Average Error: 28.4 → 28.5
Time: 9.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]
\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(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80375 = x;
        double r80376 = y;
        double r80377 = r80375 * r80376;
        double r80378 = z;
        double r80379 = r80377 + r80378;
        double r80380 = r80379 * r80376;
        double r80381 = 27464.7644705;
        double r80382 = r80380 + r80381;
        double r80383 = r80382 * r80376;
        double r80384 = 230661.510616;
        double r80385 = r80383 + r80384;
        double r80386 = r80385 * r80376;
        double r80387 = t;
        double r80388 = r80386 + r80387;
        double r80389 = a;
        double r80390 = r80376 + r80389;
        double r80391 = r80390 * r80376;
        double r80392 = b;
        double r80393 = r80391 + r80392;
        double r80394 = r80393 * r80376;
        double r80395 = c;
        double r80396 = r80394 + r80395;
        double r80397 = r80396 * r80376;
        double r80398 = i;
        double r80399 = r80397 + r80398;
        double r80400 = r80388 / r80399;
        return r80400;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80401 = x;
        double r80402 = y;
        double r80403 = r80401 * r80402;
        double r80404 = z;
        double r80405 = r80403 + r80404;
        double r80406 = r80405 * r80402;
        double r80407 = 27464.7644705;
        double r80408 = r80406 + r80407;
        double r80409 = r80408 * r80402;
        double r80410 = 230661.510616;
        double r80411 = r80409 + r80410;
        double r80412 = r80411 * r80402;
        double r80413 = t;
        double r80414 = r80412 + r80413;
        double r80415 = a;
        double r80416 = r80402 + r80415;
        double r80417 = r80416 * r80402;
        double r80418 = b;
        double r80419 = r80417 + r80418;
        double r80420 = cbrt(r80419);
        double r80421 = r80420 * r80420;
        double r80422 = r80420 * r80402;
        double r80423 = r80421 * r80422;
        double r80424 = c;
        double r80425 = r80423 + r80424;
        double r80426 = r80425 * r80402;
        double r80427 = i;
        double r80428 = r80426 + r80427;
        double r80429 = r80414 / r80428;
        return r80429;
}

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 28.4

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

  3. Applied add-cube-cbrt28.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right)} \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*28.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right)} + c\right) \cdot y + i}\]

  5. Final simplification28.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020035 +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)))