Average Error: 0.0 → 0.0
Time: 30.1s
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 r60648 = 0.70711;
        double r60649 = 2.30753;
        double r60650 = x;
        double r60651 = 0.27061;
        double r60652 = r60650 * r60651;
        double r60653 = r60649 + r60652;
        double r60654 = 1.0;
        double r60655 = 0.99229;
        double r60656 = 0.04481;
        double r60657 = r60650 * r60656;
        double r60658 = r60655 + r60657;
        double r60659 = r60650 * r60658;
        double r60660 = r60654 + r60659;
        double r60661 = r60653 / r60660;
        double r60662 = r60661 - r60650;
        double r60663 = r60648 * r60662;
        return r60663;
}
↓
double f(double x) {
        double r60664 = 0.70711;
        double r60665 = 2.30753;
        double r60666 = x;
        double r60667 = 0.27061;
        double r60668 = r60666 * r60667;
        double r60669 = r60665 + r60668;
        double r60670 = 1.0;
        double r60671 = 0.99229;
        double r60672 = 0.04481;
        double r60673 = r60666 * r60672;
        double r60674 = r60671 + r60673;
        double r60675 = r60666 * r60674;
        double r60676 = r60670 + r60675;
        double r60677 = r60669 / r60676;
        double r60678 = r60677 - r60666;
        double r60679 = r60664 * r60678;
        return r60679;
}

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 2019304 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:invErfc from math-functions-0.1.5.2, B"
  :precision binary64
  (* 0.707110000000000016 (- (/ (+ 2.30753 (* x 0.27061000000000002)) (+ 1 (* x (+ 0.992290000000000005 (* x 0.044810000000000003))))) x)))