Average Error: 28.9 → 28.9
Time: 12.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(t + y \cdot 230661.5106160000141244381666183471679688\right) + y \cdot {\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right)}^{3}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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{\left(t + y \cdot 230661.5106160000141244381666183471679688\right) + y \cdot {\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right)}^{3}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r103343 = x;
        double r103344 = y;
        double r103345 = r103343 * r103344;
        double r103346 = z;
        double r103347 = r103345 + r103346;
        double r103348 = r103347 * r103344;
        double r103349 = 27464.7644705;
        double r103350 = r103348 + r103349;
        double r103351 = r103350 * r103344;
        double r103352 = 230661.510616;
        double r103353 = r103351 + r103352;
        double r103354 = r103353 * r103344;
        double r103355 = t;
        double r103356 = r103354 + r103355;
        double r103357 = a;
        double r103358 = r103344 + r103357;
        double r103359 = r103358 * r103344;
        double r103360 = b;
        double r103361 = r103359 + r103360;
        double r103362 = r103361 * r103344;
        double r103363 = c;
        double r103364 = r103362 + r103363;
        double r103365 = r103364 * r103344;
        double r103366 = i;
        double r103367 = r103365 + r103366;
        double r103368 = r103356 / r103367;
        return r103368;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r103369 = t;
        double r103370 = y;
        double r103371 = 230661.510616;
        double r103372 = r103370 * r103371;
        double r103373 = r103369 + r103372;
        double r103374 = x;
        double r103375 = r103374 * r103370;
        double r103376 = z;
        double r103377 = r103375 + r103376;
        double r103378 = r103377 * r103370;
        double r103379 = 27464.7644705;
        double r103380 = r103378 + r103379;
        double r103381 = r103380 * r103370;
        double r103382 = cbrt(r103381);
        double r103383 = 3.0;
        double r103384 = pow(r103382, r103383);
        double r103385 = r103370 * r103384;
        double r103386 = r103373 + r103385;
        double r103387 = a;
        double r103388 = r103370 + r103387;
        double r103389 = r103388 * r103370;
        double r103390 = b;
        double r103391 = r103389 + r103390;
        double r103392 = r103391 * r103370;
        double r103393 = c;
        double r103394 = r103392 + r103393;
        double r103395 = r103394 * r103370;
        double r103396 = i;
        double r103397 = r103395 + r103396;
        double r103398 = r103386 / r103397;
        return r103398;
}

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 28.9

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

  3. Applied add-cube-cbrt28.9

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

  5. Applied *-un-lft-identity28.9

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

  6. Applied associate-/r*28.9

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

  7. Simplified28.9

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

  8. Final simplification28.9

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

Reproduce

herbie shell --seed 2019322 
(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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))