Average Error: 28.7 → 28.9
Time: 8.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}\]
\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(\left(y + a\right) \cdot y + b\right) \cdot y + 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 r54425 = x;
        double r54426 = y;
        double r54427 = r54425 * r54426;
        double r54428 = z;
        double r54429 = r54427 + r54428;
        double r54430 = r54429 * r54426;
        double r54431 = 27464.7644705;
        double r54432 = r54430 + r54431;
        double r54433 = r54432 * r54426;
        double r54434 = 230661.510616;
        double r54435 = r54433 + r54434;
        double r54436 = r54435 * r54426;
        double r54437 = t;
        double r54438 = r54436 + r54437;
        double r54439 = a;
        double r54440 = r54426 + r54439;
        double r54441 = r54440 * r54426;
        double r54442 = b;
        double r54443 = r54441 + r54442;
        double r54444 = r54443 * r54426;
        double r54445 = c;
        double r54446 = r54444 + r54445;
        double r54447 = r54446 * r54426;
        double r54448 = i;
        double r54449 = r54447 + r54448;
        double r54450 = r54438 / r54449;
        return r54450;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r54451 = 1.0;
        double r54452 = y;
        double r54453 = a;
        double r54454 = r54452 + r54453;
        double r54455 = r54454 * r54452;
        double r54456 = b;
        double r54457 = r54455 + r54456;
        double r54458 = r54457 * r54452;
        double r54459 = c;
        double r54460 = r54458 + r54459;
        double r54461 = r54460 * r54452;
        double r54462 = i;
        double r54463 = r54461 + r54462;
        double r54464 = x;
        double r54465 = r54464 * r54452;
        double r54466 = z;
        double r54467 = r54465 + r54466;
        double r54468 = r54467 * r54452;
        double r54469 = 27464.7644705;
        double r54470 = r54468 + r54469;
        double r54471 = r54470 * r54452;
        double r54472 = 230661.510616;
        double r54473 = r54471 + r54472;
        double r54474 = r54473 * r54452;
        double r54475 = t;
        double r54476 = r54474 + r54475;
        double r54477 = r54463 / r54476;
        double r54478 = r54451 / r54477;
        return r54478;
}

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 28.7

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

  3. Applied clear-num28.9

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

  4. Final simplification28.9

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

Reproduce

herbie shell --seed 2019344 
(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)))