Average Error: 0.0 → 0.0
Time: 13.9s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\sqrt[3]{{\left(\frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)}\right)}^{3}} - x\right)\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
0.7071100000000000163069557856942992657423 \cdot \left(\sqrt[3]{{\left(\frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)}\right)}^{3}} - x\right)
double f(double x) {
        double r82604 = 0.70711;
        double r82605 = 2.30753;
        double r82606 = x;
        double r82607 = 0.27061;
        double r82608 = r82606 * r82607;
        double r82609 = r82605 + r82608;
        double r82610 = 1.0;
        double r82611 = 0.99229;
        double r82612 = 0.04481;
        double r82613 = r82606 * r82612;
        double r82614 = r82611 + r82613;
        double r82615 = r82606 * r82614;
        double r82616 = r82610 + r82615;
        double r82617 = r82609 / r82616;
        double r82618 = r82617 - r82606;
        double r82619 = r82604 * r82618;
        return r82619;
}
↓
double f(double x) {
        double r82620 = 0.70711;
        double r82621 = x;
        double r82622 = 0.27061;
        double r82623 = r82621 * r82622;
        double r82624 = 2.30753;
        double r82625 = r82623 + r82624;
        double r82626 = 1.0;
        double r82627 = 0.04481;
        double r82628 = r82627 * r82621;
        double r82629 = 0.99229;
        double r82630 = r82628 + r82629;
        double r82631 = r82621 * r82630;
        double r82632 = r82626 + r82631;
        double r82633 = r82625 / r82632;
        double r82634 = 3.0;
        double r82635 = pow(r82633, r82634);
        double r82636 = cbrt(r82635);
        double r82637 = r82636 - r82621;
        double r82638 = r82620 * r82637;
        return r82638;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{\color{blue}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}}} - x\right)\]

  4. Applied add-cbrt-cube21.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\frac{\color{blue}{\sqrt[3]{\left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right)\right) \cdot \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right)}}}{\sqrt[3]{\left(\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}} - x\right)\]

  5. Applied cbrt-undiv21.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\color{blue}{\sqrt[3]{\frac{\left(\left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right) \cdot \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right)\right) \cdot \left(2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812\right)}{\left(\left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)\right) \cdot \left(1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)\right)}}} - x\right)\]

  6. Simplified0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\sqrt[3]{\color{blue}{{\left(\frac{0.2706100000000000171951342053944244980812 \cdot x + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)}\right)}^{3}}} - x\right)\]

  7. Final simplification0.0

    \[\leadsto 0.7071100000000000163069557856942992657423 \cdot \left(\sqrt[3]{{\left(\frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)}\right)}^{3}} - x\right)\]

Reproduce

herbie shell --seed 2019179 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1.0 (* x (+ 0.99229 (* x 0.04481))))) x)))