Average Error: 29.3 → 29.3
Time: 13.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y}{i + y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)}\]
\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{t + \left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y}{i + y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77407 = x;
        double r77408 = y;
        double r77409 = r77407 * r77408;
        double r77410 = z;
        double r77411 = r77409 + r77410;
        double r77412 = r77411 * r77408;
        double r77413 = 27464.7644705;
        double r77414 = r77412 + r77413;
        double r77415 = r77414 * r77408;
        double r77416 = 230661.510616;
        double r77417 = r77415 + r77416;
        double r77418 = r77417 * r77408;
        double r77419 = t;
        double r77420 = r77418 + r77419;
        double r77421 = a;
        double r77422 = r77408 + r77421;
        double r77423 = r77422 * r77408;
        double r77424 = b;
        double r77425 = r77423 + r77424;
        double r77426 = r77425 * r77408;
        double r77427 = c;
        double r77428 = r77426 + r77427;
        double r77429 = r77428 * r77408;
        double r77430 = i;
        double r77431 = r77429 + r77430;
        double r77432 = r77420 / r77431;
        return r77432;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77433 = t;
        double r77434 = x;
        double r77435 = y;
        double r77436 = r77434 * r77435;
        double r77437 = z;
        double r77438 = r77436 + r77437;
        double r77439 = r77438 * r77435;
        double r77440 = 27464.7644705;
        double r77441 = r77439 + r77440;
        double r77442 = r77441 * r77435;
        double r77443 = 230661.510616;
        double r77444 = r77442 + r77443;
        double r77445 = r77444 * r77435;
        double r77446 = r77433 + r77445;
        double r77447 = i;
        double r77448 = a;
        double r77449 = r77435 + r77448;
        double r77450 = r77449 * r77435;
        double r77451 = b;
        double r77452 = r77450 + r77451;
        double r77453 = r77452 * r77435;
        double r77454 = c;
        double r77455 = r77453 + r77454;
        double r77456 = r77435 * r77455;
        double r77457 = r77447 + r77456;
        double r77458 = r77446 / r77457;
        return r77458;
}

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 29.3

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

  3. Applied div-inv29.3

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]
  4. Using strategy rm

  5. Applied add-cube-cbrt29.5

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\color{blue}{\left(\sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}} + i}\]
  6. Using strategy rm

  7. Applied pow129.5

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \color{blue}{{\left(\frac{1}{\left(\sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i}\right)}^{1}}\]

  8. Applied pow129.5

    \[\leadsto \color{blue}{{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right)}^{1}} \cdot {\left(\frac{1}{\left(\sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i}\right)}^{1}\]

  9. Applied pow-prod-down29.5

    \[\leadsto \color{blue}{{\left(\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y} + i}\right)}^{1}}\]

  10. Simplified29.3

    \[\leadsto {\color{blue}{\left(\frac{t + \left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y}{i + y \cdot \left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right)}\right)}}^{1}\]

  11. Final simplification29.3

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

Reproduce

herbie shell --seed 2020045 
(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)))