Average Error: 0.0 → 0.0
Time: 17.3s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\sqrt[3]{\left(\frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)} \cdot \frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)}\right) \cdot \frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)}} - x\right)\]
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)} \cdot \frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)}\right) \cdot \frac{x \cdot 0.2706100000000000171951342053944244980812 + 2.307529999999999859028321225196123123169}{1 + x \cdot \left(0.04481000000000000260680366181986755691469 \cdot x + 0.992290000000000005364597654988756403327\right)}} - x\right)
double f(double x) {
        double r5619617 = 0.70711;
        double r5619618 = 2.30753;
        double r5619619 = x;
        double r5619620 = 0.27061;
        double r5619621 = r5619619 * r5619620;
        double r5619622 = r5619618 + r5619621;
        double r5619623 = 1.0;
        double r5619624 = 0.99229;
        double r5619625 = 0.04481;
        double r5619626 = r5619619 * r5619625;
        double r5619627 = r5619624 + r5619626;
        double r5619628 = r5619619 * r5619627;
        double r5619629 = r5619623 + r5619628;
        double r5619630 = r5619622 / r5619629;
        double r5619631 = r5619630 - r5619619;
        double r5619632 = r5619617 * r5619631;
        return r5619632;
}
↓
double f(double x) {
        double r5619633 = 0.70711;
        double r5619634 = x;
        double r5619635 = 0.27061;
        double r5619636 = r5619634 * r5619635;
        double r5619637 = 2.30753;
        double r5619638 = r5619636 + r5619637;
        double r5619639 = 1.0;
        double r5619640 = 0.04481;
        double r5619641 = r5619640 * r5619634;
        double r5619642 = 0.99229;
        double r5619643 = r5619641 + r5619642;
        double r5619644 = r5619634 * r5619643;
        double r5619645 = r5619639 + r5619644;
        double r5619646 = r5619638 / r5619645;
        double r5619647 = r5619646 * r5619646;
        double r5619648 = r5619647 * r5619646;
        double r5619649 = cbrt(r5619648);
        double r5619650 = r5619649 - r5619634;
        double r5619651 = r5619633 * r5619650;
        return r5619651;
}

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

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

  7. Final simplification0.0

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

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)))