Average Error: 0.1 → 0.1
Time: 22.0s
Precision: 64
\[\left(\left(-7\right) \cdot {x}^{7} + 28 \cdot {x}^{6}\right) - 56 \cdot {x}^{5}\]
\[\left(28 \cdot {x}^{6} - 7 \cdot {x}^{7}\right) - \left(\sqrt[3]{\sqrt{56}} \cdot \sqrt[3]{\sqrt{56}}\right) \cdot \left(\sqrt[3]{\sqrt{56}} \cdot \left(\sqrt{56} \cdot {x}^{5}\right)\right)\]
\left(\left(-7\right) \cdot {x}^{7} + 28 \cdot {x}^{6}\right) - 56 \cdot {x}^{5}
\left(28 \cdot {x}^{6} - 7 \cdot {x}^{7}\right) - \left(\sqrt[3]{\sqrt{56}} \cdot \sqrt[3]{\sqrt{56}}\right) \cdot \left(\sqrt[3]{\sqrt{56}} \cdot \left(\sqrt{56} \cdot {x}^{5}\right)\right)
double f(double x) {
        double r3119730 = 7.0;
        double r3119731 = -r3119730;
        double r3119732 = x;
        double r3119733 = pow(r3119732, r3119730);
        double r3119734 = r3119731 * r3119733;
        double r3119735 = 28.0;
        double r3119736 = 6.0;
        double r3119737 = pow(r3119732, r3119736);
        double r3119738 = r3119735 * r3119737;
        double r3119739 = r3119734 + r3119738;
        double r3119740 = 56.0;
        double r3119741 = 5.0;
        double r3119742 = pow(r3119732, r3119741);
        double r3119743 = r3119740 * r3119742;
        double r3119744 = r3119739 - r3119743;
        return r3119744;
}

double f(double x) {
        double r3119745 = 28.0;
        double r3119746 = x;
        double r3119747 = 6.0;
        double r3119748 = pow(r3119746, r3119747);
        double r3119749 = r3119745 * r3119748;
        double r3119750 = 7.0;
        double r3119751 = pow(r3119746, r3119750);
        double r3119752 = r3119750 * r3119751;
        double r3119753 = r3119749 - r3119752;
        double r3119754 = 56.0;
        double r3119755 = sqrt(r3119754);
        double r3119756 = cbrt(r3119755);
        double r3119757 = r3119756 * r3119756;
        double r3119758 = 5.0;
        double r3119759 = pow(r3119746, r3119758);
        double r3119760 = r3119755 * r3119759;
        double r3119761 = r3119756 * r3119760;
        double r3119762 = r3119757 * r3119761;
        double r3119763 = r3119753 - r3119762;
        return r3119763;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(-7\right) \cdot {x}^{7} + 28 \cdot {x}^{6}\right) - 56 \cdot {x}^{5}\]
  2. Simplified0.1

    \[\leadsto \color{blue}{\left(28 \cdot {x}^{6} - 7 \cdot {x}^{7}\right) - 56 \cdot {x}^{5}}\]
  3. Using strategy rm
  4. Applied add-sqr-sqrt0.1

    \[\leadsto \left(28 \cdot {x}^{6} - 7 \cdot {x}^{7}\right) - \color{blue}{\left(\sqrt{56} \cdot \sqrt{56}\right)} \cdot {x}^{5}\]
  5. Applied associate-*l*0.1

    \[\leadsto \left(28 \cdot {x}^{6} - 7 \cdot {x}^{7}\right) - \color{blue}{\sqrt{56} \cdot \left(\sqrt{56} \cdot {x}^{5}\right)}\]
  6. Using strategy rm
  7. Applied add-cube-cbrt0.2

    \[\leadsto \left(28 \cdot {x}^{6} - 7 \cdot {x}^{7}\right) - \color{blue}{\left(\left(\sqrt[3]{\sqrt{56}} \cdot \sqrt[3]{\sqrt{56}}\right) \cdot \sqrt[3]{\sqrt{56}}\right)} \cdot \left(\sqrt{56} \cdot {x}^{5}\right)\]
  8. Applied associate-*l*0.1

    \[\leadsto \left(28 \cdot {x}^{6} - 7 \cdot {x}^{7}\right) - \color{blue}{\left(\sqrt[3]{\sqrt{56}} \cdot \sqrt[3]{\sqrt{56}}\right) \cdot \left(\sqrt[3]{\sqrt{56}} \cdot \left(\sqrt{56} \cdot {x}^{5}\right)\right)}\]
  9. Final simplification0.1

    \[\leadsto \left(28 \cdot {x}^{6} - 7 \cdot {x}^{7}\right) - \left(\sqrt[3]{\sqrt{56}} \cdot \sqrt[3]{\sqrt{56}}\right) \cdot \left(\sqrt[3]{\sqrt{56}} \cdot \left(\sqrt{56} \cdot {x}^{5}\right)\right)\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "-7*pow(x, 7)+28*pow(x, 6)-56*pow(x, 5)"
  :precision binary64
  (- (+ (* (- 7) (pow x 7)) (* 28 (pow x 6))) (* 56 (pow x 5))))