Average Error: 0.0 → 0.0
Time: 2.2s
Precision: 64
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
↓
\[0.7071100000000000163069557856942992657423 \cdot \left(\frac{2.307529999999999859028321225196123123169 + x \cdot 0.2706100000000000171951342053944244980812}{1 + x \cdot \left(0.992290000000000005364597654988756403327 + x \cdot 0.04481000000000000260680366181986755691469\right)} - x\right)\]
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 r71673 = 0.70711;
        double r71674 = 2.30753;
        double r71675 = x;
        double r71676 = 0.27061;
        double r71677 = r71675 * r71676;
        double r71678 = r71674 + r71677;
        double r71679 = 1.0;
        double r71680 = 0.99229;
        double r71681 = 0.04481;
        double r71682 = r71675 * r71681;
        double r71683 = r71680 + r71682;
        double r71684 = r71675 * r71683;
        double r71685 = r71679 + r71684;
        double r71686 = r71678 / r71685;
        double r71687 = r71686 - r71675;
        double r71688 = r71673 * r71687;
        return r71688;
}
↓
double f(double x) {
        double r71689 = 0.70711;
        double r71690 = 2.30753;
        double r71691 = x;
        double r71692 = 0.27061;
        double r71693 = r71691 * r71692;
        double r71694 = r71690 + r71693;
        double r71695 = 1.0;
        double r71696 = 0.99229;
        double r71697 = 0.04481;
        double r71698 = r71691 * r71697;
        double r71699 = r71696 + r71698;
        double r71700 = r71691 * r71699;
        double r71701 = r71695 + r71700;
        double r71702 = r71694 / r71701;
        double r71703 = r71702 - r71691;
        double r71704 = r71689 * r71703;
        return r71704;
}

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 2019353 +o rules:numerics
(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)))