Average Error: 0.0 → 0.0
Time: 14.2s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[\left(-x\right) \cdot 0.7071100000000000163069557856942992657423 + \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} \cdot 0.7071100000000000163069557856942992657423\]
0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
↓
\left(-x\right) \cdot 0.7071100000000000163069557856942992657423 + \frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(x \cdot 0.04481000000000000260680366181986755691469 + 0.992290000000000005364597654988756403327\right)} \cdot 0.7071100000000000163069557856942992657423
double f(double x) {
        double r4678417 = 0.70711;
        double r4678418 = 2.30753;
        double r4678419 = x;
        double r4678420 = 0.27061;
        double r4678421 = r4678419 * r4678420;
        double r4678422 = r4678418 + r4678421;
        double r4678423 = 1.0;
        double r4678424 = 0.99229;
        double r4678425 = 0.04481;
        double r4678426 = r4678419 * r4678425;
        double r4678427 = r4678424 + r4678426;
        double r4678428 = r4678419 * r4678427;
        double r4678429 = r4678423 + r4678428;
        double r4678430 = r4678422 / r4678429;
        double r4678431 = r4678430 - r4678419;
        double r4678432 = r4678417 * r4678431;
        return r4678432;
}
↓
double f(double x) {
        double r4678433 = x;
        double r4678434 = -r4678433;
        double r4678435 = 0.70711;
        double r4678436 = r4678434 * r4678435;
        double r4678437 = 2.30753;
        double r4678438 = 0.27061;
        double r4678439 = r4678433 * r4678438;
        double r4678440 = r4678437 + r4678439;
        double r4678441 = 1.0;
        double r4678442 = 0.04481;
        double r4678443 = r4678433 * r4678442;
        double r4678444 = 0.99229;
        double r4678445 = r4678443 + r4678444;
        double r4678446 = r4678433 * r4678445;
        double r4678447 = r4678441 + r4678446;
        double r4678448 = r4678440 / r4678447;
        double r4678449 = r4678448 * r4678435;
        double r4678450 = r4678436 + r4678449;
        return r4678450;
}

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 sub-neg0.0

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

  4. Applied distribute-lft-in0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019169 
(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)))