Average Error: 0.0 → 0.0
Time: 20.8s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
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(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)
double f(double x) {
        double r57405 = 0.70711;
        double r57406 = 2.30753;
        double r57407 = x;
        double r57408 = 0.27061;
        double r57409 = r57407 * r57408;
        double r57410 = r57406 + r57409;
        double r57411 = 1.0;
        double r57412 = 0.99229;
        double r57413 = 0.04481;
        double r57414 = r57407 * r57413;
        double r57415 = r57412 + r57414;
        double r57416 = r57407 * r57415;
        double r57417 = r57411 + r57416;
        double r57418 = r57410 / r57417;
        double r57419 = r57418 - r57407;
        double r57420 = r57405 * r57419;
        return r57420;
}
↓
double f(double x) {
        double r57421 = 0.70711;
        double r57422 = 2.30753;
        double r57423 = x;
        double r57424 = 0.27061;
        double r57425 = r57423 * r57424;
        double r57426 = r57422 + r57425;
        double r57427 = 1.0;
        double r57428 = 0.99229;
        double r57429 = 0.04481;
        double r57430 = r57423 * r57429;
        double r57431 = r57428 + r57430;
        double r57432 = r57423 * r57431;
        double r57433 = r57427 + r57432;
        double r57434 = r57426 / r57433;
        double r57435 = r57434 - r57423;
        double r57436 = r57421 * r57435;
        return r57436;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.70711 (- (/ (+ 2.30753 (* x 0.27061)) (+ 1 (* x (+ 0.99229 (* x 0.04481))))) x)))