Average Error: 28.7 → 28.8
Time: 8.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y} + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\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(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y} + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\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 r71548 = x;
        double r71549 = y;
        double r71550 = r71548 * r71549;
        double r71551 = z;
        double r71552 = r71550 + r71551;
        double r71553 = r71552 * r71549;
        double r71554 = 27464.7644705;
        double r71555 = r71553 + r71554;
        double r71556 = r71555 * r71549;
        double r71557 = 230661.510616;
        double r71558 = r71556 + r71557;
        double r71559 = r71558 * r71549;
        double r71560 = t;
        double r71561 = r71559 + r71560;
        double r71562 = a;
        double r71563 = r71549 + r71562;
        double r71564 = r71563 * r71549;
        double r71565 = b;
        double r71566 = r71564 + r71565;
        double r71567 = r71566 * r71549;
        double r71568 = c;
        double r71569 = r71567 + r71568;
        double r71570 = r71569 * r71549;
        double r71571 = i;
        double r71572 = r71570 + r71571;
        double r71573 = r71561 / r71572;
        return r71573;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71574 = x;
        double r71575 = y;
        double r71576 = r71574 * r71575;
        double r71577 = z;
        double r71578 = r71576 + r71577;
        double r71579 = r71578 * r71575;
        double r71580 = cbrt(r71579);
        double r71581 = r71580 * r71580;
        double r71582 = r71581 * r71580;
        double r71583 = 27464.7644705;
        double r71584 = r71582 + r71583;
        double r71585 = r71584 * r71575;
        double r71586 = 230661.510616;
        double r71587 = r71585 + r71586;
        double r71588 = r71587 * r71575;
        double r71589 = t;
        double r71590 = r71588 + r71589;
        double r71591 = a;
        double r71592 = r71575 + r71591;
        double r71593 = r71592 * r71575;
        double r71594 = b;
        double r71595 = r71593 + r71594;
        double r71596 = r71595 * r71575;
        double r71597 = c;
        double r71598 = r71596 + r71597;
        double r71599 = r71598 * r71575;
        double r71600 = i;
        double r71601 = r71599 + r71600;
        double r71602 = r71590 / r71601;
        return r71602;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt28.8

    \[\leadsto \frac{\left(\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}} + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Final simplification28.8

    \[\leadsto \frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y} + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019353 
(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)))