Average Error: 28.8 → 28.9
Time: 2.3m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}\]
\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{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3725348 = x;
        double r3725349 = y;
        double r3725350 = r3725348 * r3725349;
        double r3725351 = z;
        double r3725352 = r3725350 + r3725351;
        double r3725353 = r3725352 * r3725349;
        double r3725354 = 27464.7644705;
        double r3725355 = r3725353 + r3725354;
        double r3725356 = r3725355 * r3725349;
        double r3725357 = 230661.510616;
        double r3725358 = r3725356 + r3725357;
        double r3725359 = r3725358 * r3725349;
        double r3725360 = t;
        double r3725361 = r3725359 + r3725360;
        double r3725362 = a;
        double r3725363 = r3725349 + r3725362;
        double r3725364 = r3725363 * r3725349;
        double r3725365 = b;
        double r3725366 = r3725364 + r3725365;
        double r3725367 = r3725366 * r3725349;
        double r3725368 = c;
        double r3725369 = r3725367 + r3725368;
        double r3725370 = r3725369 * r3725349;
        double r3725371 = i;
        double r3725372 = r3725370 + r3725371;
        double r3725373 = r3725361 / r3725372;
        return r3725373;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3725374 = t;
        double r3725375 = y;
        double r3725376 = z;
        double r3725377 = x;
        double r3725378 = r3725377 * r3725375;
        double r3725379 = r3725376 + r3725378;
        double r3725380 = r3725375 * r3725379;
        double r3725381 = 27464.7644705;
        double r3725382 = r3725380 + r3725381;
        double r3725383 = r3725375 * r3725382;
        double r3725384 = 230661.510616;
        double r3725385 = r3725383 + r3725384;
        double r3725386 = r3725385 * r3725375;
        double r3725387 = r3725374 + r3725386;
        double r3725388 = c;
        double r3725389 = b;
        double r3725390 = a;
        double r3725391 = r3725375 + r3725390;
        double r3725392 = r3725391 * r3725375;
        double r3725393 = r3725389 + r3725392;
        double r3725394 = cbrt(r3725393);
        double r3725395 = r3725394 * r3725394;
        double r3725396 = r3725394 * r3725375;
        double r3725397 = r3725395 * r3725396;
        double r3725398 = r3725388 + r3725397;
        double r3725399 = r3725375 * r3725398;
        double r3725400 = i;
        double r3725401 = r3725399 + r3725400;
        double r3725402 = r3725387 / r3725401;
        return r3725402;
}

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

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

  3. Applied add-cube-cbrt28.9

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

  4. Applied associate-*l*28.9

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

  5. Final simplification28.9

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

Reproduce

herbie shell --seed 2019172 
(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)))