Average Error: 28.7 → 28.8
Time: 7.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\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 r91379 = x;
        double r91380 = y;
        double r91381 = r91379 * r91380;
        double r91382 = z;
        double r91383 = r91381 + r91382;
        double r91384 = r91383 * r91380;
        double r91385 = 27464.7644705;
        double r91386 = r91384 + r91385;
        double r91387 = r91386 * r91380;
        double r91388 = 230661.510616;
        double r91389 = r91387 + r91388;
        double r91390 = r91389 * r91380;
        double r91391 = t;
        double r91392 = r91390 + r91391;
        double r91393 = a;
        double r91394 = r91380 + r91393;
        double r91395 = r91394 * r91380;
        double r91396 = b;
        double r91397 = r91395 + r91396;
        double r91398 = r91397 * r91380;
        double r91399 = c;
        double r91400 = r91398 + r91399;
        double r91401 = r91400 * r91380;
        double r91402 = i;
        double r91403 = r91401 + r91402;
        double r91404 = r91392 / r91403;
        return r91404;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91405 = x;
        double r91406 = y;
        double r91407 = r91405 * r91406;
        double r91408 = z;
        double r91409 = r91407 + r91408;
        double r91410 = r91409 * r91406;
        double r91411 = 27464.7644705;
        double r91412 = r91410 + r91411;
        double r91413 = r91412 * r91406;
        double r91414 = cbrt(r91413);
        double r91415 = r91414 * r91414;
        double r91416 = r91415 * r91414;
        double r91417 = 230661.510616;
        double r91418 = r91416 + r91417;
        double r91419 = r91418 * r91406;
        double r91420 = t;
        double r91421 = r91419 + r91420;
        double r91422 = a;
        double r91423 = r91406 + r91422;
        double r91424 = r91423 * r91406;
        double r91425 = b;
        double r91426 = r91424 + r91425;
        double r91427 = r91426 * r91406;
        double r91428 = c;
        double r91429 = r91427 + r91428;
        double r91430 = r91429 * r91406;
        double r91431 = i;
        double r91432 = r91430 + r91431;
        double r91433 = r91421 / r91432;
        return r91433;
}

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

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

  4. Final simplification28.8

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

Reproduce

herbie shell --seed 2020065 
(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)))