Average Error: 28.7 → 28.8
Time: 8.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} + c\right) \cdot y + i}\]
\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(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y} \cdot \sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right) \cdot \sqrt[3]{\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 r63398 = x;
        double r63399 = y;
        double r63400 = r63398 * r63399;
        double r63401 = z;
        double r63402 = r63400 + r63401;
        double r63403 = r63402 * r63399;
        double r63404 = 27464.7644705;
        double r63405 = r63403 + r63404;
        double r63406 = r63405 * r63399;
        double r63407 = 230661.510616;
        double r63408 = r63406 + r63407;
        double r63409 = r63408 * r63399;
        double r63410 = t;
        double r63411 = r63409 + r63410;
        double r63412 = a;
        double r63413 = r63399 + r63412;
        double r63414 = r63413 * r63399;
        double r63415 = b;
        double r63416 = r63414 + r63415;
        double r63417 = r63416 * r63399;
        double r63418 = c;
        double r63419 = r63417 + r63418;
        double r63420 = r63419 * r63399;
        double r63421 = i;
        double r63422 = r63420 + r63421;
        double r63423 = r63411 / r63422;
        return r63423;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r63424 = x;
        double r63425 = y;
        double r63426 = r63424 * r63425;
        double r63427 = z;
        double r63428 = r63426 + r63427;
        double r63429 = r63428 * r63425;
        double r63430 = 27464.7644705;
        double r63431 = r63429 + r63430;
        double r63432 = r63431 * r63425;
        double r63433 = 230661.510616;
        double r63434 = r63432 + r63433;
        double r63435 = r63434 * r63425;
        double r63436 = t;
        double r63437 = r63435 + r63436;
        double r63438 = a;
        double r63439 = r63425 + r63438;
        double r63440 = r63439 * r63425;
        double r63441 = b;
        double r63442 = r63440 + r63441;
        double r63443 = r63442 * r63425;
        double r63444 = cbrt(r63443);
        double r63445 = r63444 * r63444;
        double r63446 = r63445 * r63444;
        double r63447 = c;
        double r63448 = r63446 + r63447;
        double r63449 = r63448 * r63425;
        double r63450 = i;
        double r63451 = r63449 + r63450;
        double r63452 = r63437 / r63451;
        return r63452;
}

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

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

  3. Applied add-cube-cbrt28.8

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

  4. Final simplification28.8

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

Reproduce

herbie shell --seed 2020047 
(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)))