Average Error: 19.8 → 10.0
Time: 17.9s
Precision: 64
\[\frac{9 \cdot ac - 3 \cdot {b}^{2}}{9 \cdot {a}^{2}}\]
\[\frac{\frac{ac - \left(\frac{\sqrt{{b}^{2}}}{9} \cdot 3\right) \cdot \sqrt{{b}^{2}}}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}\]
\frac{9 \cdot ac - 3 \cdot {b}^{2}}{9 \cdot {a}^{2}}
\frac{\frac{ac - \left(\frac{\sqrt{{b}^{2}}}{9} \cdot 3\right) \cdot \sqrt{{b}^{2}}}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}
double f(double ac, double b, double a) {
        double r3035706 = 9.0;
        double r3035707 = ac;
        double r3035708 = r3035706 * r3035707;
        double r3035709 = 3.0;
        double r3035710 = b;
        double r3035711 = 2.0;
        double r3035712 = pow(r3035710, r3035711);
        double r3035713 = r3035709 * r3035712;
        double r3035714 = r3035708 - r3035713;
        double r3035715 = a;
        double r3035716 = pow(r3035715, r3035711);
        double r3035717 = r3035706 * r3035716;
        double r3035718 = r3035714 / r3035717;
        return r3035718;
}

double f(double ac, double b, double a) {
        double r3035719 = ac;
        double r3035720 = b;
        double r3035721 = 2.0;
        double r3035722 = pow(r3035720, r3035721);
        double r3035723 = sqrt(r3035722);
        double r3035724 = 9.0;
        double r3035725 = r3035723 / r3035724;
        double r3035726 = 3.0;
        double r3035727 = r3035725 * r3035726;
        double r3035728 = r3035727 * r3035723;
        double r3035729 = r3035719 - r3035728;
        double r3035730 = a;
        double r3035731 = 2.0;
        double r3035732 = r3035721 / r3035731;
        double r3035733 = pow(r3035730, r3035732);
        double r3035734 = r3035729 / r3035733;
        double r3035735 = r3035734 / r3035733;
        return r3035735;
}

Error

Bits error versus ac

Bits error versus b

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 19.8

    \[\frac{9 \cdot ac - 3 \cdot {b}^{2}}{9 \cdot {a}^{2}}\]
  2. Simplified19.6

    \[\leadsto \color{blue}{\frac{ac - \frac{{b}^{2}}{9} \cdot 3}{{a}^{2}}}\]
  3. Using strategy rm
  4. Applied sqr-pow19.6

    \[\leadsto \frac{ac - \frac{{b}^{2}}{9} \cdot 3}{\color{blue}{{a}^{\left(\frac{2}{2}\right)} \cdot {a}^{\left(\frac{2}{2}\right)}}}\]
  5. Applied associate-/r*10.0

    \[\leadsto \color{blue}{\frac{\frac{ac - \frac{{b}^{2}}{9} \cdot 3}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}}\]
  6. Using strategy rm
  7. Applied *-un-lft-identity10.0

    \[\leadsto \frac{\frac{ac - \frac{{b}^{2}}{\color{blue}{1 \cdot 9}} \cdot 3}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}\]
  8. Applied add-sqr-sqrt10.0

    \[\leadsto \frac{\frac{ac - \frac{\color{blue}{\sqrt{{b}^{2}} \cdot \sqrt{{b}^{2}}}}{1 \cdot 9} \cdot 3}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}\]
  9. Applied times-frac10.0

    \[\leadsto \frac{\frac{ac - \color{blue}{\left(\frac{\sqrt{{b}^{2}}}{1} \cdot \frac{\sqrt{{b}^{2}}}{9}\right)} \cdot 3}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}\]
  10. Applied associate-*l*10.0

    \[\leadsto \frac{\frac{ac - \color{blue}{\frac{\sqrt{{b}^{2}}}{1} \cdot \left(\frac{\sqrt{{b}^{2}}}{9} \cdot 3\right)}}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}\]
  11. Final simplification10.0

    \[\leadsto \frac{\frac{ac - \left(\frac{\sqrt{{b}^{2}}}{9} \cdot 3\right) \cdot \sqrt{{b}^{2}}}{{a}^{\left(\frac{2}{2}\right)}}}{{a}^{\left(\frac{2}{2}\right)}}\]

Reproduce

herbie shell --seed 1 
(FPCore (ac b a)
  :name "(9ac-3b^2)/(9a^2)"
  :precision binary64
  (/ (- (* 9 ac) (* 3 (pow b 2))) (* 9 (pow a 2))))