Average Error: 29.5 → 29.5
Time: 13.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\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 + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\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 r80376 = x;
        double r80377 = y;
        double r80378 = r80376 * r80377;
        double r80379 = z;
        double r80380 = r80378 + r80379;
        double r80381 = r80380 * r80377;
        double r80382 = 27464.7644705;
        double r80383 = r80381 + r80382;
        double r80384 = r80383 * r80377;
        double r80385 = 230661.510616;
        double r80386 = r80384 + r80385;
        double r80387 = r80386 * r80377;
        double r80388 = t;
        double r80389 = r80387 + r80388;
        double r80390 = a;
        double r80391 = r80377 + r80390;
        double r80392 = r80391 * r80377;
        double r80393 = b;
        double r80394 = r80392 + r80393;
        double r80395 = r80394 * r80377;
        double r80396 = c;
        double r80397 = r80395 + r80396;
        double r80398 = r80397 * r80377;
        double r80399 = i;
        double r80400 = r80398 + r80399;
        double r80401 = r80389 / r80400;
        return r80401;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80402 = x;
        double r80403 = y;
        double r80404 = r80402 * r80403;
        double r80405 = z;
        double r80406 = r80404 + r80405;
        double r80407 = r80406 * r80403;
        double r80408 = 27464.7644705;
        double r80409 = r80407 + r80408;
        double r80410 = r80409 * r80403;
        double r80411 = 230661.510616;
        double r80412 = r80410 + r80411;
        double r80413 = r80412 * r80403;
        double r80414 = t;
        double r80415 = r80413 + r80414;
        double r80416 = a;
        double r80417 = r80403 + r80416;
        double r80418 = r80417 * r80403;
        double r80419 = b;
        double r80420 = r80418 + r80419;
        double r80421 = r80420 * r80403;
        double r80422 = c;
        double r80423 = r80421 + r80422;
        double r80424 = r80423 * r80403;
        double r80425 = i;
        double r80426 = r80424 + r80425;
        double r80427 = r80415 / r80426;
        return r80427;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Final simplification29.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(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)))