Average Error: 28.7 → 28.8
Time: 9.0s
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 r93621 = x;
        double r93622 = y;
        double r93623 = r93621 * r93622;
        double r93624 = z;
        double r93625 = r93623 + r93624;
        double r93626 = r93625 * r93622;
        double r93627 = 27464.7644705;
        double r93628 = r93626 + r93627;
        double r93629 = r93628 * r93622;
        double r93630 = 230661.510616;
        double r93631 = r93629 + r93630;
        double r93632 = r93631 * r93622;
        double r93633 = t;
        double r93634 = r93632 + r93633;
        double r93635 = a;
        double r93636 = r93622 + r93635;
        double r93637 = r93636 * r93622;
        double r93638 = b;
        double r93639 = r93637 + r93638;
        double r93640 = r93639 * r93622;
        double r93641 = c;
        double r93642 = r93640 + r93641;
        double r93643 = r93642 * r93622;
        double r93644 = i;
        double r93645 = r93643 + r93644;
        double r93646 = r93634 / r93645;
        return r93646;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r93647 = x;
        double r93648 = y;
        double r93649 = r93647 * r93648;
        double r93650 = z;
        double r93651 = r93649 + r93650;
        double r93652 = r93651 * r93648;
        double r93653 = cbrt(r93652);
        double r93654 = r93653 * r93653;
        double r93655 = r93654 * r93653;
        double r93656 = 27464.7644705;
        double r93657 = r93655 + r93656;
        double r93658 = r93657 * r93648;
        double r93659 = 230661.510616;
        double r93660 = r93658 + r93659;
        double r93661 = r93660 * r93648;
        double r93662 = t;
        double r93663 = r93661 + r93662;
        double r93664 = a;
        double r93665 = r93648 + r93664;
        double r93666 = r93665 * r93648;
        double r93667 = b;
        double r93668 = r93666 + r93667;
        double r93669 = r93668 * r93648;
        double r93670 = c;
        double r93671 = r93669 + r93670;
        double r93672 = r93671 * r93648;
        double r93673 = i;
        double r93674 = r93672 + r93673;
        double r93675 = r93663 / r93674;
        return r93675;
}

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)))