Average Error: 29.0 → 29.0
Time: 1.4m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(230661.5106160000141244381666183471679688 + \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right) \cdot y}{y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) + i}\]
\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(230661.5106160000141244381666183471679688 + \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right) \cdot y}{y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4784332 = x;
        double r4784333 = y;
        double r4784334 = r4784332 * r4784333;
        double r4784335 = z;
        double r4784336 = r4784334 + r4784335;
        double r4784337 = r4784336 * r4784333;
        double r4784338 = 27464.7644705;
        double r4784339 = r4784337 + r4784338;
        double r4784340 = r4784339 * r4784333;
        double r4784341 = 230661.510616;
        double r4784342 = r4784340 + r4784341;
        double r4784343 = r4784342 * r4784333;
        double r4784344 = t;
        double r4784345 = r4784343 + r4784344;
        double r4784346 = a;
        double r4784347 = r4784333 + r4784346;
        double r4784348 = r4784347 * r4784333;
        double r4784349 = b;
        double r4784350 = r4784348 + r4784349;
        double r4784351 = r4784350 * r4784333;
        double r4784352 = c;
        double r4784353 = r4784351 + r4784352;
        double r4784354 = r4784353 * r4784333;
        double r4784355 = i;
        double r4784356 = r4784354 + r4784355;
        double r4784357 = r4784345 / r4784356;
        return r4784357;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4784358 = t;
        double r4784359 = 230661.510616;
        double r4784360 = y;
        double r4784361 = x;
        double r4784362 = r4784360 * r4784361;
        double r4784363 = z;
        double r4784364 = r4784362 + r4784363;
        double r4784365 = r4784364 * r4784360;
        double r4784366 = 27464.7644705;
        double r4784367 = r4784365 + r4784366;
        double r4784368 = cbrt(r4784360);
        double r4784369 = r4784368 * r4784368;
        double r4784370 = r4784367 * r4784369;
        double r4784371 = r4784370 * r4784368;
        double r4784372 = r4784359 + r4784371;
        double r4784373 = r4784372 * r4784360;
        double r4784374 = r4784358 + r4784373;
        double r4784375 = b;
        double r4784376 = a;
        double r4784377 = r4784376 + r4784360;
        double r4784378 = r4784360 * r4784377;
        double r4784379 = r4784375 + r4784378;
        double r4784380 = r4784360 * r4784379;
        double r4784381 = c;
        double r4784382 = r4784380 + r4784381;
        double r4784383 = r4784360 * r4784382;
        double r4784384 = i;
        double r4784385 = r4784383 + r4784384;
        double r4784386 = r4784374 / r4784385;
        return r4784386;
}

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 29.0

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

  3. Applied add-cube-cbrt29.0

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

  4. Applied associate-*r*29.0

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

  5. Final simplification29.0

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

Reproduce

herbie shell --seed 2019200 
(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)))