Average Error: 28.4 → 28.5
Time: 8.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]
\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 r86366 = x;
        double r86367 = y;
        double r86368 = r86366 * r86367;
        double r86369 = z;
        double r86370 = r86368 + r86369;
        double r86371 = r86370 * r86367;
        double r86372 = 27464.7644705;
        double r86373 = r86371 + r86372;
        double r86374 = r86373 * r86367;
        double r86375 = 230661.510616;
        double r86376 = r86374 + r86375;
        double r86377 = r86376 * r86367;
        double r86378 = t;
        double r86379 = r86377 + r86378;
        double r86380 = a;
        double r86381 = r86367 + r86380;
        double r86382 = r86381 * r86367;
        double r86383 = b;
        double r86384 = r86382 + r86383;
        double r86385 = r86384 * r86367;
        double r86386 = c;
        double r86387 = r86385 + r86386;
        double r86388 = r86387 * r86367;
        double r86389 = i;
        double r86390 = r86388 + r86389;
        double r86391 = r86379 / r86390;
        return r86391;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r86392 = x;
        double r86393 = y;
        double r86394 = r86392 * r86393;
        double r86395 = z;
        double r86396 = r86394 + r86395;
        double r86397 = r86396 * r86393;
        double r86398 = 27464.7644705;
        double r86399 = r86397 + r86398;
        double r86400 = r86399 * r86393;
        double r86401 = 230661.510616;
        double r86402 = r86400 + r86401;
        double r86403 = r86402 * r86393;
        double r86404 = t;
        double r86405 = r86403 + r86404;
        double r86406 = a;
        double r86407 = r86393 + r86406;
        double r86408 = r86407 * r86393;
        double r86409 = b;
        double r86410 = r86408 + r86409;
        double r86411 = cbrt(r86410);
        double r86412 = r86411 * r86411;
        double r86413 = r86411 * r86393;
        double r86414 = r86412 * r86413;
        double r86415 = c;
        double r86416 = r86414 + r86415;
        double r86417 = r86416 * r86393;
        double r86418 = i;
        double r86419 = r86417 + r86418;
        double r86420 = r86405 / r86419;
        return r86420;
}

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 
(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)))