r3986295;
        double r3986297 = r3986296 * r3986286;
        double r3986298 = r3986285 + r3986297;
        double r3986299 = i;
        double r3986300 = c;
        double r3986301 = cbrt(r3986286);
        double r3986302 = r3986301 * r3986301;
        double r3986303 = a;
        double r3986304 = r3986286 + r3986303;
        double r3986305 = b;
        double r3986306 = fma(r3986304, r3986286, r3986305);
        double r3986307 = r3986302 * r3986306;
        double r3986308 = r3986307 * r3986301;
        double r3986309 = r3986300 + r3986308;
        double r3986310 = r3986286 * r3986309;
        double r3986311 = r3986299 + r3986310;
        double r3986312 = r3986298 / r3986311;
        return r3986312;
}

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

Derivation

  1. Initial program 28.6

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

  3. Applied add-cube-cbrt28.7

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

  4. Applied associate-*r*28.7

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

  5. Simplified28.7

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

  6. Final simplification28.7

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(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)))