Average Error: 29.5 → 29.8
Time: 8.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{1}{\frac{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r56348 = x;
        double r56349 = y;
        double r56350 = r56348 * r56349;
        double r56351 = z;
        double r56352 = r56350 + r56351;
        double r56353 = r56352 * r56349;
        double r56354 = 27464.7644705;
        double r56355 = r56353 + r56354;
        double r56356 = r56355 * r56349;
        double r56357 = 230661.510616;
        double r56358 = r56356 + r56357;
        double r56359 = r56358 * r56349;
        double r56360 = t;
        double r56361 = r56359 + r56360;
        double r56362 = a;
        double r56363 = r56349 + r56362;
        double r56364 = r56363 * r56349;
        double r56365 = b;
        double r56366 = r56364 + r56365;
        double r56367 = r56366 * r56349;
        double r56368 = c;
        double r56369 = r56367 + r56368;
        double r56370 = r56369 * r56349;
        double r56371 = i;
        double r56372 = r56370 + r56371;
        double r56373 = r56361 / r56372;
        return r56373;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r56374 = 1.0;
        double r56375 = y;
        double r56376 = a;
        double r56377 = r56375 + r56376;
        double r56378 = r56377 * r56375;
        double r56379 = b;
        double r56380 = r56378 + r56379;
        double r56381 = cbrt(r56380);
        double r56382 = r56381 * r56381;
        double r56383 = r56381 * r56375;
        double r56384 = r56382 * r56383;
        double r56385 = c;
        double r56386 = r56384 + r56385;
        double r56387 = r56386 * r56375;
        double r56388 = i;
        double r56389 = r56387 + r56388;
        double r56390 = x;
        double r56391 = r56390 * r56375;
        double r56392 = z;
        double r56393 = r56391 + r56392;
        double r56394 = r56393 * r56375;
        double r56395 = 27464.7644705;
        double r56396 = r56394 + r56395;
        double r56397 = r56396 * r56375;
        double r56398 = 230661.510616;
        double r56399 = r56397 + r56398;
        double r56400 = r56399 * r56375;
        double r56401 = t;
        double r56402 = r56400 + r56401;
        double r56403 = r56389 / r56402;
        double r56404 = r56374 / r56403;
        return r56404;
}

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 29.5

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt29.6

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\color{blue}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right)} \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*29.6

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right)} + c\right) \cdot y + i}\]
  5. Using strategy rm

  6. Applied clear-num29.8

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}}\]

  7. Final simplification29.8

    \[\leadsto \frac{1}{\frac{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}\]

Reproduce

herbie shell --seed 2019356 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))