Average Error: 28.1 → 28.2
Time: 28.6s
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 r1280327 = x;
        double r1280328 = y;
        double r1280329 = r1280327 * r1280328;
        double r1280330 = z;
        double r1280331 = r1280329 + r1280330;
        double r1280332 = r1280331 * r1280328;
        double r1280333 = 27464.7644705;
        double r1280334 = r1280332 + r1280333;
        double r1280335 = r1280334 * r1280328;
        double r1280336 = 230661.510616;
        double r1280337 = r1280335 + r1280336;
        double r1280338 = r1280337 * r1280328;
        double r1280339 = t;
        double r1280340 = r1280338 + r1280339;
        double r1280341 = a;
        double r1280342 = r1280328 + r1280341;
        double r1280343 = r1280342 * r1280328;
        double r1280344 = b;
        double r1280345 = r1280343 + r1280344;
        double r1280346 = r1280345 * r1280328;
        double r1280347 = c;
        double r1280348 = r1280346 + r1280347;
        double r1280349 = r1280348 * r1280328;
        double r1280350 = i;
        double r1280351 = r1280349 + r1280350;
        double r1280352 = r1280340 / r1280351;
        return r1280352;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1280353 = y;
        double r1280354 = 230661.510616;
        double r1280355 = z;
        double r1280356 = x;
        double r1280357 = r1280356 * r1280353;
        double r1280358 = r1280355 + r1280357;
        double r1280359 = r1280353 * r1280358;
        double r1280360 = cbrt(r1280359);
        double r1280361 = r1280360 * r1280360;
        double r1280362 = r1280361 * r1280360;
        double r1280363 = 27464.7644705;
        double r1280364 = r1280362 + r1280363;
        double r1280365 = r1280364 * r1280353;
        double r1280366 = r1280354 + r1280365;
        double r1280367 = r1280353 * r1280366;
        double r1280368 = t;
        double r1280369 = r1280367 + r1280368;
        double r1280370 = c;
        double r1280371 = b;
        double r1280372 = a;
        double r1280373 = r1280353 + r1280372;
        double r1280374 = r1280353 * r1280373;
        double r1280375 = r1280371 + r1280374;
        double r1280376 = r1280375 * r1280353;
        double r1280377 = r1280370 + r1280376;
        double r1280378 = r1280353 * r1280377;
        double r1280379 = i;
        double r1280380 = r1280378 + r1280379;
        double r1280381 = r1280369 / r1280380;
        return r1280381;
}

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 28.1

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

  3. Applied add-cube-cbrt28.2

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

  4. Final simplification28.2

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

Reproduce

herbie shell --seed 2019128 +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)))