Average Error: 29.5 → 29.5
Time: 28.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\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 r75332 = x;
        double r75333 = y;
        double r75334 = r75332 * r75333;
        double r75335 = z;
        double r75336 = r75334 + r75335;
        double r75337 = r75336 * r75333;
        double r75338 = 27464.7644705;
        double r75339 = r75337 + r75338;
        double r75340 = r75339 * r75333;
        double r75341 = 230661.510616;
        double r75342 = r75340 + r75341;
        double r75343 = r75342 * r75333;
        double r75344 = t;
        double r75345 = r75343 + r75344;
        double r75346 = a;
        double r75347 = r75333 + r75346;
        double r75348 = r75347 * r75333;
        double r75349 = b;
        double r75350 = r75348 + r75349;
        double r75351 = r75350 * r75333;
        double r75352 = c;
        double r75353 = r75351 + r75352;
        double r75354 = r75353 * r75333;
        double r75355 = i;
        double r75356 = r75354 + r75355;
        double r75357 = r75345 / r75356;
        return r75357;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r75358 = x;
        double r75359 = y;
        double r75360 = r75358 * r75359;
        double r75361 = z;
        double r75362 = r75360 + r75361;
        double r75363 = r75362 * r75359;
        double r75364 = 27464.7644705;
        double r75365 = r75363 + r75364;
        double r75366 = r75365 * r75359;
        double r75367 = 230661.510616;
        double r75368 = r75366 + r75367;
        double r75369 = r75368 * r75359;
        double r75370 = t;
        double r75371 = r75369 + r75370;
        double r75372 = 1.0;
        double r75373 = a;
        double r75374 = r75359 + r75373;
        double r75375 = r75374 * r75359;
        double r75376 = b;
        double r75377 = r75375 + r75376;
        double r75378 = r75377 * r75359;
        double r75379 = c;
        double r75380 = r75378 + r75379;
        double r75381 = r75380 * r75359;
        double r75382 = i;
        double r75383 = r75381 + r75382;
        double r75384 = r75372 / r75383;
        double r75385 = r75371 * r75384;
        return r75385;
}

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 div-inv29.5

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

  4. Final simplification29.5

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

Reproduce

herbie shell --seed 2019209 
(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)))